From 4d5afc9767595ed13ffddb4a517cdeb45fd31461 Mon Sep 17 00:00:00 2001 From: stratospher <44024636+stratospher@users.noreply.github.com> Date: Mon, 4 Apr 2022 00:01:57 +0530 Subject: [PATCH] Squashed 'src/secp256k1/' changes from 0559fc6e4..f997dadf5 f997dadf5 Add ellsq testing to CI ce03649fb Elligator Squared module c9ca664d5 doc: Describe Jacobi calculation in safegcd_implementation.md c880f7613 Native jacobi symbol algorithm 0a40a4861 Merge bitcoin-core/secp256k1#1049: Faster fixed-input ecmult tests 070e77221 Faster fixed-input ecmult tests c8aa516b5 Merge bitcoin-core/secp256k1#1064: Modulo-reduce msg32 inside RFC6979 nonce fn to match spec. Fixes #1063 45f37b650 Modulo-reduce msg32 inside RFC6979 nonce fn to match spec. Fixes #1063. a1102b121 Merge bitcoin-core/secp256k1#1029: Simpler and faster ecdh skew fixup e82144edf Fixup skew before global Z fixup 40b624c90 Add tests for _gej_cmov 8c13a9bfe ECDH skews by 0 or 1 151509943 Simpler and faster ecdh skew fixup 39a36db94 Merge bitcoin-core/secp256k1#1054: tests: Fix test whose result is implementation-defined a310e79ee Merge bitcoin-core/secp256k1#1052: Use xoshiro256++ instead of RFC6979 for tests 423b6d19d Merge bitcoin-core/secp256k1#964: Add release-process.md 9281c9f4e Merge bitcoin-core/secp256k1#1053: ecmult: move `_ecmult_odd_multiples_table_globalz_windowa` 77a19750b Use xoshiro256++ PRNG instead of RFC6979 in tests 5f2efe684 secp256k1_testrand_int(2**N) -> secp256k1_testrand_bits(N) 05e049b73 ecmult: move `_ecmult_odd_multiples_table_globalz_windowa` 3d7cbafb5 tests: Fix test whose result is implementation-defined 3ed0d02bf doc: add CHANGELOG template 6f42dc16c doc: add release_process.md 0bd3e4243 build: set library version to 0.0.0 explicitly b4b02fd8c build: change libsecp version from 0.1 to 0.1.0-pre 09971a3ff Merge bitcoin-core/secp256k1#1047: ci: Various improvements 0b83b203e Merge bitcoin-core/secp256k1#1030: doc: Fix upper bounds + cleanup in field_5x52_impl.h comment 1287786c7 doc: Add comment to top of field_10x26_impl.h 58da5bd58 doc: Fix upper bounds + cleanup in field_5x52_impl.h comment b39d431ae Merge bitcoin-core/secp256k1#1044: Add another ecmult_multi test b4ac1a1d5 ci: Run valgrind/memcheck tasks with 2 CPUs e70acab60 ci: Use Cirrus "greedy" flag to use idle CPU time when available d07e30176 ci: Update brew on macOS 22382f0ea ci: Test different ecmult window sizes a69df3ad2 Merge bitcoin-core/secp256k1#816: Improve checks at top of _fe_negate methods 22d25c8e0 Add another ecmult_multi test 515e7953c Improve checks at top of _fe_negate methods 26a022a3a ci: Remove STATICPRECOMPUTATION 10461d8bd precompute_ecmult: Always compute all tables up to default WINDOW_G be6944ade Merge bitcoin-core/secp256k1#1042: Follow-ups to making all tables fully static e05da9e48 Fix c++ build c45386d99 Cleanup preprocessor indentation in precompute{,d}_ecmult{,_gen} 19d96e15f Split off .c file from precomputed_ecmult.h 1a6691ada Split off .c file from precomputed_ecmult_gen.h bb3633141 Simplify precompute_ecmult_print_* 38cd84a0c Compute ecmult tables at runtime for tests_exhaustive e458ec26d Move ecmult table computation code to separate file fc1bf9f15 Split ecmult table computation and printing 31feab053 Rename function secp256k1_ecmult_gen_{create_prec -> compute}_table 725370c3f Rename ecmult_gen_prec -> ecmult_gen_compute_table 075252c1b Rename ecmult_static_pre_g -> precomputed_ecmult 7cf47f72b Rename ecmult_gen_static_prec_table -> precomputed_ecmult_gen f95b8106d Rename gen_ecmult_static_pre_g -> precompute_ecmult bae77685e Rename gen_ecmult_gen_static_prec_table -> precompute_ecmult_gen git-subtree-dir: src/secp256k1 git-subtree-split: f997dadf592131054d1cfca6175730e53dee52a1 --- .cirrus.yml | 85 ++-- .gitattributes | 4 +- .gitignore | 4 +- Makefile.am | 61 +-- ci/cirrus.sh | 4 +- configure.ac | 41 +- doc/CHANGELOG.md | 12 + doc/release-process.md | 14 + doc/safegcd_implementation.md | 31 +- include/secp256k1_ellsq.h | 78 ++++ src/bench.c | 9 + src/bench_internal.c | 12 + src/ecmult_compute_table.h | 16 + src/ecmult_compute_table_impl.h | 49 +++ src/ecmult_const_impl.h | 89 ++-- ..._gen_prec.h => ecmult_gen_compute_table.h} | 8 +- ...impl.h => ecmult_gen_compute_table_impl.h} | 10 +- src/ecmult_gen_impl.h | 2 +- src/ecmult_impl.h | 21 +- src/field.h | 3 + src/field_10x26_impl.h | 41 ++ src/field_5x52_impl.h | 48 ++- src/gen_ecmult_static_pre_g.c | 131 ------ src/group.h | 3 + src/group_impl.h | 8 + src/modinv32.h | 4 + src/modinv32_impl.h | 174 +++++++- src/modinv64.h | 4 + src/modinv64_impl.h | 155 ++++++- src/modules/ellsq/Makefile.am.include | 4 + src/modules/ellsq/bench_impl.h | 67 +++ src/modules/ellsq/main_impl.h | 305 ++++++++++++++ src/modules/ellsq/tests_impl.h | 166 ++++++++ src/modules/schnorrsig/tests_impl.h | 8 +- src/precompute_ecmult.c | 96 +++++ ...c_prec_table.c => precompute_ecmult_gen.c} | 43 +- ...lt_static_pre_g.h => precomputed_ecmult.c} | 231 ++--------- src/precomputed_ecmult.h | 35 ++ ..._prec_table.h => precomputed_ecmult_gen.c} | 22 +- src/precomputed_ecmult_gen.h | 26 ++ src/secp256k1.c | 12 +- src/testrand.h | 7 +- src/testrand_impl.h | 73 +++- src/tests.c | 384 ++++++++++++++++-- src/tests_exhaustive.c | 8 +- 45 files changed, 2016 insertions(+), 592 deletions(-) create mode 100644 doc/CHANGELOG.md create mode 100644 doc/release-process.md create mode 100644 include/secp256k1_ellsq.h create mode 100644 src/ecmult_compute_table.h create mode 100644 src/ecmult_compute_table_impl.h rename src/{ecmult_gen_prec.h => ecmult_gen_compute_table.h} (60%) rename src/{ecmult_gen_prec_impl.h => ecmult_gen_compute_table_impl.h} (90%) delete mode 100644 src/gen_ecmult_static_pre_g.c create mode 100644 src/modules/ellsq/Makefile.am.include create mode 100644 src/modules/ellsq/bench_impl.h create mode 100644 src/modules/ellsq/main_impl.h create mode 100644 src/modules/ellsq/tests_impl.h create mode 100644 src/precompute_ecmult.c rename src/{gen_ecmult_gen_static_prec_table.c => precompute_ecmult_gen.c} (61%) rename src/{ecmult_static_pre_g.h => precomputed_ecmult.c} (99%) create mode 100644 src/precomputed_ecmult.h rename src/{ecmult_gen_static_prec_table.h => precomputed_ecmult_gen.c} (99%) create mode 100644 src/precomputed_ecmult_gen.h diff --git a/.cirrus.yml b/.cirrus.yml index 35a9a4536726c3..ac41b73e7f285c 100644 --- a/.cirrus.yml +++ b/.cirrus.yml @@ -4,10 +4,10 @@ env: # Specific warnings can be disabled with -Wno-error=foo. # -pedantic-errors is not equivalent to -Werror=pedantic and thus not implied by -Werror according to the GCC manual. WERROR_CFLAGS: -Werror -pedantic-errors - MAKEFLAGS: -j2 + MAKEFLAGS: -j4 BUILD: check ### secp256k1 config - STATICPRECOMPUTATION: yes + ECMULTWINDOW: auto ECMULTGENPRECISION: auto ASM: no WIDEMUL: auto @@ -18,6 +18,7 @@ env: ECDH: no RECOVERY: no SCHNORRSIG: no + ELLSQ: no ### test options SECP256K1_TEST_ITERS: BENCH: yes @@ -50,28 +51,32 @@ merge_base_script_snippet: &MERGE_BASE - git config --global user.name "ci" - git merge FETCH_HEAD # Merge base to detect silent merge conflicts -task: - name: "x86_64: Linux (Debian stable)" +linux_container_snippet: &LINUX_CONTAINER container: dockerfile: ci/linux-debian.Dockerfile # Reduce number of CPUs to be able to do more builds in parallel. cpu: 1 + # Gives us more CPUs for free if they're available. + greedy: true # More than enough for our scripts. memory: 1G + +task: + name: "x86_64: Linux (Debian stable)" + << : *LINUX_CONTAINER matrix: &ENV_MATRIX - env: {WIDEMUL: int64, RECOVERY: yes} - - env: {WIDEMUL: int64, ECDH: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes} + - env: {WIDEMUL: int64, ECDH: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes, ELLSQ: yes} - env: {WIDEMUL: int128} - - env: {WIDEMUL: int128, RECOVERY: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes} + - env: {WIDEMUL: int128, RECOVERY: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes, ELLSQ: yes} - env: {WIDEMUL: int128, ECDH: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes} - env: {WIDEMUL: int128, ASM: x86_64} - - env: { RECOVERY: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes} - - env: { STATICPRECOMPUTATION: no} + - env: { RECOVERY: yes, EXPERIMENTAL: yes, SCHNORRSIG: yes, ELLSQ: yes} - env: {BUILD: distcheck, WITH_VALGRIND: no, CTIMETEST: no, BENCH: no} - env: {CPPFLAGS: -DDETERMINISTIC} - env: {CFLAGS: -O0, CTIMETEST: no} - - env: { ECMULTGENPRECISION: 2 } - - env: { ECMULTGENPRECISION: 8 } + - env: { ECMULTGENPRECISION: 2, ECMULTWINDOW: 2 } + - env: { ECMULTGENPRECISION: 8, ECMULTWINDOW: 4 } matrix: - env: CC: gcc @@ -84,13 +89,11 @@ task: task: name: "i686: Linux (Debian stable)" - container: - dockerfile: ci/linux-debian.Dockerfile - cpu: 1 - memory: 1G + << : *LINUX_CONTAINER env: HOST: i686-linux-gnu ECDH: yes + ELLSQ: yes RECOVERY: yes EXPERIMENTAL: yes SCHNORRSIG: yes @@ -134,8 +137,9 @@ task: ## - rm /tmp/.com.apple.dt.CommandLineTools.installondemand.in-progress ## brew_valgrind_pre_script: + - brew update - brew config - - brew tap --shallow LouisBrunner/valgrind + - brew tap LouisBrunner/valgrind # Fetch valgrind source but don't build it yet. - brew fetch --HEAD LouisBrunner/valgrind/valgrind brew_valgrind_cache: @@ -165,16 +169,14 @@ task: task: name: "s390x (big-endian): Linux (Debian stable, QEMU)" - container: - dockerfile: ci/linux-debian.Dockerfile - cpu: 1 - memory: 1G + << : *LINUX_CONTAINER env: WRAPPER_CMD: qemu-s390x SECP256K1_TEST_ITERS: 16 HOST: s390x-linux-gnu WITH_VALGRIND: no ECDH: yes + ELLSQ: yes RECOVERY: yes EXPERIMENTAL: yes SCHNORRSIG: yes @@ -188,16 +190,14 @@ task: task: name: "ARM32: Linux (Debian stable, QEMU)" - container: - dockerfile: ci/linux-debian.Dockerfile - cpu: 1 - memory: 1G + << : *LINUX_CONTAINER env: WRAPPER_CMD: qemu-arm SECP256K1_TEST_ITERS: 16 HOST: arm-linux-gnueabihf WITH_VALGRIND: no ECDH: yes + ELLSQ: tes RECOVERY: yes EXPERIMENTAL: yes SCHNORRSIG: yes @@ -212,16 +212,14 @@ task: task: name: "ARM64: Linux (Debian stable, QEMU)" - container: - dockerfile: ci/linux-debian.Dockerfile - cpu: 1 - memory: 1G + << : *LINUX_CONTAINER env: WRAPPER_CMD: qemu-aarch64 SECP256K1_TEST_ITERS: 16 HOST: aarch64-linux-gnu WITH_VALGRIND: no ECDH: yes + ELLSQ: yes RECOVERY: yes EXPERIMENTAL: yes SCHNORRSIG: yes @@ -233,16 +231,14 @@ task: task: name: "ppc64le: Linux (Debian stable, QEMU)" - container: - dockerfile: ci/linux-debian.Dockerfile - cpu: 1 - memory: 1G + << : *LINUX_CONTAINER env: WRAPPER_CMD: qemu-ppc64le SECP256K1_TEST_ITERS: 16 HOST: powerpc64le-linux-gnu WITH_VALGRIND: no ECDH: yes + ELLSQ: yes RECOVERY: yes EXPERIMENTAL: yes SCHNORRSIG: yes @@ -254,16 +250,14 @@ task: task: name: "x86_64 (mingw32-w64): Windows (Debian stable, Wine)" - container: - dockerfile: ci/linux-debian.Dockerfile - cpu: 1 - memory: 1G + << : *LINUX_CONTAINER env: WRAPPER_CMD: wine64-stable SECP256K1_TEST_ITERS: 16 HOST: x86_64-w64-mingw32 WITH_VALGRIND: no ECDH: yes + ELLSQ: yes RECOVERY: yes EXPERIMENTAL: yes SCHNORRSIG: yes @@ -275,23 +269,25 @@ task: # Sanitizers task: - container: - dockerfile: ci/linux-debian.Dockerfile - cpu: 1 - memory: 2G + << : *LINUX_CONTAINER env: ECDH: yes + ELLSQ: yes RECOVERY: yes EXPERIMENTAL: yes SCHNORRSIG: yes CTIMETEST: no matrix: - name: "Valgrind (memcheck)" + container: + cpu: 2 env: # The `--error-exitcode` is required to make the test fail if valgrind found errors, otherwise it'll return 0 (https://www.valgrind.org/docs/manual/manual-core.html) WRAPPER_CMD: "valgrind --error-exitcode=42" SECP256K1_TEST_ITERS: 2 - name: "UBSan, ASan, LSan" + container: + memory: 2G env: CFLAGS: "-fsanitize=undefined,address -g" UBSAN_OPTIONS: "print_stacktrace=1:halt_on_error=1" @@ -302,11 +298,10 @@ task: matrix: - env: ASM: auto - STATICPRECOMPUTATION: yes - env: ASM: no - STATICPRECOMPUTATION: no ECMULTGENPRECISION: 2 + ECMULTWINDOW: 2 matrix: - env: CC: clang @@ -320,18 +315,16 @@ task: task: name: "C++ -fpermissive" - container: - dockerfile: ci/linux-debian.Dockerfile - cpu: 1 - memory: 1G + << : *LINUX_CONTAINER env: # ./configure correctly errors out when given CC=g++. # We hack around this by passing CC=g++ only to make. CC: gcc - MAKEFLAGS: -j2 CC=g++ CFLAGS=-fpermissive\ -g + MAKEFLAGS: -j4 CC=g++ CFLAGS=-fpermissive\ -g WERROR_CFLAGS: EXPERIMENTAL: yes ECDH: yes + ELLSQ: yes RECOVERY: yes SCHNORRSIG: yes << : *MERGE_BASE diff --git a/.gitattributes b/.gitattributes index a0fa567da81b58..30efb2244fee74 100644 --- a/.gitattributes +++ b/.gitattributes @@ -1,2 +1,2 @@ -src/ecmult_static_pre_g.h linguist-generated -src/ecmult_gen_static_prec_table.h linguist-generated +src/precomputed_ecmult.c linguist-generated +src/precomputed_ecmult_gen.c linguist-generated diff --git a/.gitignore b/.gitignore index 22cd50050135e7..cb52998ad6ef2e 100644 --- a/.gitignore +++ b/.gitignore @@ -3,8 +3,8 @@ bench_ecmult bench_internal tests exhaustive_tests -gen_ecmult_gen_static_prec_table -gen_ecmult_static_pre_g +precompute_ecmult_gen +precompute_ecmult valgrind_ctime_test *.exe *.so diff --git a/Makefile.am b/Makefile.am index 7ea29bc6e3fd58..287f1b7059bcb1 100644 --- a/Makefile.am +++ b/Makefile.am @@ -26,12 +26,14 @@ noinst_HEADERS += src/eckey.h noinst_HEADERS += src/eckey_impl.h noinst_HEADERS += src/ecmult.h noinst_HEADERS += src/ecmult_impl.h +noinst_HEADERS += src/ecmult_compute_table.h +noinst_HEADERS += src/ecmult_compute_table_impl.h noinst_HEADERS += src/ecmult_const.h noinst_HEADERS += src/ecmult_const_impl.h noinst_HEADERS += src/ecmult_gen.h noinst_HEADERS += src/ecmult_gen_impl.h -noinst_HEADERS += src/ecmult_gen_prec.h -noinst_HEADERS += src/ecmult_gen_prec_impl.h +noinst_HEADERS += src/ecmult_gen_compute_table.h +noinst_HEADERS += src/ecmult_gen_compute_table_impl.h noinst_HEADERS += src/field_10x26.h noinst_HEADERS += src/field_10x26_impl.h noinst_HEADERS += src/field_5x52.h @@ -42,6 +44,8 @@ noinst_HEADERS += src/modinv32.h noinst_HEADERS += src/modinv32_impl.h noinst_HEADERS += src/modinv64.h noinst_HEADERS += src/modinv64_impl.h +noinst_HEADERS += src/precomputed_ecmult.h +noinst_HEADERS += src/precomputed_ecmult_gen.h noinst_HEADERS += src/assumptions.h noinst_HEADERS += src/util.h noinst_HEADERS += src/scratch.h @@ -60,12 +64,17 @@ noinst_HEADERS += contrib/lax_der_parsing.c noinst_HEADERS += contrib/lax_der_privatekey_parsing.h noinst_HEADERS += contrib/lax_der_privatekey_parsing.c +PRECOMPUTED_LIB = libsecp256k1_precomputed.la +noinst_LTLIBRARIES = $(PRECOMPUTED_LIB) +libsecp256k1_precomputed_la_SOURCES = src/precomputed_ecmult.c src/precomputed_ecmult_gen.c +libsecp256k1_precomputed_la_CPPFLAGS = $(SECP_INCLUDES) + if USE_EXTERNAL_ASM COMMON_LIB = libsecp256k1_common.la -noinst_LTLIBRARIES = $(COMMON_LIB) else COMMON_LIB = endif +noinst_LTLIBRARIES += $(COMMON_LIB) pkgconfigdir = $(libdir)/pkgconfig pkgconfig_DATA = libsecp256k1.pc @@ -78,8 +87,8 @@ endif libsecp256k1_la_SOURCES = src/secp256k1.c libsecp256k1_la_CPPFLAGS = -I$(top_srcdir)/include -I$(top_srcdir)/src $(SECP_INCLUDES) -libsecp256k1_la_LIBADD = $(SECP_LIBS) $(COMMON_LIB) -libsecp256k1_la_LDFLAGS = -no-undefined +libsecp256k1_la_LIBADD = $(SECP_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB) +libsecp256k1_la_LDFLAGS = -no-undefined -version-info $(LIB_VERSION_CURRENT):$(LIB_VERSION_REVISION):$(LIB_VERSION_AGE) if VALGRIND_ENABLED libsecp256k1_la_CPPFLAGS += -DVALGRIND @@ -91,10 +100,10 @@ noinst_PROGRAMS += bench bench_internal bench_ecmult bench_SOURCES = src/bench.c bench_LDADD = libsecp256k1.la $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB) bench_internal_SOURCES = src/bench_internal.c -bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB) +bench_internal_LDADD = $(SECP_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB) bench_internal_CPPFLAGS = $(SECP_INCLUDES) bench_ecmult_SOURCES = src/bench_ecmult.c -bench_ecmult_LDADD = $(SECP_LIBS) $(COMMON_LIB) +bench_ecmult_LDADD = $(SECP_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB) bench_ecmult_CPPFLAGS = $(SECP_INCLUDES) endif @@ -112,7 +121,7 @@ endif if !ENABLE_COVERAGE tests_CPPFLAGS += -DVERIFY endif -tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB) +tests_LDADD = $(SECP_LIBS) $(SECP_TEST_LIBS) $(COMMON_LIB) $(PRECOMPUTED_LIB) tests_LDFLAGS = -static TESTS += tests endif @@ -124,22 +133,23 @@ exhaustive_tests_CPPFLAGS = $(SECP_INCLUDES) if !ENABLE_COVERAGE exhaustive_tests_CPPFLAGS += -DVERIFY endif +# Note: do not include $(PRECOMPUTED_LIB) in exhaustive_tests (it uses runtime-generated tables). exhaustive_tests_LDADD = $(SECP_LIBS) $(COMMON_LIB) exhaustive_tests_LDFLAGS = -static TESTS += exhaustive_tests endif ### Precomputed tables -EXTRA_PROGRAMS = gen_ecmult_static_pre_g gen_ecmult_gen_static_prec_table +EXTRA_PROGRAMS = precompute_ecmult precompute_ecmult_gen CLEANFILES = $(EXTRA_PROGRAMS) -gen_ecmult_static_pre_g_SOURCES = src/gen_ecmult_static_pre_g.c -gen_ecmult_static_pre_g_CPPFLAGS = $(SECP_INCLUDES) -gen_ecmult_static_pre_g_LDADD = $(SECP_LIBS) $(COMMON_LIB) +precompute_ecmult_SOURCES = src/precompute_ecmult.c +precompute_ecmult_CPPFLAGS = $(SECP_INCLUDES) +precompute_ecmult_LDADD = $(SECP_LIBS) $(COMMON_LIB) -gen_ecmult_gen_static_prec_table_SOURCES = src/gen_ecmult_gen_static_prec_table.c -gen_ecmult_gen_static_prec_table_CPPFLAGS = $(SECP_INCLUDES) -gen_ecmult_gen_static_prec_table_LDADD = $(SECP_LIBS) $(COMMON_LIB) +precompute_ecmult_gen_SOURCES = src/precompute_ecmult_gen.c +precompute_ecmult_gen_CPPFLAGS = $(SECP_INCLUDES) +precompute_ecmult_gen_LDADD = $(SECP_LIBS) $(COMMON_LIB) # See Automake manual, Section "Errors with distclean". # We don't list any dependencies for the prebuilt files here because @@ -147,15 +157,14 @@ gen_ecmult_gen_static_prec_table_LDADD = $(SECP_LIBS) $(COMMON_LIB) # build by a normal user) depends on mtimes, and thus is very fragile. # This means that rebuilds of the prebuilt files always need to be # forced by deleting them, e.g., by invoking `make clean-precomp`. -src/ecmult_static_pre_g.h: - $(MAKE) $(AM_MAKEFLAGS) gen_ecmult_static_pre_g$(EXEEXT) - ./gen_ecmult_static_pre_g$(EXEEXT) -src/ecmult_gen_static_prec_table.h: - $(MAKE) $(AM_MAKEFLAGS) gen_ecmult_gen_static_prec_table$(EXEEXT) - ./gen_ecmult_gen_static_prec_table$(EXEEXT) - -PRECOMP = src/ecmult_gen_static_prec_table.h src/ecmult_static_pre_g.h -noinst_HEADERS += $(PRECOMP) +src/precomputed_ecmult.c: + $(MAKE) $(AM_MAKEFLAGS) precompute_ecmult$(EXEEXT) + ./precompute_ecmult$(EXEEXT) +src/precomputed_ecmult_gen.c: + $(MAKE) $(AM_MAKEFLAGS) precompute_ecmult_gen$(EXEEXT) + ./precompute_ecmult_gen$(EXEEXT) + +PRECOMP = src/precomputed_ecmult_gen.c src/precomputed_ecmult.c precomp: $(PRECOMP) # Ensure the prebuilt files will be build first (only if they don't exist, @@ -184,3 +193,7 @@ endif if ENABLE_MODULE_SCHNORRSIG include src/modules/schnorrsig/Makefile.am.include endif + +if ENABLE_MODULE_ELLSQ +include src/modules/ellsq/Makefile.am.include +endif diff --git a/ci/cirrus.sh b/ci/cirrus.sh index e27b34782e17f3..6f6b7051c7f492 100755 --- a/ci/cirrus.sh +++ b/ci/cirrus.sh @@ -15,8 +15,10 @@ valgrind --version || true ./configure \ --enable-experimental="$EXPERIMENTAL" \ --with-test-override-wide-multiply="$WIDEMUL" --with-asm="$ASM" \ - --enable-ecmult-static-precomputation="$STATICPRECOMPUTATION" --with-ecmult-gen-precision="$ECMULTGENPRECISION" \ + --with-ecmult-window="$ECMULTWINDOW" \ + --with-ecmult-gen-precision="$ECMULTGENPRECISION" \ --enable-module-ecdh="$ECDH" --enable-module-recovery="$RECOVERY" \ + --enable-module-ellsq="$ELLSQ" \ --enable-module-schnorrsig="$SCHNORRSIG" \ --with-valgrind="$WITH_VALGRIND" \ --host="$HOST" $EXTRAFLAGS diff --git a/configure.ac b/configure.ac index 94feea7bb72d2a..7ce1601c8f9166 100644 --- a/configure.ac +++ b/configure.ac @@ -1,5 +1,24 @@ AC_PREREQ([2.60]) -AC_INIT([libsecp256k1],[0.1]) + +# The package (a.k.a. release) version is based on semantic versioning 2.0.0 of +# the API. All changes in experimental modules are treated as +# backwards-compatible and therefore at most increase the minor version. +define(_PKG_VERSION_MAJOR, 0) +define(_PKG_VERSION_MINOR, 1) +define(_PKG_VERSION_BUILD, 0) +define(_PKG_VERSION_IS_RELEASE, false) + +# The library version is based on libtool versioning of the ABI. The set of +# rules for updating the version can be found here: +# https://www.gnu.org/software/libtool/manual/html_node/Updating-version-info.html +# All changes in experimental modules are treated as if they don't affect the +# interface and therefore only increase the revision. +define(_LIB_VERSION_CURRENT, 0) +define(_LIB_VERSION_REVISION, 0) +define(_LIB_VERSION_AGE, 0) + +AC_INIT([libsecp256k1],m4_join([.], _PKG_VERSION_MAJOR, _PKG_VERSION_MINOR, _PKG_VERSION_BUILD)m4_if(_PKG_VERSION_IS_RELEASE, [true], [], [-pre]),[https://github.com/bitcoin-core/secp256k1/issues],[libsecp256k1],[https://github.com/bitcoin-core/secp256k1]) + AC_CONFIG_AUX_DIR([build-aux]) AC_CONFIG_MACRO_DIR([build-aux/m4]) AC_CANONICAL_HOST @@ -136,6 +155,11 @@ AC_ARG_ENABLE(module_schnorrsig, [enable_module_schnorrsig=$enableval], [enable_module_schnorrsig=no]) +AC_ARG_ENABLE(module_ellsq, + AS_HELP_STRING([--enable-module-ellsq],[enable Elligator^2 module (experimental)]), + [enable_module_ellsq=$enableval], + [enable_module_ellsq=no]) + AC_ARG_ENABLE(external_default_callbacks, AS_HELP_STRING([--enable-external-default-callbacks],[enable external default callback functions [default=no]]), [use_external_default_callbacks=$enableval], @@ -152,7 +176,7 @@ AC_ARG_WITH([ecmult-window], [AS_HELP_STRING([--with-ecmult-window=SIZE|auto], [window size for ecmult precomputation for verification, specified as integer in range [2..24].] [Larger values result in possibly better performance at the cost of an exponentially larger precomputed table.] [The table will store 2^(SIZE-1) * 64 bytes of data but can be larger in memory due to platform-specific padding and alignment.] -[A window size larger than 15 will require you delete the prebuilt ecmult_static_pre_g.h file so that it can be rebuilt.] +[A window size larger than 15 will require you delete the prebuilt precomputed_ecmult.c file so that it can be rebuilt.] [For very large window sizes, use "make -j 1" to reduce memory use during compilation.] ["auto" is a reasonable setting for desktop machines (currently 15). [default=auto]] )], @@ -333,6 +357,10 @@ if test x"$enable_module_extrakeys" = x"yes"; then AC_DEFINE(ENABLE_MODULE_EXTRAKEYS, 1, [Define this symbol to enable the extrakeys module]) fi +if test x"$enable_module_ellsq" = x"yes"; then + AC_DEFINE(ENABLE_MODULE_ELLSQ, 1, [Define this symbol to enable the Elligator^2 module]) +fi + if test x"$use_external_default_callbacks" = x"yes"; then AC_DEFINE(USE_EXTERNAL_DEFAULT_CALLBACKS, 1, [Define this symbol if an external implementation of the default callbacks is used]) fi @@ -347,6 +375,7 @@ if test x"$enable_experimental" = x"yes"; then AC_MSG_NOTICE([Experimental features do not have stable APIs or properties, and may not be safe for production use.]) AC_MSG_NOTICE([Building extrakeys module: $enable_module_extrakeys]) AC_MSG_NOTICE([Building schnorrsig module: $enable_module_schnorrsig]) + AC_MSG_NOTICE([Building Elligator^2 module: $enable_module_ellsq]) AC_MSG_NOTICE([******]) else if test x"$enable_module_extrakeys" = x"yes"; then @@ -355,6 +384,9 @@ else if test x"$enable_module_schnorrsig" = x"yes"; then AC_MSG_ERROR([schnorrsig module is experimental. Use --enable-experimental to allow.]) fi + if test x"$enable_module_ellsq" = x"yes"; then + AC_MSG_ERROR([Elligator^2 module is experimental. Use --enable-experimental to allow.]) + fi if test x"$set_asm" = x"arm"; then AC_MSG_ERROR([ARM assembly optimization is experimental. Use --enable-experimental to allow.]) fi @@ -379,8 +411,12 @@ AM_CONDITIONAL([ENABLE_MODULE_ECDH], [test x"$enable_module_ecdh" = x"yes"]) AM_CONDITIONAL([ENABLE_MODULE_RECOVERY], [test x"$enable_module_recovery" = x"yes"]) AM_CONDITIONAL([ENABLE_MODULE_EXTRAKEYS], [test x"$enable_module_extrakeys" = x"yes"]) AM_CONDITIONAL([ENABLE_MODULE_SCHNORRSIG], [test x"$enable_module_schnorrsig" = x"yes"]) +AM_CONDITIONAL([ENABLE_MODULE_ELLSQ], [test x"$enable_module_ellsq" = x"yes"]) AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$use_external_asm" = x"yes"]) AM_CONDITIONAL([USE_ASM_ARM], [test x"$set_asm" = x"arm"]) +AC_SUBST(LIB_VERSION_CURRENT, _LIB_VERSION_CURRENT) +AC_SUBST(LIB_VERSION_REVISION, _LIB_VERSION_REVISION) +AC_SUBST(LIB_VERSION_AGE, _LIB_VERSION_AGE) # Make sure nothing new is exported so that we don't break the cache. PKGCONFIG_PATH_TEMP="$PKG_CONFIG_PATH" @@ -399,6 +435,7 @@ echo " module ecdh = $enable_module_ecdh" echo " module recovery = $enable_module_recovery" echo " module extrakeys = $enable_module_extrakeys" echo " module schnorrsig = $enable_module_schnorrsig" +echo " module ellsq = $enable_module_ellsq" echo echo " asm = $set_asm" echo " ecmult window size = $set_ecmult_window" diff --git a/doc/CHANGELOG.md b/doc/CHANGELOG.md new file mode 100644 index 00000000000000..3c4c2e4583756b --- /dev/null +++ b/doc/CHANGELOG.md @@ -0,0 +1,12 @@ +# Changelog + +This file is currently only a template for future use. + +Each change falls into one of the following categories: Added, Changed, Deprecated, Removed, Fixed or Security. + +## [Unreleased] + +## [MAJOR.MINOR.PATCH] - YYYY-MM-DD + +### Added/Changed/Deprecated/Removed/Fixed/Security +- [Title with link to Pull Request](https://link-to-pr) diff --git a/doc/release-process.md b/doc/release-process.md new file mode 100644 index 00000000000000..a35b8a9db31515 --- /dev/null +++ b/doc/release-process.md @@ -0,0 +1,14 @@ +# Release Process + +1. Open PR to master that + 1. adds release notes to `doc/CHANGELOG.md` and + 2. if this is **not** a patch release, updates `_PKG_VERSION_{MAJOR,MINOR}` and `_LIB_VERSIONS_*` in `configure.ac` +2. After the PR is merged, + * if this is **not** a patch release, create a release branch with name `MAJOR.MINOR`. + Make sure that the branch contains the right commits. + Create commit on the release branch that sets `_PKG_VERSION_IS_RELEASE` in `configure.ac` to `true`. + * if this **is** a patch release, open a pull request with the bugfixes to the `MAJOR.MINOR` branch. + Also include the release note commit bump `_PKG_VERSION_BUILD` and `_LIB_VERSIONS_*` in `configure.ac`. +4. Tag the commit with `git tag -s vMAJOR.MINOR.PATCH`. +5. Push branch and tag with `git push origin --tags`. +6. Create a new GitHub release with a link to the corresponding entry in `doc/CHANGELOG.md`. diff --git a/doc/safegcd_implementation.md b/doc/safegcd_implementation.md index 063aa8efae05a1..c1cdd0cfe178f6 100644 --- a/doc/safegcd_implementation.md +++ b/doc/safegcd_implementation.md @@ -1,7 +1,7 @@ # The safegcd implementation in libsecp256k1 explained -This document explains the modular inverse implementation in the `src/modinv*.h` files. It is based -on the paper +This document explains the modular inverse and Jacobi symbol implementations in the `src/modinv*.h` files. +It is based on the paper ["Fast constant-time gcd computation and modular inversion"](https://gcd.cr.yp.to/papers.html#safegcd) by Daniel J. Bernstein and Bo-Yin Yang. The references below are for the Date: 2019.04.13 version. @@ -769,3 +769,30 @@ def modinv_var(M, Mi, x): d, e = update_de(d, e, t, M, Mi) return normalize(f, d, Mi) ``` + +## 8. From GCDs to Jacobi symbol + +We can also use a similar approach to calculate Jacobi symbol *(x | M)* by keeping track of an extra variable *j*, for which at every step *(x | M) = j (g | f)*. As we update *f* and *g*, we make corresponding updates to *j* using [properties of the Jacobi symbol](https://en.wikipedia.org/wiki/Jacobi_symbol#Properties). In particular, we update *j* whenever we divide *g* by *2* or swap *f* and *g*; these updates depend only on the values of *f* and *g* modulo *4* or *8*, and can thus be applied very quickly. Overall, this calculation is slightly simpler than the one for modular inverse because we no longer need to keep track of *d* and *e*. + +However, one difficulty of this approach is that the Jacobi symbol *(a | n)* is only defined for positive odd integers *n*, whereas in the original safegcd algorithm, *f, g* can take negative values. We resolve this by using the following modified steps: + +```python + # Before + if delta > 0 and g & 1: + delta, f, g = 1 - delta, g, (g - f) // 2 + + # After + if delta > 0 and g & 1: + delta, f, g = 1 - delta, g, (g + f) // 2 +``` + +The algorithm is still correct, since the changed divstep, called a "posdivstep" (see section 8.4 and E.5 in the paper) preserves *gcd(f, g)*. However, there's no proof that the modified algorithm will converge. The justification for posdivsteps is completely empirical: in practice, it appears that the vast majority of inputs converge to *f=g=gcd(f0, g0)* in a number of steps proportional to their logarithm. + +Note that: +- We require inputs to satisfy *gcd(x, M) = 1*. +- We need to update the termination condition from *g=0* to *f=1*. +- We deal with the case where *g=0* on input specially. + +We account for the possibility of nonconvergence by only performing a bounded number of posdivsteps, and then falling back to square-root based Jacobi calculation if a solution has not yet been found. + +The optimizations in sections 3-7 above are described in the context of the original divsteps, but in the C implementation we also adapt most of them (not including "avoiding modulus operations", since it's not necessary to track *d, e*, and "constant-time operation", since we never calculate Jacobi symbols for secret data) to the posdivsteps version. diff --git a/include/secp256k1_ellsq.h b/include/secp256k1_ellsq.h new file mode 100644 index 00000000000000..e01937e352f821 --- /dev/null +++ b/include/secp256k1_ellsq.h @@ -0,0 +1,78 @@ +#ifndef SECP256K1_ELLSQ_H +#define SECP256K1_ELLSQ_H + +#include "secp256k1.h" + +#ifdef __cplusplus +extern "C" { +#endif + +/* This module provides an implementation of the Elligator Squared encoding + * for secp256k1 public keys. Given a uniformly random public key, this + * produces a 64-byte encoding that is indistinguishable from uniformly + * random bytes. + * + * Elligator Squared is described in https://eprint.iacr.org/2014/043.pdf by + * Mehdi Tibouchi. The mapping function used is described in + * https://www.di.ens.fr/~fouque/pub/latincrypt12.pdf by Fouque and Tibouchi. + * + * Let f be the function from field elements to curve points, defined as + * follows: + * f(t): + * - Let c = 0xa2d2ba93507f1df233770c2a797962cc61f6d15da14ecd47d8d27ae1cd5f852 + * - Let x1 = (c - 1)/2 - c*t^2 / (t^2 + 8) (mod p) + * - Let x2 = (-c - 1)/2 + c*t^2 / (t^2 + 8) (mod p) + * - Let x3 = 1 - (t^2 + 8)^2 / (3*t^2) (mod p) + * - Let x be the first of [x1,x2,x3] that is an X coordinate on the curve + * (at least one of them is, for any field element t). + * - Let y be the the corresponding Y coordinate to x, with the same parity + * as t (even if t is even, odd if t is odd). + * - Return the curve point with coordinates (x, y). + * + * Then an Elligator Squared encoding of P consists of the 32-byte big-endian + * encodings of field elements u1 and u2 concatenated, where f(u1)+f(u2) = P. + * The encoding algorithm is described in the paper, and effectively picks a + * uniformly random pair (u1,u2) among those which encode P. + * + * To make the encoding able to deal with all inputs, if f(u1)+f(u2) is the + * point at infinity, the decoding is defined to be f(u1) instead. + */ + +/* Construct a 64-byte Elligator Squared encoding of a given pubkey. + * + * Returns: 1 when pubkey is valid. + * Args: ctx: pointer to a context object + * Out: ell64: pointer to a 64-byte array to be filled + * In: rnd32: pointer to 32 bytes of entropy (must be unpredictable) + * pubkey: a pointer to a secp256k1_pubkey containing an + * initialized public key + * + * This function runs in variable time. + */ +SECP256K1_API int secp256k1_ellsq_encode( + const secp256k1_context* ctx, + unsigned char *ell64, + const unsigned char *rnd32, + const secp256k1_pubkey *pubkey +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4); + +/** Decode a 64-bytes Elligator Squared encoded public key. + * + * Returns: always 1 + * Args: ctx: pointer to a context object + * Out: pubkey: pointer to a secp256k1_pubkey that will be filled + * In: ell64: pointer to a 64-byte array to decode + * + * This function runs in variable time. + */ +SECP256K1_API int secp256k1_ellsq_decode( + const secp256k1_context* ctx, + secp256k1_pubkey *pubkey, + const unsigned char *ell64 +) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3); + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_ELLSQ_H */ diff --git a/src/bench.c b/src/bench.c index d5937b763f08f8..9ce5b51437196e 100644 --- a/src/bench.c +++ b/src/bench.c @@ -133,6 +133,10 @@ static void bench_sign_run(void* arg, int iters) { # include "modules/schnorrsig/bench_impl.h" #endif +#ifdef ENABLE_MODULE_ELLSQ +# include "modules/ellsq/bench_impl.h" +#endif + int main(int argc, char** argv) { int i; secp256k1_pubkey pubkey; @@ -230,5 +234,10 @@ int main(int argc, char** argv) { run_schnorrsig_bench(iters, argc, argv); #endif +#ifdef ENABLE_MODULE_ELLSQ + /* Elligator squared signature benchmarks */ + run_ellsq_bench(iters, argc, argv); +#endif + return 0; } diff --git a/src/bench_internal.c b/src/bench_internal.c index aed82161273d9e..379f9a9f0f95de 100644 --- a/src/bench_internal.c +++ b/src/bench_internal.c @@ -209,6 +209,17 @@ void bench_field_sqrt(void* arg, int iters) { CHECK(j <= iters); } +void bench_field_jacobi_var(void* arg, int iters) { + int i, j = 0; + bench_inv *data = (bench_inv*)arg; + + for (i = 0; i < iters; i++) { + j += secp256k1_fe_jacobi_var(&data->fe[0]); + secp256k1_fe_add(&data->fe[0], &data->fe[1]); + } + CHECK(j <= iters); +} + void bench_group_double_var(void* arg, int iters) { int i; bench_inv *data = (bench_inv*)arg; @@ -360,6 +371,7 @@ int main(int argc, char **argv) { if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "mul")) run_benchmark("field_mul", bench_field_mul, bench_setup, NULL, &data, 10, iters*10); if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse", bench_field_inverse, bench_setup, NULL, &data, 10, iters); if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse_var", bench_field_inverse_var, bench_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "jacobi")) run_benchmark("field_jacobi_var", bench_field_jacobi_var, bench_setup, NULL, &data, 10, iters); if (d || have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt", bench_field_sqrt, bench_setup, NULL, &data, 10, iters); if (d || have_flag(argc, argv, "group") || have_flag(argc, argv, "double")) run_benchmark("group_double_var", bench_group_double_var, bench_setup, NULL, &data, 10, iters*10); diff --git a/src/ecmult_compute_table.h b/src/ecmult_compute_table.h new file mode 100644 index 00000000000000..665f87ff3d5b5d --- /dev/null +++ b/src/ecmult_compute_table.h @@ -0,0 +1,16 @@ +/***************************************************************************************************** + * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *****************************************************************************************************/ + +#ifndef SECP256K1_ECMULT_COMPUTE_TABLE_H +#define SECP256K1_ECMULT_COMPUTE_TABLE_H + +/* Construct table of all odd multiples of gen in range 1..(2**(window_g-1)-1). */ +static void secp256k1_ecmult_compute_table(secp256k1_ge_storage* table, int window_g, const secp256k1_gej* gen); + +/* Like secp256k1_ecmult_compute_table, but one for both gen and gen*2^128. */ +static void secp256k1_ecmult_compute_two_tables(secp256k1_ge_storage* table, secp256k1_ge_storage* table_128, int window_g, const secp256k1_ge* gen); + +#endif /* SECP256K1_ECMULT_COMPUTE_TABLE_H */ diff --git a/src/ecmult_compute_table_impl.h b/src/ecmult_compute_table_impl.h new file mode 100644 index 00000000000000..69d59ce595604e --- /dev/null +++ b/src/ecmult_compute_table_impl.h @@ -0,0 +1,49 @@ +/***************************************************************************************************** + * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *****************************************************************************************************/ + +#ifndef SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H +#define SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H + +#include "ecmult_compute_table.h" +#include "group_impl.h" +#include "field_impl.h" +#include "ecmult.h" +#include "util.h" + +static void secp256k1_ecmult_compute_table(secp256k1_ge_storage* table, int window_g, const secp256k1_gej* gen) { + secp256k1_gej gj; + secp256k1_ge ge, dgen; + int j; + + gj = *gen; + secp256k1_ge_set_gej_var(&ge, &gj); + secp256k1_ge_to_storage(&table[0], &ge); + + secp256k1_gej_double_var(&gj, gen, NULL); + secp256k1_ge_set_gej_var(&dgen, &gj); + + for (j = 1; j < ECMULT_TABLE_SIZE(window_g); ++j) { + secp256k1_gej_set_ge(&gj, &ge); + secp256k1_gej_add_ge_var(&gj, &gj, &dgen, NULL); + secp256k1_ge_set_gej_var(&ge, &gj); + secp256k1_ge_to_storage(&table[j], &ge); + } +} + +/* Like secp256k1_ecmult_compute_table, but one for both gen and gen*2^128. */ +static void secp256k1_ecmult_compute_two_tables(secp256k1_ge_storage* table, secp256k1_ge_storage* table_128, int window_g, const secp256k1_ge* gen) { + secp256k1_gej gj; + int i; + + secp256k1_gej_set_ge(&gj, gen); + secp256k1_ecmult_compute_table(table, window_g, &gj); + for (i = 0; i < 128; ++i) { + secp256k1_gej_double_var(&gj, &gj, NULL); + } + secp256k1_ecmult_compute_table(table_128, window_g, &gj); +} + +#endif /* SECP256K1_ECMULT_COMPUTE_TABLE_IMPL_H */ diff --git a/src/ecmult_const_impl.h b/src/ecmult_const_impl.h index 30b151ff9abdd5..3d198dcedead8d 100644 --- a/src/ecmult_const_impl.h +++ b/src/ecmult_const_impl.h @@ -12,6 +12,22 @@ #include "ecmult_const.h" #include "ecmult_impl.h" +/** Fill a table 'pre' with precomputed odd multiples of a. + * + * The resulting point set is brought to a single constant Z denominator, stores the X and Y + * coordinates as ge_storage points in pre, and stores the global Z in globalz. + * It only operates on tables sized for WINDOW_A wnaf multiples. + */ +static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) { + secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)]; + + /* Compute the odd multiples in Jacobian form. */ + secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a); + /* Bring them to the same Z denominator. */ + secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr); +} + /* This is like `ECMULT_TABLE_GET_GE` but is constant time */ #define ECMULT_CONST_TABLE_GET_GE(r,pre,n,w) do { \ int m = 0; \ @@ -40,7 +56,6 @@ secp256k1_fe_cmov(&(r)->y, &neg_y, (n) != abs_n); \ } while(0) - /** Convert a number to WNAF notation. * The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val. * It has the following guarantees: @@ -56,7 +71,7 @@ */ static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w, int size) { int global_sign; - int skew = 0; + int skew; int word = 0; /* 1 2 3 */ @@ -64,9 +79,7 @@ static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w int u; int flip; - int bit; - secp256k1_scalar s; - int not_neg_one; + secp256k1_scalar s = *scalar; VERIFY_CHECK(w > 0); VERIFY_CHECK(size > 0); @@ -74,33 +87,19 @@ static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w /* Note that we cannot handle even numbers by negating them to be odd, as is * done in other implementations, since if our scalars were specified to have * width < 256 for performance reasons, their negations would have width 256 - * and we'd lose any performance benefit. Instead, we use a technique from - * Section 4.2 of the Okeya/Tagaki paper, which is to add either 1 (for even) - * or 2 (for odd) to the number we are encoding, returning a skew value indicating + * and we'd lose any performance benefit. Instead, we use a variation of a + * technique from Section 4.2 of the Okeya/Tagaki paper, which is to add 1 to the + * number we are encoding when it is even, returning a skew value indicating * this, and having the caller compensate after doing the multiplication. * * In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in * particular, to ensure that the outputs from the endomorphism-split fit into - * 128 bits). If we negate, the parity of our number flips, inverting which of - * {1, 2} we want to add to the scalar when ensuring that it's odd. Further - * complicating things, -1 interacts badly with `secp256k1_scalar_cadd_bit` and - * we need to special-case it in this logic. */ - flip = secp256k1_scalar_is_high(scalar); - /* We add 1 to even numbers, 2 to odd ones, noting that negation flips parity */ - bit = flip ^ !secp256k1_scalar_is_even(scalar); - /* We check for negative one, since adding 2 to it will cause an overflow */ - secp256k1_scalar_negate(&s, scalar); - not_neg_one = !secp256k1_scalar_is_one(&s); - s = *scalar; - secp256k1_scalar_cadd_bit(&s, bit, not_neg_one); - /* If we had negative one, flip == 1, s.d[0] == 0, bit == 1, so caller expects - * that we added two to it and flipped it. In fact for -1 these operations are - * identical. We only flipped, but since skewing is required (in the sense that - * the skew must be 1 or 2, never zero) and flipping is not, we need to change - * our flags to claim that we only skewed. */ + * 128 bits). If we negate, the parity of our number flips, affecting whether + * we want to add to the scalar to ensure that it's odd. */ + flip = secp256k1_scalar_is_high(&s); + skew = flip ^ secp256k1_scalar_is_even(&s); + secp256k1_scalar_cadd_bit(&s, 0, skew); global_sign = secp256k1_scalar_cond_negate(&s, flip); - global_sign *= not_neg_one * 2 - 1; - skew = 1 << bit; /* 4 */ u_last = secp256k1_scalar_shr_int(&s, w); @@ -214,42 +213,22 @@ static void secp256k1_ecmult_const(secp256k1_gej *r, const secp256k1_ge *a, cons } } - secp256k1_fe_mul(&r->z, &r->z, &Z); - { /* Correct for wNAF skew */ - secp256k1_ge correction = *a; - secp256k1_ge_storage correction_1_stor; - secp256k1_ge_storage correction_lam_stor; - secp256k1_ge_storage a2_stor; secp256k1_gej tmpj; - secp256k1_gej_set_ge(&tmpj, &correction); - secp256k1_gej_double_var(&tmpj, &tmpj, NULL); - secp256k1_ge_set_gej(&correction, &tmpj); - secp256k1_ge_to_storage(&correction_1_stor, a); - if (size > 128) { - secp256k1_ge_to_storage(&correction_lam_stor, a); - } - secp256k1_ge_to_storage(&a2_stor, &correction); - /* For odd numbers this is 2a (so replace it), for even ones a (so no-op) */ - secp256k1_ge_storage_cmov(&correction_1_stor, &a2_stor, skew_1 == 2); - if (size > 128) { - secp256k1_ge_storage_cmov(&correction_lam_stor, &a2_stor, skew_lam == 2); - } - - /* Apply the correction */ - secp256k1_ge_from_storage(&correction, &correction_1_stor); - secp256k1_ge_neg(&correction, &correction); - secp256k1_gej_add_ge(r, r, &correction); + secp256k1_ge_neg(&tmpa, &pre_a[0]); + secp256k1_gej_add_ge(&tmpj, r, &tmpa); + secp256k1_gej_cmov(r, &tmpj, skew_1); if (size > 128) { - secp256k1_ge_from_storage(&correction, &correction_lam_stor); - secp256k1_ge_neg(&correction, &correction); - secp256k1_ge_mul_lambda(&correction, &correction); - secp256k1_gej_add_ge(r, r, &correction); + secp256k1_ge_neg(&tmpa, &pre_a_lam[0]); + secp256k1_gej_add_ge(&tmpj, r, &tmpa); + secp256k1_gej_cmov(r, &tmpj, skew_lam); } } + + secp256k1_fe_mul(&r->z, &r->z, &Z); } #endif /* SECP256K1_ECMULT_CONST_IMPL_H */ diff --git a/src/ecmult_gen_prec.h b/src/ecmult_gen_compute_table.h similarity index 60% rename from src/ecmult_gen_prec.h rename to src/ecmult_gen_compute_table.h index 0cfcde9b7994a3..e577158d923492 100644 --- a/src/ecmult_gen_prec.h +++ b/src/ecmult_gen_compute_table.h @@ -4,11 +4,11 @@ * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ -#ifndef SECP256K1_ECMULT_GEN_PREC_H -#define SECP256K1_ECMULT_GEN_PREC_H +#ifndef SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H +#define SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H #include "ecmult_gen.h" -static void secp256k1_ecmult_gen_create_prec_table(secp256k1_ge_storage* table, const secp256k1_ge* gen, int bits); +static void secp256k1_ecmult_gen_compute_table(secp256k1_ge_storage* table, const secp256k1_ge* gen, int bits); -#endif /* SECP256K1_ECMULT_GEN_PREC_H */ +#endif /* SECP256K1_ECMULT_GEN_COMPUTE_TABLE_H */ diff --git a/src/ecmult_gen_prec_impl.h b/src/ecmult_gen_compute_table_impl.h similarity index 90% rename from src/ecmult_gen_prec_impl.h rename to src/ecmult_gen_compute_table_impl.h index bac76c8b13bb85..ff6a2992dc997d 100644 --- a/src/ecmult_gen_prec_impl.h +++ b/src/ecmult_gen_compute_table_impl.h @@ -4,16 +4,16 @@ * file COPYING or https://www.opensource.org/licenses/mit-license.php.* ***********************************************************************/ -#ifndef SECP256K1_ECMULT_GEN_PREC_IMPL_H -#define SECP256K1_ECMULT_GEN_PREC_IMPL_H +#ifndef SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H +#define SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H -#include "ecmult_gen_prec.h" +#include "ecmult_gen_compute_table.h" #include "group_impl.h" #include "field_impl.h" #include "ecmult_gen.h" #include "util.h" -static void secp256k1_ecmult_gen_create_prec_table(secp256k1_ge_storage* table, const secp256k1_ge* gen, int bits) { +static void secp256k1_ecmult_gen_compute_table(secp256k1_ge_storage* table, const secp256k1_ge* gen, int bits) { int g = ECMULT_GEN_PREC_G(bits); int n = ECMULT_GEN_PREC_N(bits); @@ -78,4 +78,4 @@ static void secp256k1_ecmult_gen_create_prec_table(secp256k1_ge_storage* table, free(prec); } -#endif /* SECP256K1_ECMULT_GEN_PREC_IMPL_H */ +#endif /* SECP256K1_ECMULT_GEN_COMPUTE_TABLE_IMPL_H */ diff --git a/src/ecmult_gen_impl.h b/src/ecmult_gen_impl.h index 6a6ab9a4b517b7..2c8a503acc4831 100644 --- a/src/ecmult_gen_impl.h +++ b/src/ecmult_gen_impl.h @@ -12,7 +12,7 @@ #include "group.h" #include "ecmult_gen.h" #include "hash_impl.h" -#include "ecmult_gen_static_prec_table.h" +#include "precomputed_ecmult_gen.h" static void secp256k1_ecmult_gen_context_build(secp256k1_ecmult_gen_context *ctx) { secp256k1_ecmult_gen_blind(ctx, NULL); diff --git a/src/ecmult_impl.h b/src/ecmult_impl.h index 5bd4d4d23dc1aa..52af941fb1062f 100644 --- a/src/ecmult_impl.h +++ b/src/ecmult_impl.h @@ -14,7 +14,7 @@ #include "group.h" #include "scalar.h" #include "ecmult.h" -#include "ecmult_static_pre_g.h" +#include "precomputed_ecmult.h" #if defined(EXHAUSTIVE_TEST_ORDER) /* We need to lower these values for exhaustive tests because @@ -96,25 +96,6 @@ static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, sec secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z); } -/** Fill a table 'pre' with precomputed odd multiples of a. - * - * The resulting point set is brought to a single constant Z denominator, stores the X and Y - * coordinates as ge_storage points in pre, and stores the global Z in rz. - * It only operates on tables sized for WINDOW_A wnaf multiples. - * - * To compute a*P + b*G, we compute a table for P using this function, - * and use the precomputed table in for G. - */ -static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) { - secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)]; - secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)]; - - /* Compute the odd multiples in Jacobian form. */ - secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a); - /* Bring them to the same Z denominator. */ - secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr); -} - /** The following two macro retrieves a particular odd multiple from a table * of precomputed multiples. */ #define ECMULT_TABLE_GET_GE(r,pre,n,w) do { \ diff --git a/src/field.h b/src/field.h index 55679a2fc130aa..1f2a5af34430e4 100644 --- a/src/field.h +++ b/src/field.h @@ -124,4 +124,7 @@ static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_f /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag); +/** Compute the Jacobi symbol of a / p. 0 if a=0; 1 if a square; -1 if a non-square. */ +static int secp256k1_fe_jacobi_var(const secp256k1_fe *a); + #endif /* SECP256K1_FIELD_H */ diff --git a/src/field_10x26_impl.h b/src/field_10x26_impl.h index 4363e727e76e8d..13aa27440ff69f 100644 --- a/src/field_10x26_impl.h +++ b/src/field_10x26_impl.h @@ -11,6 +11,15 @@ #include "field.h" #include "modinv32_impl.h" +/** See the comment at the top of field_5x52_impl.h for more details. + * + * Here, we represent field elements as 10 uint32_t's in base 2^26, least significant first, + * where limbs can contain >26 bits. + * A magnitude M means: + * - 2*M*(2^22-1) is the max (inclusive) of the most significant limb + * - 2*M*(2^26-1) is the max (inclusive) of the remaining limbs + */ + #ifdef VERIFY static void secp256k1_fe_verify(const secp256k1_fe *a) { const uint32_t *d = a->n; @@ -391,6 +400,10 @@ SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k #ifdef VERIFY VERIFY_CHECK(a->magnitude <= m); secp256k1_fe_verify(a); + VERIFY_CHECK(0x3FFFC2FUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m); + VERIFY_CHECK(0x3FFFFBFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m); + VERIFY_CHECK(0x3FFFFFFUL * 2 * (m + 1) >= 0x3FFFFFFUL * 2 * m); + VERIFY_CHECK(0x03FFFFFUL * 2 * (m + 1) >= 0x03FFFFFUL * 2 * m); #endif r->n[0] = 0x3FFFC2FUL * 2 * (m + 1) - a->n[0]; r->n[1] = 0x3FFFFBFUL * 2 * (m + 1) - a->n[1]; @@ -1255,4 +1268,32 @@ static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) { VERIFY_CHECK(secp256k1_fe_normalizes_to_zero(r) == secp256k1_fe_normalizes_to_zero(&tmp)); } +static int secp256k1_fe_jacobi_var(const secp256k1_fe *x) { + secp256k1_fe tmp; + secp256k1_modinv32_signed30 s; + int ret; + + tmp = *x; + secp256k1_fe_normalize_var(&tmp); + secp256k1_fe_to_signed30(&s, &tmp); + ret = secp256k1_jacobi32_maybe_var(&s, &secp256k1_const_modinfo_fe); + if (ret == -2) { + /* secp256k1_jacobi32_maybe_var failed to compute the Jacobi symbol. Fall back + * to computing a square root. This should be extremely rare with random + * input. */ + secp256k1_fe dummy; + ret = 2*secp256k1_fe_sqrt(&dummy, &tmp) - 1; +#ifdef VERIFY + } else { + secp256k1_fe dummy; + if (secp256k1_fe_is_zero(&tmp)) { + VERIFY_CHECK(ret == 0); + } else { + VERIFY_CHECK(ret == 2*secp256k1_fe_sqrt(&dummy, &tmp) - 1); + } +#endif + } + return ret; +} + #endif /* SECP256K1_FIELD_REPR_IMPL_H */ diff --git a/src/field_5x52_impl.h b/src/field_5x52_impl.h index b56bdd13534c43..947cee5547733a 100644 --- a/src/field_5x52_impl.h +++ b/src/field_5x52_impl.h @@ -22,11 +22,18 @@ #endif /** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F, - * represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular, - * each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element - * is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations - * accept any input with magnitude at most M, and have different rules for propagating magnitude to their - * output. + * represented as 5 uint64_t's in base 2^52, least significant first. Note that the limbs are allowed to + * contain >52 bits each. + * + * Each field element has a 'magnitude' associated with it. Internally, a magnitude M means: + * - 2*M*(2^48-1) is the max (inclusive) of the most significant limb + * - 2*M*(2^52-1) is the max (inclusive) of the remaining limbs + * + * Operations have different rules for propagating magnitude to their outputs. If an operation takes a + * magnitude M as a parameter, that means the magnitude of input field elements can be at most M (inclusive). + * + * Each field element also has a 'normalized' flag. A field element is normalized if its magnitude is either + * 0 or 1, and its value is already reduced modulo the order of the field. */ #ifdef VERIFY @@ -377,6 +384,9 @@ SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k #ifdef VERIFY VERIFY_CHECK(a->magnitude <= m); secp256k1_fe_verify(a); + VERIFY_CHECK(0xFFFFEFFFFFC2FULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m); + VERIFY_CHECK(0xFFFFFFFFFFFFFULL * 2 * (m + 1) >= 0xFFFFFFFFFFFFFULL * 2 * m); + VERIFY_CHECK(0x0FFFFFFFFFFFFULL * 2 * (m + 1) >= 0x0FFFFFFFFFFFFULL * 2 * m); #endif r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0]; r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1]; @@ -577,4 +587,32 @@ static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *x) { #endif } +static int secp256k1_fe_jacobi_var(const secp256k1_fe *x) { + secp256k1_fe tmp; + secp256k1_modinv64_signed62 s; + int ret; + + tmp = *x; + secp256k1_fe_normalize_var(&tmp); + secp256k1_fe_to_signed62(&s, &tmp); + ret = secp256k1_jacobi64_maybe_var(&s, &secp256k1_const_modinfo_fe); + if (ret == -2) { + /* secp256k1_jacobi64_maybe_var failed to compute the Jacobi symbol. Fall back + * to computing a square root. This should be extremely rare with random + * input. */ + secp256k1_fe dummy; + ret = 2*secp256k1_fe_sqrt(&dummy, &tmp) - 1; +#ifdef VERIFY + } else { + secp256k1_fe dummy; + if (secp256k1_fe_is_zero(&tmp)) { + VERIFY_CHECK(ret == 0); + } else { + VERIFY_CHECK(ret == 2*secp256k1_fe_sqrt(&dummy, &tmp) - 1); + } +#endif + } + return ret; +} + #endif /* SECP256K1_FIELD_REPR_IMPL_H */ diff --git a/src/gen_ecmult_static_pre_g.c b/src/gen_ecmult_static_pre_g.c deleted file mode 100644 index ba1d1f17d7d96b..00000000000000 --- a/src/gen_ecmult_static_pre_g.c +++ /dev/null @@ -1,131 +0,0 @@ -/***************************************************************************************************** - * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or https://www.opensource.org/licenses/mit-license.php. * - *****************************************************************************************************/ - -#include -#include - -/* Autotools creates libsecp256k1-config.h, of which ECMULT_WINDOW_SIZE is needed. - ifndef guard so downstream users can define their own if they do not use autotools. */ -#if !defined(ECMULT_WINDOW_SIZE) -#include "libsecp256k1-config.h" -#endif - -#include "../include/secp256k1.h" -#include "assumptions.h" -#include "util.h" -#include "field_impl.h" -#include "group_impl.h" -#include "ecmult.h" - -void print_table(FILE *fp, const char *name, int window_g, const secp256k1_gej *gen, int with_conditionals) { - static secp256k1_gej gj; - static secp256k1_ge ge, dgen; - static secp256k1_ge_storage ges; - int j; - int i; - - gj = *gen; - secp256k1_ge_set_gej_var(&ge, &gj); - secp256k1_ge_to_storage(&ges, &ge); - - fprintf(fp, "static const secp256k1_ge_storage %s[ECMULT_TABLE_SIZE(WINDOW_G)] = {\n", name); - fprintf(fp, " S(%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32 - ",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32")\n", - SECP256K1_GE_STORAGE_CONST_GET(ges)); - - secp256k1_gej_double_var(&gj, gen, NULL); - secp256k1_ge_set_gej_var(&dgen, &gj); - - j = 1; - for(i = 3; i <= window_g; ++i) { - if (with_conditionals) { - fprintf(fp, "#if ECMULT_TABLE_SIZE(WINDOW_G) > %ld\n", ECMULT_TABLE_SIZE(i-1)); - } - for(;j < ECMULT_TABLE_SIZE(i); ++j) { - secp256k1_gej_set_ge(&gj, &ge); - secp256k1_gej_add_ge_var(&gj, &gj, &dgen, NULL); - secp256k1_ge_set_gej_var(&ge, &gj); - secp256k1_ge_to_storage(&ges, &ge); - - fprintf(fp, ",S(%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32 - ",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32")\n", - SECP256K1_GE_STORAGE_CONST_GET(ges)); - } - if (with_conditionals) { - fprintf(fp, "#endif\n"); - } - } - fprintf(fp, "};\n"); -} - -void print_two_tables(FILE *fp, int window_g, const secp256k1_ge *g, int with_conditionals) { - secp256k1_gej gj; - int i; - - secp256k1_gej_set_ge(&gj, g); - print_table(fp, "secp256k1_pre_g", window_g, &gj, with_conditionals); - for (i = 0; i < 128; ++i) { - secp256k1_gej_double_var(&gj, &gj, NULL); - } - print_table(fp, "secp256k1_pre_g_128", window_g, &gj, with_conditionals); -} - -int main(void) { - const secp256k1_ge g = SECP256K1_G; - const secp256k1_ge g_13 = SECP256K1_G_ORDER_13; - const secp256k1_ge g_199 = SECP256K1_G_ORDER_199; - const int window_g_13 = 4; - const int window_g_199 = 8; - FILE* fp; - - fp = fopen("src/ecmult_static_pre_g.h","w"); - if (fp == NULL) { - fprintf(stderr, "Could not open src/ecmult_static_pre_g.h for writing!\n"); - return -1; - } - - fprintf(fp, "/* This file was automatically generated by gen_ecmult_static_pre_g. */\n"); - fprintf(fp, "/* This file contains an array secp256k1_pre_g with odd multiples of the base point G and\n"); - fprintf(fp, " * an array secp256k1_pre_g_128 with odd multiples of 2^128*G for accelerating the computation of a*P + b*G.\n"); - fprintf(fp, " */\n"); - fprintf(fp, "#ifndef SECP256K1_ECMULT_STATIC_PRE_G_H\n"); - fprintf(fp, "#define SECP256K1_ECMULT_STATIC_PRE_G_H\n"); - fprintf(fp, "#include \"group.h\"\n"); - fprintf(fp, "#ifdef S\n"); - fprintf(fp, " #error macro identifier S already in use.\n"); - fprintf(fp, "#endif\n"); - fprintf(fp, "#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) " - "SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u," - "0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)\n"); - fprintf(fp, "#if ECMULT_TABLE_SIZE(ECMULT_WINDOW_SIZE) > %ld\n", ECMULT_TABLE_SIZE(ECMULT_WINDOW_SIZE)); - fprintf(fp, " #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting ecmult_static_pre_g.h before the build.\n"); - fprintf(fp, "#endif\n"); - fprintf(fp, "#if defined(EXHAUSTIVE_TEST_ORDER)\n"); - fprintf(fp, "#if EXHAUSTIVE_TEST_ORDER == 13\n"); - fprintf(fp, "#define WINDOW_G %d\n", window_g_13); - - print_two_tables(fp, window_g_13, &g_13, 0); - - fprintf(fp, "#elif EXHAUSTIVE_TEST_ORDER == 199\n"); - fprintf(fp, "#define WINDOW_G %d\n", window_g_199); - - print_two_tables(fp, window_g_199, &g_199, 0); - - fprintf(fp, "#else\n"); - fprintf(fp, " #error No known generator for the specified exhaustive test group order.\n"); - fprintf(fp, "#endif\n"); - fprintf(fp, "#else /* !defined(EXHAUSTIVE_TEST_ORDER) */\n"); - fprintf(fp, "#define WINDOW_G ECMULT_WINDOW_SIZE\n"); - - print_two_tables(fp, ECMULT_WINDOW_SIZE, &g, 1); - - fprintf(fp, "#endif\n"); - fprintf(fp, "#undef S\n"); - fprintf(fp, "#endif\n"); - fclose(fp); - - return 0; -} diff --git a/src/group.h b/src/group.h index b9cd334dae26c7..0b55ad73c6d4a1 100644 --- a/src/group.h +++ b/src/group.h @@ -124,6 +124,9 @@ static void secp256k1_ge_to_storage(secp256k1_ge_storage *r, const secp256k1_ge /** Convert a group element back from the storage type. */ static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storage *a); +/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ +static void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag); + /** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/ static void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag); diff --git a/src/group_impl.h b/src/group_impl.h index bce9fbdad56424..f02891de775ac9 100644 --- a/src/group_impl.h +++ b/src/group_impl.h @@ -642,6 +642,14 @@ static void secp256k1_ge_from_storage(secp256k1_ge *r, const secp256k1_ge_storag r->infinity = 0; } +static SECP256K1_INLINE void secp256k1_gej_cmov(secp256k1_gej *r, const secp256k1_gej *a, int flag) { + secp256k1_fe_cmov(&r->x, &a->x, flag); + secp256k1_fe_cmov(&r->y, &a->y, flag); + secp256k1_fe_cmov(&r->z, &a->z, flag); + + r->infinity ^= (r->infinity ^ a->infinity) & flag; +} + static SECP256K1_INLINE void secp256k1_ge_storage_cmov(secp256k1_ge_storage *r, const secp256k1_ge_storage *a, int flag) { secp256k1_fe_storage_cmov(&r->x, &a->x, flag); secp256k1_fe_storage_cmov(&r->y, &a->y, flag); diff --git a/src/modinv32.h b/src/modinv32.h index 0efdda9ab5e2ef..263bda20b8a3d9 100644 --- a/src/modinv32.h +++ b/src/modinv32.h @@ -39,4 +39,8 @@ static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256 /* Same as secp256k1_modinv32_var, but constant time in x (not in the modulus). */ static void secp256k1_modinv32(secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo); +/* Compute the Jacobi symbol for (x | modinfo->modulus). Either x must be 0, or x must be coprime with + * modulus. All limbs of x must be non-negative. Returns -2 if the result cannot be computed. */ +static int secp256k1_jacobi32_maybe_var(const secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo); + #endif /* SECP256K1_MODINV32_H */ diff --git a/src/modinv32_impl.h b/src/modinv32_impl.h index 661c5fc04c9883..93bc576675eb6d 100644 --- a/src/modinv32_impl.h +++ b/src/modinv32_impl.h @@ -232,6 +232,21 @@ static int32_t secp256k1_modinv32_divsteps_30(int32_t zeta, uint32_t f0, uint32_ return zeta; } +/* inv256[i] = -(2*i+1)^-1 (mod 256) */ +static const uint8_t secp256k1_modinv32_inv256[128] = { + 0xFF, 0x55, 0x33, 0x49, 0xC7, 0x5D, 0x3B, 0x11, 0x0F, 0xE5, 0xC3, 0x59, + 0xD7, 0xED, 0xCB, 0x21, 0x1F, 0x75, 0x53, 0x69, 0xE7, 0x7D, 0x5B, 0x31, + 0x2F, 0x05, 0xE3, 0x79, 0xF7, 0x0D, 0xEB, 0x41, 0x3F, 0x95, 0x73, 0x89, + 0x07, 0x9D, 0x7B, 0x51, 0x4F, 0x25, 0x03, 0x99, 0x17, 0x2D, 0x0B, 0x61, + 0x5F, 0xB5, 0x93, 0xA9, 0x27, 0xBD, 0x9B, 0x71, 0x6F, 0x45, 0x23, 0xB9, + 0x37, 0x4D, 0x2B, 0x81, 0x7F, 0xD5, 0xB3, 0xC9, 0x47, 0xDD, 0xBB, 0x91, + 0x8F, 0x65, 0x43, 0xD9, 0x57, 0x6D, 0x4B, 0xA1, 0x9F, 0xF5, 0xD3, 0xE9, + 0x67, 0xFD, 0xDB, 0xB1, 0xAF, 0x85, 0x63, 0xF9, 0x77, 0x8D, 0x6B, 0xC1, + 0xBF, 0x15, 0xF3, 0x09, 0x87, 0x1D, 0xFB, 0xD1, 0xCF, 0xA5, 0x83, 0x19, + 0x97, 0xAD, 0x8B, 0xE1, 0xDF, 0x35, 0x13, 0x29, 0xA7, 0x3D, 0x1B, 0xF1, + 0xEF, 0xC5, 0xA3, 0x39, 0xB7, 0xCD, 0xAB, 0x01 +}; + /* Compute the transition matrix and eta for 30 divsteps (variable time). * * Input: eta: initial eta @@ -243,21 +258,6 @@ static int32_t secp256k1_modinv32_divsteps_30(int32_t zeta, uint32_t f0, uint32_ * Implements the divsteps_n_matrix_var function from the explanation. */ static int32_t secp256k1_modinv32_divsteps_30_var(int32_t eta, uint32_t f0, uint32_t g0, secp256k1_modinv32_trans2x2 *t) { - /* inv256[i] = -(2*i+1)^-1 (mod 256) */ - static const uint8_t inv256[128] = { - 0xFF, 0x55, 0x33, 0x49, 0xC7, 0x5D, 0x3B, 0x11, 0x0F, 0xE5, 0xC3, 0x59, - 0xD7, 0xED, 0xCB, 0x21, 0x1F, 0x75, 0x53, 0x69, 0xE7, 0x7D, 0x5B, 0x31, - 0x2F, 0x05, 0xE3, 0x79, 0xF7, 0x0D, 0xEB, 0x41, 0x3F, 0x95, 0x73, 0x89, - 0x07, 0x9D, 0x7B, 0x51, 0x4F, 0x25, 0x03, 0x99, 0x17, 0x2D, 0x0B, 0x61, - 0x5F, 0xB5, 0x93, 0xA9, 0x27, 0xBD, 0x9B, 0x71, 0x6F, 0x45, 0x23, 0xB9, - 0x37, 0x4D, 0x2B, 0x81, 0x7F, 0xD5, 0xB3, 0xC9, 0x47, 0xDD, 0xBB, 0x91, - 0x8F, 0x65, 0x43, 0xD9, 0x57, 0x6D, 0x4B, 0xA1, 0x9F, 0xF5, 0xD3, 0xE9, - 0x67, 0xFD, 0xDB, 0xB1, 0xAF, 0x85, 0x63, 0xF9, 0x77, 0x8D, 0x6B, 0xC1, - 0xBF, 0x15, 0xF3, 0x09, 0x87, 0x1D, 0xFB, 0xD1, 0xCF, 0xA5, 0x83, 0x19, - 0x97, 0xAD, 0x8B, 0xE1, 0xDF, 0x35, 0x13, 0x29, 0xA7, 0x3D, 0x1B, 0xF1, - 0xEF, 0xC5, 0xA3, 0x39, 0xB7, 0xCD, 0xAB, 0x01 - }; - /* Transformation matrix; see comments in secp256k1_modinv32_divsteps_30. */ uint32_t u = 1, v = 0, q = 0, r = 1; uint32_t f = f0, g = g0, m; @@ -297,7 +297,7 @@ static int32_t secp256k1_modinv32_divsteps_30_var(int32_t eta, uint32_t f0, uint VERIFY_CHECK(limit > 0 && limit <= 30); m = (UINT32_MAX >> (32 - limit)) & 255U; /* Find what multiple of f must be added to g to cancel its bottom min(limit, 8) bits. */ - w = (g * inv256[(f >> 1) & 127]) & m; + w = (g * secp256k1_modinv32_inv256[(f >> 1) & 127]) & m; /* Do so. */ g += f * w; q += u * w; @@ -317,6 +317,83 @@ static int32_t secp256k1_modinv32_divsteps_30_var(int32_t eta, uint32_t f0, uint return eta; } +/* Compute the transition matrix and eta for 30 posdivsteps (variable time, eta=-delta), and keeps track + * of the Jacobi symbol along the way. f0 and g0 must be f and g mod 2^32 rather than 2^30, because + * Jacobi tracking requires knowing (f mod 8) rather than just (f mod 2). + * + * Input: eta: initial eta + * f0: bottom limb of initial f + * g0: bottom limb of initial g + * Output: t: transition matrix + * Return: final eta + */ +static int32_t secp256k1_modinv32_posdivsteps_30_var(int32_t eta, uint32_t f0, uint32_t g0, secp256k1_modinv32_trans2x2 *t, int *jacp) { + /* Transformation matrix. */ + uint32_t u = 1, v = 0, q = 0, r = 1; + uint32_t f = f0, g = g0, m; + uint16_t w; + int i = 30, limit, zeros; + int jac = *jacp; + + for (;;) { + /* Use a sentinel bit to count zeros only up to i. */ + zeros = secp256k1_ctz32_var(g | (UINT32_MAX << i)); + /* Perform zeros divsteps at once; they all just divide g by two. */ + g >>= zeros; + u <<= zeros; + v <<= zeros; + eta -= zeros; + i -= zeros; + /* Update the bottom bit of jac: when dividing g by an odd power of 2, + * if (f mod 8) is 3 or 5, the Jacobi symbol changes sign. */ + jac ^= (zeros & ((f >> 1) ^ (f >> 2))); + /* We're done once we've done 30 posdivsteps. */ + if (i == 0) break; + VERIFY_CHECK((f & 1) == 1); + VERIFY_CHECK((g & 1) == 1); + VERIFY_CHECK((u * f0 + v * g0) == f << (30 - i)); + VERIFY_CHECK((q * f0 + r * g0) == g << (30 - i)); + /* If eta is negative, negate it and replace f,g with g,f. */ + if (eta < 0) { + uint32_t tmp; + eta = -eta; + /* Update bottom bit of jac: when swapping f and g, the Jacobi symbol changes sign + * if both f and g are 3 mod 4. */ + jac ^= ((f & g) >> 1); + tmp = f; f = g; g = tmp; + tmp = u; u = q; q = tmp; + tmp = v; v = r; r = tmp; + } + /* eta is now >= 0. In what follows we're going to cancel out the bottom bits of g. No more + * than i can be cancelled out (as we'd be done before that point), and no more than eta+1 + * can be done as its sign will flip once that happens. */ + limit = ((int)eta + 1) > i ? i : ((int)eta + 1); + /* m is a mask for the bottom min(limit, 8) bits (our table only supports 8 bits). */ + VERIFY_CHECK(limit > 0 && limit <= 30); + m = (UINT32_MAX >> (32 - limit)) & 255U; + /* Find what multiple of f must be added to g to cancel its bottom min(limit, 8) bits. */ + w = (g * secp256k1_modinv32_inv256[(f >> 1) & 127]) & m; + /* Do so. */ + g += f * w; + q += u * w; + r += v * w; + VERIFY_CHECK((g & m) == 0); + } + /* Return data in t and return value. */ + t->u = (int32_t)u; + t->v = (int32_t)v; + t->q = (int32_t)q; + t->r = (int32_t)r; + /* The determinant of t must be a power of two. This guarantees that multiplication with t + * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which + * will be divided out again). As each divstep's individual matrix has determinant 2 or -2, + * the aggregate of 30 of them will have determinant 2^30 or -2^30. */ + VERIFY_CHECK((int64_t)t->u * t->r - (int64_t)t->v * t->q == ((int64_t)1) << 30 || + (int64_t)t->u * t->r - (int64_t)t->v * t->q == -(((int64_t)1) << 30)); + *jacp = jac; + return eta; +} + /* Compute (t/2^30) * [d, e] mod modulus, where t is a transition matrix for 30 divsteps. * * On input and output, d and e are in range (-2*modulus,modulus). All output limbs will be in range @@ -584,4 +661,69 @@ static void secp256k1_modinv32_var(secp256k1_modinv32_signed30 *x, const secp256 *x = d; } +/* Compute the Jacobi symbol of x modulo modinfo->modulus (variable time). gcd(x,modulus) must be 1, or x must be 0. */ +static int secp256k1_jacobi32_maybe_var(const secp256k1_modinv32_signed30 *x, const secp256k1_modinv32_modinfo *modinfo) { + /* Start with f=modulus, g=x, eta=-1. */ + secp256k1_modinv32_signed30 f = modinfo->modulus; + secp256k1_modinv32_signed30 g = *x; + int j, len = 9; + int32_t eta = -1; /* eta = -delta; delta is initially 1 */ + int32_t cond, fn, gn; + int jac = 0; + int count; + + VERIFY_CHECK(g.v[0] >= 0 && g.v[1] >= 0 && g.v[2] >= 0 && g.v[3] >= 0 && g.v[4] >= 0 && g.v[5] >= 0 && g.v[6] >= 0 && g.v[7] >= 0 && g.v[8] >= 0); + + /* The loop below does not converge for input g=0. Deal with this case specifically. */ + if (!(g.v[0] | g.v[1] | g.v[2] | g.v[3] | g.v[4] | g.v[5] | g.v[6] | g.v[7] | g.v[8])) return 0; + + /* Do up to 50 iterations of 30 posdivsteps (up to 1500 steps; more is extremely rare) each until f=1. + * In VERIFY mode use a lower number of iterations (750, close to the median 756), so failure actually occurs. */ +#ifdef VERIFY + for (count = 0; count < 25; ++count) { +#else + for (count = 0; count < 50; ++count) { +#endif + /* Compute transition matrix and new eta after 30 posdivsteps. */ + secp256k1_modinv32_trans2x2 t; + eta = secp256k1_modinv32_posdivsteps_30_var(eta, f.v[0] | ((uint32_t)f.v[1] << 30), g.v[0] | ((uint32_t)g.v[1] << 30), &t, &jac); + /* Update f,g using that transition matrix. */ +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + secp256k1_modinv32_update_fg_30_var(len, &f, &g, &t); + /* If the bottom limb of f is 1, there is a chance that f=1. */ + if (f.v[0] == 1) { + cond = 0; + /* Check if the other limbs are also 0. */ + for (j = 1; j < len; ++j) { + cond |= f.v[j]; + } + /* If so, we're done. */ + if (cond == 0) return 1 - 2*(jac & 1); + } + + /* Determine if len>1 and limb (len-1) of both f and g is 0. */ + fn = f.v[len - 1]; + gn = g.v[len - 1]; + cond = ((int32_t)len - 2) >> 31; + cond |= fn; + cond |= gn; + /* If so, reduce length. */ + if (cond == 0) --len; +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */ + VERIFY_CHECK(secp256k1_modinv32_mul_cmp_30(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + } + + /* The loop failed to converge to f=g after 1500 iterations. Return -2, indicating unknown result. */ + return -2; +} + #endif /* SECP256K1_MODINV32_IMPL_H */ diff --git a/src/modinv64.h b/src/modinv64.h index da506dfa9f722e..e432fcbe8d57a5 100644 --- a/src/modinv64.h +++ b/src/modinv64.h @@ -43,4 +43,8 @@ static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256 /* Same as secp256k1_modinv64_var, but constant time in x (not in the modulus). */ static void secp256k1_modinv64(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo); +/* Compute the Jacobi symbol for (x | modinfo->modulus). Either x must be 0, or x must be coprime with + * modulus. All limbs of x must be non-negative. Returns -2 if the result cannot be computed. */ +static int secp256k1_jacobi64_maybe_var(const secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo); + #endif /* SECP256K1_MODINV64_H */ diff --git a/src/modinv64_impl.h b/src/modinv64_impl.h index 0743a9c8210d2d..2d0d33d77767a4 100644 --- a/src/modinv64_impl.h +++ b/src/modinv64_impl.h @@ -256,7 +256,7 @@ static int64_t secp256k1_modinv64_divsteps_62_var(int64_t eta, uint64_t f0, uint tmp = v; v = r; r = -tmp; /* Use a formula to cancel out up to 6 bits of g. Also, no more than i can be cancelled * out (as we'd be done before that point), and no more than eta+1 can be done as its - * will flip again once that happens. */ + * sign will flip again once that happens. */ limit = ((int)eta + 1) > i ? i : ((int)eta + 1); VERIFY_CHECK(limit > 0 && limit <= 62); /* m is a mask for the bottom min(limit, 6) bits. */ @@ -294,6 +294,94 @@ static int64_t secp256k1_modinv64_divsteps_62_var(int64_t eta, uint64_t f0, uint return eta; } +/* Compute the transition matrix and eta for 62 posdivsteps (variable time, eta=-delta), and keeps track + * of the Jacobi symbol along the way. f0 and g0 must be f and g mod 2^64 rather than 2^62, because + * Jacobi tracking requires knowing (f mod 8) rather than just (f mod 2). + * + * Input: eta: initial eta + * f0: bottom limb of initial f + * g0: bottom limb of initial g + * Output: t: transition matrix + * Return: final eta + */ +static int64_t secp256k1_modinv64_posdivsteps_62_var(int64_t eta, uint64_t f0, uint64_t g0, secp256k1_modinv64_trans2x2 *t, int *jacp) { + /* Transformation matrix; see comments in secp256k1_modinv64_divsteps_62. */ + uint64_t u = 1, v = 0, q = 0, r = 1; + uint64_t f = f0, g = g0, m; + uint32_t w; + int i = 62, limit, zeros; + int jac = *jacp; + + for (;;) { + /* Use a sentinel bit to count zeros only up to i. */ + zeros = secp256k1_ctz64_var(g | (UINT64_MAX << i)); + /* Perform zeros divsteps at once; they all just divide g by two. */ + g >>= zeros; + u <<= zeros; + v <<= zeros; + eta -= zeros; + i -= zeros; + /* Update the bottom bit of jac: when dividing g by an odd power of 2, + * if (f mod 8) is 3 or 5, the Jacobi symbol changes sign. */ + jac ^= (zeros & ((f >> 1) ^ (f >> 2))); + /* We're done once we've done 62 posdivsteps. */ + if (i == 0) break; + VERIFY_CHECK((f & 1) == 1); + VERIFY_CHECK((g & 1) == 1); + VERIFY_CHECK((u * f0 + v * g0) == f << (62 - i)); + VERIFY_CHECK((q * f0 + r * g0) == g << (62 - i)); + /* If eta is negative, negate it and replace f,g with g,f. */ + if (eta < 0) { + uint64_t tmp; + eta = -eta; + tmp = f; f = g; g = tmp; + tmp = u; u = q; q = tmp; + tmp = v; v = r; r = tmp; + /* Update bottom bit of jac: when swapping f and g, the Jacobi symbol changes sign + * if both f and g are 3 mod 4. */ + jac ^= ((f & g) >> 1); + /* Use a formula to cancel out up to 6 bits of g. Also, no more than i can be cancelled + * out (as we'd be done before that point), and no more than eta+1 can be done as its + * sign will flip again once that happens. */ + limit = ((int)eta + 1) > i ? i : ((int)eta + 1); + VERIFY_CHECK(limit > 0 && limit <= 62); + /* m is a mask for the bottom min(limit, 6) bits. */ + m = (UINT64_MAX >> (64 - limit)) & 63U; + /* Find what multiple of f must be added to g to cancel its bottom min(limit, 6) + * bits. */ + w = (f * g * (f * f - 2)) & m; + } else { + /* In this branch, use a simpler formula that only lets us cancel up to 4 bits of g, as + * eta tends to be smaller here. */ + limit = ((int)eta + 1) > i ? i : ((int)eta + 1); + VERIFY_CHECK(limit > 0 && limit <= 62); + /* m is a mask for the bottom min(limit, 4) bits. */ + m = (UINT64_MAX >> (64 - limit)) & 15U; + /* Find what multiple of f must be added to g to cancel its bottom min(limit, 4) + * bits. */ + w = f + (((f + 1) & 4) << 1); + w = (-w * g) & m; + } + g += f * w; + q += u * w; + r += v * w; + VERIFY_CHECK((g & m) == 0); + } + /* Return data in t and return value. */ + t->u = (int64_t)u; + t->v = (int64_t)v; + t->q = (int64_t)q; + t->r = (int64_t)r; + /* The determinant of t must be a power of two. This guarantees that multiplication with t + * does not change the gcd of f and g, apart from adding a power-of-2 factor to it (which + * will be divided out again). As each divstep's individual matrix has determinant 2 or -2, + * the aggregate of 62 of them will have determinant 2^62 or -2^62. */ + VERIFY_CHECK((int128_t)t->u * t->r - (int128_t)t->v * t->q == ((int128_t)1) << 62 || + (int128_t)t->u * t->r - (int128_t)t->v * t->q == -(((int128_t)1) << 62)); + *jacp = jac; + return eta; +} + /* Compute (t/2^62) * [d, e] mod modulus, where t is a transition matrix scaled by 2^62. * * On input and output, d and e are in range (-2*modulus,modulus). All output limbs will be in range @@ -590,4 +678,69 @@ static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256 *x = d; } +/* Compute the Jacobi symbol of x modulo modinfo->modulus (variable time). gcd(x,modulus) must be 1, or x must be 0. */ +static int secp256k1_jacobi64_maybe_var(const secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo) { + /* Start with f=modulus, g=x, eta=-1. */ + secp256k1_modinv64_signed62 f = modinfo->modulus; + secp256k1_modinv64_signed62 g = *x; + int j, len = 5; + int64_t eta = -1; /* eta = -delta; delta is initially 1 */ + int64_t cond, fn, gn; + int jac = 0; + int count; + + VERIFY_CHECK(g.v[0] >= 0 && g.v[1] >= 0 && g.v[2] >= 0 && g.v[3] >= 0 && g.v[4] >= 0); + + /* The loop below does not converge for input g=0. Deal with this case specifically. */ + if (!(g.v[0] | g.v[1] | g.v[2] | g.v[3] | g.v[4])) return 0; + + /* Do up to 25 iterations of 62 posdivsteps (up to 1550 steps; more is extremely rare) each until f=1. + * In VERIFY mode use a lower number of iterations (744, close to the median 756), so failure actually occurs. */ +#ifdef VERIFY + for (count = 0; count < 12; ++count) { +#else + for (count = 0; count < 25; ++count) { +#endif + /* Compute transition matrix and new eta after 62 posdivsteps. */ + secp256k1_modinv64_trans2x2 t; + eta = secp256k1_modinv64_posdivsteps_62_var(eta, f.v[0] | ((uint64_t)f.v[1] << 62), g.v[0] | ((uint64_t)g.v[1] << 62), &t, &jac); + /* Update f,g using that transition matrix. */ +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + secp256k1_modinv64_update_fg_62_var(len, &f, &g, &t); + /* If the bottom limb of f is 1, there is a chance that f=1. */ + if (f.v[0] == 1) { + cond = 0; + /* Check if the other limbs are also 0. */ + for (j = 1; j < len; ++j) { + cond |= f.v[j]; + } + /* If so, we're done. */ + if (cond == 0) return 1 - 2*(jac & 1); + } + + /* Determine if len>1 and limb (len-1) of both f and g is 0. */ + fn = f.v[len - 1]; + gn = g.v[len - 1]; + cond = ((int64_t)len - 2) >> 63; + cond |= fn; + cond |= gn; + /* If so, reduce length. */ + if (cond == 0) --len; +#ifdef VERIFY + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 0) > 0); /* f > 0 */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&f, len, &modinfo->modulus, 1) <= 0); /* f <= modulus */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 0) > 0); /* g > 0 */ + VERIFY_CHECK(secp256k1_modinv64_mul_cmp_62(&g, len, &modinfo->modulus, 1) < 0); /* g < modulus */ +#endif + } + + /* The loop failed to converge to f=g after 1550 iterations. Return -2, indicating unknown result. */ + return -2; +} + #endif /* SECP256K1_MODINV64_IMPL_H */ diff --git a/src/modules/ellsq/Makefile.am.include b/src/modules/ellsq/Makefile.am.include new file mode 100644 index 00000000000000..313dae95269598 --- /dev/null +++ b/src/modules/ellsq/Makefile.am.include @@ -0,0 +1,4 @@ +include_HEADERS += include/secp256k1_ellsq.h +noinst_HEADERS += src/modules/ellsq/bench_impl.h +noinst_HEADERS += src/modules/ellsq/main_impl.h +noinst_HEADERS += src/modules/ellsq/tests_impl.h diff --git a/src/modules/ellsq/bench_impl.h b/src/modules/ellsq/bench_impl.h new file mode 100644 index 00000000000000..fd71aa6e58b65f --- /dev/null +++ b/src/modules/ellsq/bench_impl.h @@ -0,0 +1,67 @@ +/*********************************************************************** + * Copyright (c) 2021 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ELLSQ_BENCH_H +#define SECP256K1_MODULE_ELLSQ_BENCH_H + +#include "../include/secp256k1_ellsq.h" + +typedef struct { + secp256k1_context *ctx; + secp256k1_pubkey point; + unsigned char rnd64[64]; +} bench_ellsq_data; + +static void bench_ellsq_setup(void* arg) { + bench_ellsq_data *data = (bench_ellsq_data*)arg; + const unsigned char point[] = { + 0x03, + 0x54, 0x94, 0xc1, 0x5d, 0x32, 0x09, 0x97, 0x06, + 0xc2, 0x37, 0x5f, 0x94, 0x34, 0x87, 0x45, 0xfd, + 0x75, 0x7c, 0xe3, 0x0e, 0x4e, 0x8c, 0x90, 0xfb, + 0xa2, 0xba, 0xd1, 0x84, 0xf8, 0x83, 0xc6, 0x9f + }; + CHECK(secp256k1_ec_pubkey_parse(data->ctx, &data->point, point, sizeof(point)) == 1); +} + +static void bench_ellsq_encode(void* arg, int iters) { + int i; + bench_ellsq_data *data = (bench_ellsq_data*)arg; + + for (i = 0; i < iters; i++) { + data->rnd64[29] ^= 145; + CHECK(secp256k1_ellsq_encode(data->ctx, data->rnd64, data->rnd64 + 16, &data->point) == 1); + } +} + +static void bench_ellsq_decode(void* arg, int iters) { + int i; + secp256k1_pubkey out; + bench_ellsq_data *data = (bench_ellsq_data*)arg; + + for (i = 0; i < iters; i++) { + data->rnd64[13] ^= 247; + data->rnd64[47] ^= 113; + CHECK(secp256k1_ellsq_decode(data->ctx, &out, data->rnd64) == 1); + memcpy(data->rnd64, &out.data, 64); + } +} + +void run_ellsq_bench(int iters, int argc, char** argv) { + bench_ellsq_data data; + int d = argc == 1; + + /* create a context with no capabilities */ + data.ctx = secp256k1_context_create(SECP256K1_FLAGS_TYPE_CONTEXT); + memset(data.rnd64, 11, sizeof(data.rnd64)); + + if (d || have_flag(argc, argv, "ellsq") || have_flag(argc, argv, "encode") || have_flag(argc, argv, "ellsq_encode")) run_benchmark("ellsq_encode", bench_ellsq_encode, bench_ellsq_setup, NULL, &data, 10, iters); + if (d || have_flag(argc, argv, "ellsq") || have_flag(argc, argv, "decode") || have_flag(argc, argv, "ellsq_decode")) run_benchmark("ellsq_decode", bench_ellsq_decode, bench_ellsq_setup, NULL, &data, 10, iters); + + secp256k1_context_destroy(data.ctx); +} + +#endif /* SECP256K1_MODULE_ELLSQ_BENCH_H */ diff --git a/src/modules/ellsq/main_impl.h b/src/modules/ellsq/main_impl.h new file mode 100644 index 00000000000000..81b2b9c7745cc0 --- /dev/null +++ b/src/modules/ellsq/main_impl.h @@ -0,0 +1,305 @@ +/*********************************************************************** + * Copyright (c) 2021 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ELLSQ_MAIN_H +#define SECP256K1_MODULE_ELLSQ_MAIN_H + +#include "../../../include/secp256k1.h" +#include "../../../include/secp256k1_ellsq.h" +#include "../../hash.h" + +/* c1 = the square root of -3 ((-3)**((p+1)/4)). */ +static const secp256k1_fe secp256k1_ellsq_c1 = SECP256K1_FE_CONST(0x0a2d2ba9, 0x3507f1df, 0x233770c2, 0xa797962c, 0xc61f6d15, 0xda14ecd4, 0x7d8d27ae, 0x1cd5f852); +/* c2 = (c1-1)/2 (a cube root of 1). */ +static const secp256k1_fe secp256k1_ellsq_c2 = SECP256K1_FE_CONST(0x851695d4, 0x9a83f8ef, 0x919bb861, 0x53cbcb16, 0x630fb68a, 0xed0a766a, 0x3ec693d6, 0x8e6afa40); +/* c3 = (-c1-1)/2 (another cube root of 1). */ +static const secp256k1_fe secp256k1_ellsq_c3 = SECP256K1_FE_CONST(0x7ae96a2b, 0x657c0710, 0x6e64479e, 0xac3434e9, 0x9cf04975, 0x12f58995, 0xc1396c28, 0x719501ee); +/* c4 = 16*(c1-1) */ +static const secp256k1_fe secp256k1_ellsq_c4 = SECP256K1_FE_CONST(0xa2d2ba93, 0x507f1df2, 0x33770c2a, 0x797962cc, 0x61f6d15d, 0xa14ecd47, 0xd8d27ae1, 0xcd5f8510); +/* c5 = 1/2 */ +static const secp256k1_fe secp256k1_ellsq_c5 = SECP256K1_FE_CONST(0x7fffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7ffffe18); + +/* Given a field element u, compute a group element out. This functions results in a + * non-infinity point on the curve for every possible input u. It implements the function + * f defined in secp256k1_ellsq.h. + */ +static void secp256k1_ellsq_fe_to_ge_var(secp256k1_ge* out, const secp256k1_fe* u) { + secp256k1_fe t0, t1, t2, t3, t4, x, y; + int ret; + secp256k1_fe_sqr(&t0, u); + secp256k1_fe_set_int(&t1, 8); + secp256k1_fe_add(&t1, &t0); + secp256k1_fe_mul(&t3, &t0, &secp256k1_ellsq_c1); + secp256k1_fe_negate(&t3, &t3, 1); + secp256k1_fe_mul(&t2, &t1, &secp256k1_ellsq_c2); + secp256k1_fe_add(&t2, &t3); + secp256k1_fe_sqr(&t4, &t1); + secp256k1_fe_sqr(&t4, &t4); + secp256k1_fe_mul_int(&t4, 7); + secp256k1_fe_sqr(&t3, &t2); + secp256k1_fe_mul(&t3, &t3, &t2); + secp256k1_fe_mul(&t3, &t3, &t1); + secp256k1_fe_add(&t3, &t4); + if (secp256k1_fe_jacobi_var(&t3) >= 0) { + ret = secp256k1_fe_sqrt(&t4, &t3); + VERIFY_CHECK(ret); + secp256k1_fe_inv_var(&t1, &t1); + secp256k1_fe_mul(&x, &t1, &t2); + secp256k1_fe_sqr(&t1, &t1); + secp256k1_fe_mul(&y, &t1, &t4); + } else { + secp256k1_fe_add(&t2, &t1); + secp256k1_fe_negate(&t2, &t2, 5); + secp256k1_fe_sqr(&t3, &t2); + secp256k1_fe_mul(&t3, &t3, &t2); + secp256k1_fe_mul(&t3, &t3, &t1); + secp256k1_fe_add(&t3, &t4); + if (secp256k1_fe_jacobi_var(&t3) >= 0) { + ret = secp256k1_fe_sqrt(&t4, &t3); + VERIFY_CHECK(ret); + secp256k1_fe_inv_var(&t1, &t1); + secp256k1_fe_mul(&x, &t1, &t2); + secp256k1_fe_sqr(&t1, &t1); + secp256k1_fe_mul(&y, &t1, &t4); + } else { + secp256k1_fe_mul_int(&t0, 3); + secp256k1_fe_inv_var(&t0, &t0); + secp256k1_fe_sqr(&t1, &t1); + secp256k1_fe_mul(&t0, &t0, &t1); + secp256k1_fe_negate(&t0, &t0, 1); + secp256k1_fe_set_int(&x, 1); + secp256k1_fe_add(&x, &t0); + secp256k1_fe_sqr(&t0, &x); + secp256k1_fe_mul(&t0, &t0, &x); + secp256k1_fe_set_int(&t1, 7); + secp256k1_fe_add(&t1, &t0); + ret = secp256k1_fe_sqrt(&y, &t1); + VERIFY_CHECK(ret); + } + } + t0 = *u; + secp256k1_fe_normalize_var(&y); + secp256k1_fe_normalize_var(&t0); + if (secp256k1_fe_is_odd(&y) != secp256k1_fe_is_odd(&t0)) secp256k1_fe_negate(&y, &y, 1); + secp256k1_ge_set_xy(out, &x, &y); +} + +/* Given a point on the curve p, and an integer branch value i in [0,4), compute a + * field element out which secp256k1_ellsq_fe_to_ge_var would map back to p, or + * fail. Combining all non-failing outs for a given p, over all values of i, + * results in the set of all preimages of p under secp256k1_ellsq_fe_to_ge_var. No + * two (p, i) inputs map to the same out, if successful. + * + * i=0 will compute a preimage that maps to p using the "x1" above. + * i=1 will compute a preimage that maps to p using the "x2" above. + * i=2 and i=3 will compute a preimage that maps to using the "x3" above. + * + * All of them will fail if no preimage under the respective x formula exists. + * When i>0, the function will fail when the would-be preimage maps to the curve + * using a lowered-numbered x (so i=1 fails when its x1 lands on the curve, and + * i=2 and i=3 fail when its x1 or x2 land on the curve). In addition, failure is + * returned when a lowered-value i would result in the same preimage. + */ +static int secp256k1_ellsq_ge_to_fe_var(secp256k1_fe* out, const secp256k1_ge* p, int i) { + int ret; + secp256k1_fe t0, t1, t2, t3, u, x = p->x, y = p->y; + secp256k1_fe_normalize_var(&x); + secp256k1_fe_normalize_var(&y); + VERIFY_CHECK(i >= 0); + VERIFY_CHECK(i < 4); + if (i < 2) { + t0 = x; + secp256k1_fe_mul_int(&t0, 2); + secp256k1_fe_set_int(&t1, 1); + secp256k1_fe_add(&t0, &t1); + secp256k1_fe_negate(&t1, &t0, 3); + secp256k1_fe_add(&t1, &secp256k1_ellsq_c1); + secp256k1_fe_add(&t0, &secp256k1_ellsq_c1); + secp256k1_fe_mul(&t2, &t0, &t1); + secp256k1_fe_mul_int(&t2, 8); + if (secp256k1_fe_jacobi_var(&t2) < 0) return 0; + if (i == 0) { + if (secp256k1_fe_normalizes_to_zero_var(&t0)) return 0; + if (secp256k1_fe_normalizes_to_zero_var(&t1) && secp256k1_fe_is_odd(&y)) return 0; + ret = secp256k1_fe_sqrt(&t1, &t2); + VERIFY_CHECK(ret); + secp256k1_fe_inv_var(&t0, &t0); + secp256k1_fe_mul(&u, &t0, &t1); + } else { /* i == 1 */ + secp256k1_fe_set_int(&t0, 1); + secp256k1_fe_add(&t0, &x); + secp256k1_fe_negate(&t0, &t0, 2); + secp256k1_fe_sqr(&t3, &t0); + secp256k1_fe_mul(&t0, &t0, &t3); + secp256k1_fe_set_int(&t3, 7); + secp256k1_fe_add(&t0, &t3); + if (secp256k1_fe_jacobi_var(&t0) >= 0) return 0; + ret = secp256k1_fe_sqrt(&t0, &t2); + VERIFY_CHECK(ret); + secp256k1_fe_inv_var(&t1, &t1); + secp256k1_fe_mul(&u, &t0, &t1); + } + } else { + t0 = x; + secp256k1_fe_mul_int(&t0, 6); + secp256k1_fe_set_int(&t1, 26); + secp256k1_fe_add(&t0, &t1); + secp256k1_fe_sqr(&t1, &t0); + secp256k1_fe_set_int(&t2, 1024); + secp256k1_fe_negate(&t2, &t2, 1); + secp256k1_fe_add(&t2, &t1); + if (secp256k1_fe_jacobi_var(&t2) < 0) return 0; + ret = secp256k1_fe_sqrt(&t1, &t2); + VERIFY_CHECK(ret); + if (i == 3) { + if (secp256k1_fe_normalizes_to_zero_var(&t1)) return 0; + secp256k1_fe_negate(&t1, &t1, 1); + } + secp256k1_fe_negate(&t0, &t0, 7); + secp256k1_fe_add(&t0, &t1); + if (secp256k1_fe_jacobi_var(&t0) < 0) return 0; + secp256k1_fe_set_int(&t1, 32); + secp256k1_fe_normalize_weak(&t0); + secp256k1_fe_add(&t1, &t0); + secp256k1_fe_mul(&t2, &t0, &secp256k1_ellsq_c3); + secp256k1_fe_add(&t2, &secp256k1_ellsq_c4); + secp256k1_fe_sqr(&t3, &t2); + secp256k1_fe_mul(&t3, &t3, &t2); + secp256k1_fe_mul(&t3, &t3, &t1); + secp256k1_fe_sqr(&t1, &t1); + secp256k1_fe_sqr(&t1, &t1); + secp256k1_fe_mul_int(&t1, 7); + secp256k1_fe_add(&t3, &t1); + if (secp256k1_fe_jacobi_var(&t3) >= 0) return 0; + ret = secp256k1_fe_sqrt(&u, &t0); + VERIFY_CHECK(ret); + secp256k1_fe_mul(&u, &u, &secp256k1_ellsq_c5); + } + secp256k1_fe_normalize_var(&u); + if (secp256k1_fe_is_odd(&u) != secp256k1_fe_is_odd(&y)) { + secp256k1_fe_negate(&u, &u, 1); + } + *out = u; + return 1; +} + +int secp256k1_ellsq_encode(const secp256k1_context* ctx, unsigned char *ell64, const unsigned char *rnd32, const secp256k1_pubkey *pubkey) { + secp256k1_ge p; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(ell64 != NULL); + ARG_CHECK(rnd32 != NULL); + ARG_CHECK(pubkey != NULL); + + if (secp256k1_pubkey_load(ctx, &p, pubkey)) { + uint32_t cnt = 0; + /* Field elements and branch values are extracted from + * SHA256("secp256k1_ellsq_encode\x00" + uint32{cnt} + rnd32 + X + byte{Y & 1}) + * for consecutive values of cnt. cnt==0 is first used to populate a pool of + * 128 2-bit branch values. The 128 cnt values that follow are used to + * generate field elements u1. cnt==129 (and multiples thereof) are used to + * repopulate the pool and start over, if that were ever necessary. */ + unsigned char hashdata[23 + 4 + 32 + 32 + 1] = "secp256k1_ellsq_encode"; + /* Pool of 2-bit branch values. */ + unsigned char branch_hash[32]; + /* Number of 2-bit values in branch_hash left. */ + int branches_left = 0; + /* Fill up hashdata, excluding i. */ + memcpy(hashdata + 23 + 4, rnd32, 32); + secp256k1_fe_get_b32(hashdata + 23 + 4 + 32, &p.x); + hashdata[4 + 23 + 32 + 32] = secp256k1_fe_is_odd(&p.y); + while (1) { + int branch; + secp256k1_fe u1, u2; + secp256k1_ge q; + secp256k1_gej qj; + /* If the pool of branch values is empty, populate it. */ + if (branches_left == 0) { + secp256k1_sha256 hash; + hashdata[23 + 0] = cnt; + hashdata[23 + 1] = cnt >> 8; + hashdata[23 + 2] = cnt >> 16; + hashdata[23 + 3] = cnt >> 24; + secp256k1_sha256_initialize(&hash); + secp256k1_sha256_write(&hash, hashdata, sizeof(hashdata)); + secp256k1_sha256_finalize(&hash, branch_hash); + ++cnt; + branches_left = 128; + } + /* Take a 2-bit branch value from the branch pool. */ + --branches_left; + branch = (branch_hash[(127 - branches_left) >> 2] >> (((127 - branches_left) & 3) << 1)) & 3; + /* Compute a new u1 value by hashing (a potential first 32 bytes of the output). */ + { + secp256k1_sha256 hash; + hashdata[23 + 0] = cnt; + hashdata[23 + 1] = cnt >> 8; + hashdata[23 + 2] = cnt >> 16; + hashdata[23 + 3] = cnt >> 24; + secp256k1_sha256_initialize(&hash); + secp256k1_sha256_write(&hash, hashdata, sizeof(hashdata)); + secp256k1_sha256_finalize(&hash, ell64); + ++cnt; + } + if (!secp256k1_fe_set_b32(&u1, ell64)) continue; + /* Compute the remainder Q to encode in the last 32 bytes of the output. */ + secp256k1_ellsq_fe_to_ge_var(&q, &u1); + secp256k1_ge_neg(&q, &q); + secp256k1_gej_set_ge(&qj, &q); + secp256k1_gej_add_ge_var(&qj, &qj, &p, NULL); + if (!secp256k1_gej_is_infinity(&qj)) { + secp256k1_ge_set_gej_var(&q, &qj); + } else { + /* If Q=P-f(u1) is infinity, it means we're trying to encode P=f(u1). + * While no u2 exists such that f(u2)=Q in that case, it is still + * possible to encode P due to the special rule that if f(u1)+f(u2) + * is infinity, the result of decoding is f(u1). + * In other words, we're not trying to reach f(u2)=P-f(u1), but + * f(u2)=-f(u1) instead. -f(u1) is exactly what the variable q + * already holds at this point. Note that if u1 is generated using + * a secure hash function, the probability of reaching this branch + * is negligible. */ + } + /* Try to find a u2 value which encodes Q. */ + if (secp256k1_ellsq_ge_to_fe_var(&u2, &q, branch)) { + /* If that succeeds, store it in the output. */ + secp256k1_fe_normalize_var(&u2); + secp256k1_fe_get_b32(ell64 + 32, &u2); + break; + } + } + memset(hashdata, 0, sizeof(hashdata)); + return 1; + } + /* Only returned in case the provided pubkey is invalid. */ + return 0; +} + +int secp256k1_ellsq_decode(const secp256k1_context* ctx, secp256k1_pubkey *pubkey, const unsigned char *ell64) { + secp256k1_fe f1, f2; + secp256k1_ge p1, p2; + secp256k1_gej acc; + VERIFY_CHECK(ctx != NULL); + ARG_CHECK(pubkey != NULL); + ARG_CHECK(ell64 != NULL); + + secp256k1_fe_set_b32(&f1, ell64); + secp256k1_fe_set_b32(&f2, ell64 + 32); + secp256k1_ellsq_fe_to_ge_var(&p1, &f1); + secp256k1_ellsq_fe_to_ge_var(&p2, &f2); + secp256k1_gej_set_ge(&acc, &p1); + secp256k1_gej_add_ge_var(&acc, &acc, &p2, NULL); + if (!secp256k1_gej_is_infinity(&acc)) { + secp256k1_ge_set_gej_var(&p1, &acc); + } else { + /* f(u1)+f(u2) is infinity. In that case the decoding is defined to be + * equal to f(u1) instead. f(u1) is already stored in the p1 variable + * at this point. */ + } + secp256k1_pubkey_save(pubkey, &p1); + return 1; +} + +#endif diff --git a/src/modules/ellsq/tests_impl.h b/src/modules/ellsq/tests_impl.h new file mode 100644 index 00000000000000..9b74663cf42f84 --- /dev/null +++ b/src/modules/ellsq/tests_impl.h @@ -0,0 +1,166 @@ +/*********************************************************************** + * Copyright (c) 2021 Pieter Wuile * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php.* + ***********************************************************************/ + +#ifndef SECP256K1_MODULE_ELLSQ_TESTS_H +#define SECP256K1_MODULE_ELLSQ_TESTS_H + +#include "../../../include/secp256k1_ellsq.h" + +struct ellsq_test { + secp256k1_ge point; + int enc_bitmap; + secp256k1_fe encs[4]; +}; + +/* Set of (point, encodings) test vectors, selected to maximize branch coverage. + * Created using an independent implementation. */ +static const struct ellsq_test ellsq_tests[] = { + {SECP256K1_GE_CONST(0xc27fb7a3, 0x283a7d3e, 0xc9f96421, 0x545ef6f5, 0x8ace7b71, 0x06c8a1b9, 0x07c0ae8a, 0x7598159c, 0xe05a060e, 0x839ef79f, 0xc0c1267c, 0xa17880c9, 0x584cdd34, 0xc05f9695, 0x55482207, 0xe6851f2a), 15, {SECP256K1_FE_CONST(0xc0ad127a, 0xa36824d6, 0x5b1f5be7, 0x4de1aa25, 0xbc4d5cbe, 0xcee15462, 0x0a12682a, 0xfc87df98), SECP256K1_FE_CONST(0xd40fd5bc, 0x51992484, 0x8f13273b, 0x1d857cba, 0x42d45e78, 0x9eaa4e47, 0xf458b83a, 0xbd5f8d1c), SECP256K1_FE_CONST(0xde636141, 0x7deb440b, 0x3a305924, 0x43635cf9, 0xcf42f9b5, 0xf5b891c1, 0x1e119f09, 0x71b570ac), SECP256K1_FE_CONST(0xd55135ce, 0x41bb4d05, 0x5b3757f4, 0xaf1d6537, 0x137376d7, 0x5270caae, 0xda68382d, 0x25d00708)}}, + {SECP256K1_GE_CONST(0x3f5ada4e, 0x8f646ec9, 0x10ffc1a2, 0xb74d94bb, 0xb1860631, 0xa3c2a349, 0xeddf55ca, 0xfd49cce9, 0x28ad9d8d, 0x77d9cd87, 0xf80aaa34, 0x8e9ad1b4, 0x40353d7a, 0x6e717714, 0x60425319, 0x38f530c3), 15, {SECP256K1_FE_CONST(0xac42348f, 0x1b356822, 0x5bb7d4c0, 0x0feab37e, 0xa5fb7fbb, 0x0cc3879d, 0xc74e2dda, 0xf9a393bf), SECP256K1_FE_CONST(0xda7a45b2, 0x6c87dcb6, 0x4a934c1d, 0xc841d250, 0xf98af5f0, 0x511be2a3, 0x82d17bab, 0xe1e4a533), SECP256K1_FE_CONST(0xc3d9b9a6, 0x570ca9c8, 0xa640fc75, 0x945850b2, 0xcc86b6d6, 0x399b4496, 0x4288d76d, 0x832a32d7), SECP256K1_FE_CONST(0xbf5ebc2f, 0x4060abe7, 0x884a1fa7, 0xcc0883cb, 0x97535c5a, 0x31dc6df4, 0xc6968e9d, 0x8554f3b1)}}, + {SECP256K1_GE_CONST(0xf5f74fab, 0x3ebbbcfd, 0xdcaef6cc, 0xd14eb934, 0xf9435a4e, 0x4a1ed2d8, 0x75352c47, 0x306d6c2f, 0xea6a5b2a, 0xe109897d, 0x046e1504, 0xf7a382d6, 0x1eb49a8a, 0xae8852ef, 0x48e29466, 0x194d9e66), 12, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0xe8362df2, 0x38e0405b, 0x49218747, 0x74f9ebca, 0x36dfe21b, 0x1a49ae2d, 0x0fa23fd4, 0x11a262a6), SECP256K1_FE_CONST(0x9e453426, 0xac973155, 0x19d11d63, 0xc3bb27ee, 0x89a7ec85, 0x5661dce4, 0xe428f6cc, 0x0be059cc)}}, + {SECP256K1_GE_CONST(0x977694f6, 0x6f0a3005, 0x2c638916, 0x61432fa0, 0x605528a7, 0xad87d829, 0x5c9eb9a3, 0x973c6fed, 0x16515f14, 0x00186fec, 0x67f6314c, 0x8a9e2d43, 0x3d2020e9, 0x38f86465, 0x39f749a1, 0x51a793ed), 12, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x8f091a42, 0xce496be8, 0x877d43fc, 0x2f2b2927, 0x42c9c1fb, 0x0dfe570b, 0x9c9fbd3e, 0x04afa709), SECP256K1_FE_CONST(0xb5930cf1, 0x4db355a5, 0xa92b9f78, 0x9390b59a, 0x013c8e27, 0x7c41ddd6, 0xd8221622, 0x93d39141)}}, + {SECP256K1_GE_CONST(0x9c970ce9, 0x39e8a4ec, 0x70237f33, 0xad858370, 0xc9d30e8a, 0xadaac257, 0x546d1e16, 0xf374973b, 0x95755fab, 0x1bcae32e, 0xc811c63f, 0xb1e56da8, 0x97a1e140, 0xb1aae97e, 0x0b6ae6c5, 0x3879f51c), 13, {SECP256K1_FE_CONST(0xa7424f55, 0x60b58ceb, 0xbb9a6ee1, 0x5fc41b18, 0xf282b2cd, 0xd9e2fb4d, 0x02626c1a, 0xc0a89ec4), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0xd7016e9b, 0x94db9b4c, 0x5bc61c87, 0xaf3b3c9c, 0x72707e5e, 0x48332958, 0xce5371bf, 0xd501a006), SECP256K1_FE_CONST(0xe95cd3a1, 0x2cff74bd, 0x6761a782, 0x61f73f0d, 0x755a80f6, 0x39ccd117, 0x136f9963, 0xf422b82a)}}, + {SECP256K1_GE_CONST(0x48206211, 0x5e6fc771, 0x738b4859, 0x4da66901, 0xa0a8c36e, 0xa61122b7, 0x745cf5fe, 0xec932b64, 0x01c9e1a1, 0x59effb22, 0x4442c868, 0x9119fd26, 0x8cdca070, 0x7edbefb6, 0xea81d5f6, 0x86333768), 13, {SECP256K1_FE_CONST(0xf1047fb9, 0x4cfa6dcd, 0x202e1acc, 0xa85afc88, 0x46381925, 0x7adf32aa, 0x25e19e52, 0xbf3cadd8), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x94dc1b2b, 0x6a24bbdb, 0x36afab1a, 0x6e036e7f, 0xdf1ded22, 0x915bf761, 0x97e5e5a5, 0xc6261582), SECP256K1_FE_CONST(0x8dd664ba, 0x47061bac, 0x0c99d727, 0xac2ade9f, 0xf8d33aff, 0x995a7a28, 0x97f2968c, 0x558ef724)}}, + {SECP256K1_GE_CONST(0x47e54d7b, 0x86025d30, 0x248b18e6, 0xc6b2b128, 0x3f8eb11e, 0x60d11cad, 0xf59884ea, 0x56939f5a, 0xb618d932, 0x6110c200, 0xcbed144f, 0xc6376800, 0xd8ba0de1, 0xd87fa02d, 0x17d1d58d, 0x9652c498), 3, {SECP256K1_FE_CONST(0x8797d6a9, 0xe3614b34, 0x80e43cb6, 0x936cd932, 0xbe4eee02, 0x1e47e067, 0x2d1d9f2f, 0xd0148558), SECP256K1_FE_CONST(0xb19c75d0, 0xb4856c81, 0xb467f8f5, 0xb9f8d849, 0x0e5296f0, 0x4c60d639, 0x6f772b7f, 0x427c5d38), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x8fa5ffb5, 0x597068f6, 0x06785a63, 0x1f74cd6f, 0x8b16e94b, 0xe6cee831, 0x2970e0ec, 0xa9ecda52, 0x6c4f0efe, 0xf1d0eef2, 0xe3281b13, 0x4f29289f, 0x0a9d7b4d, 0xb3118c5f, 0x1d2d1da4, 0x75569ebf), 3, {SECP256K1_FE_CONST(0xe66995d0, 0x9cfdddda, 0xadf4b4ec, 0xc00270ed, 0xaeaacf01, 0x2db38d37, 0xe4143baf, 0x0ae7dfa3), SECP256K1_FE_CONST(0xfe0d264e, 0x3121942c, 0xd5126e26, 0x0766f36c, 0x3a08a689, 0x4e8ec172, 0xf3fdb252, 0x70def1ad), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x016a682d, 0x1df4f869, 0xb32c48b0, 0xa9b442a1, 0x493949fb, 0x85d951d1, 0x21c1143b, 0xd3d5c1af, 0x38d33fe5, 0xd3f9b4b9, 0x82e37dff, 0x7561428d, 0x47ef4ddf, 0x654bd959, 0x51b04e90, 0xa3be50e7), 0, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x1ec42424, 0xb4d2226f, 0x83f94258, 0xc737d0da, 0xf93a4eb1, 0x1d9b9e3f, 0xd500d5b9, 0xc3aa7c71, 0x84975819, 0xb703da77, 0xca98bd3c, 0xd9bbdc7a, 0xf1dbc7b5, 0x85c590eb, 0xcbd417fd, 0x739ad572), 1, {SECP256K1_FE_CONST(0x945faa12, 0x7e8bf378, 0x63581bfb, 0xde084bf7, 0x63caee39, 0x1449c610, 0xc2074f86, 0xff1bf16c), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x69ee52b2, 0x88dfb06a, 0x449d3db8, 0x7602e094, 0xb4f131e3, 0xf6a4b249, 0xdc0a76ff, 0xdebe989a, 0x3922f1a4, 0xdd208f94, 0xcbac1c5d, 0x34a9278d, 0x84310781, 0x84ff4430, 0x31a14018, 0x95ffd9e6), 1, {SECP256K1_FE_CONST(0xdc1e4760, 0x15bda784, 0xa1b9527b, 0x0357786a, 0xdf2a8028, 0x03957837, 0xe10cff92, 0x5ef4ca7e), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x7ae96a2b, 0x657c0710, 0x6e64479e, 0xac3434e9, 0x9cf04975, 0x12f58995, 0xc1396c28, 0x719501ee, 0x4218f20a, 0xe6c646b3, 0x63db6860, 0x5822fb14, 0x264ca8d2, 0x587fdd6f, 0xbc750d58, 0x7e76a7ee), 0, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaa9, 0xfffffd6b, 0x3ac01550, 0x68185039, 0x6068aaf0, 0xc3f24144, 0x9a267956, 0x698833d4, 0x80c03dc5, 0x678b67cf), 4, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0xbde70df5, 0x1939b94c, 0x9c24979f, 0xa7dd04eb, 0xd9b3572d, 0xa7802290, 0x438af2a6, 0x81895441), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x9ddddd8e, 0xc1814a29, 0x3fcca202, 0xebfbe14e, 0x5d808dda, 0x142eee64, 0xc6108381, 0xe99e5cff, 0xb5072d55, 0x37223f39, 0x3e4176d2, 0xcfd93c86, 0x82ca2c22, 0xcd25ec40, 0x877296bd, 0xbb7c08f6), 3, {SECP256K1_FE_CONST(0xadd34f27, 0xc5f90171, 0x75186c23, 0xd14f6ef2, 0xaa182896, 0x77d5373a, 0xd6c31e9f, 0xf6358ae8), SECP256K1_FE_CONST(0xf5ee8614, 0x1916fe03, 0x945d028b, 0xbc354c4a, 0x09f6d6ab, 0x1468ab9a, 0xd8742075, 0x1543c2a2), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x1ee7e9a7, 0xfcd56edf, 0xabf3712e, 0x72cc24a3, 0x0a476f5a, 0x97f77825, 0xf0308620, 0x162f31ad, 0x77bfc7de, 0xc2401a39, 0x8c5e8675, 0x417c8a7b, 0x632f5d64, 0x2f1a5059, 0x9a830b8c, 0x7981f636), 3, {SECP256K1_FE_CONST(0xb3a8d9e7, 0x368af258, 0x3785be92, 0x2ad54dfb, 0x47329513, 0x6ade2d18, 0x2f931cd6, 0x54f35d02), SECP256K1_FE_CONST(0xe1d420e5, 0xfab5c26d, 0xf4294b2b, 0x0c19eb9a, 0x188409bf, 0x48a3741f, 0x31f72acc, 0x6ea93418), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x9e24d0a5, 0xd5014164, 0x987f86bb, 0x1709305a, 0x6fd352a0, 0xa3478fae, 0x3f85e594, 0x21d72a80, 0x3729c39b, 0xbbb26d97, 0xa4ec6bf7, 0xcb4e6453, 0x058e448e, 0x7530b028, 0xd1ae345e, 0x35608d3c), 0, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x15f2f1a4, 0x339f5f2a, 0x313b9501, 0x5cad8124, 0xd054a171, 0xac2f31cf, 0x529dda7c, 0xfb6a38b4, 0xfe1d0fa5, 0x95b4f7d3, 0x63e82c29, 0x0095189f, 0x5f2be99c, 0x880be4fc, 0x9742a31b, 0x40041eda), 1, {SECP256K1_FE_CONST(0xc1c3ed27, 0x17ffabfd, 0x01132f5e, 0x54dd73c3, 0x475297e0, 0xfdbff814, 0xdc9456b8, 0x4a57b698), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0xd383134d, 0x721cf055, 0x143570e7, 0x82bb323d, 0x5c542a61, 0xe455823e, 0xd60b940f, 0x86826d54, 0x5a88e50b, 0x3f59874e, 0x84dab4a2, 0x07d34623, 0xd836c376, 0xc68dded3, 0xc095a716, 0xf563e4fc), 1, {SECP256K1_FE_CONST(0xe4d2660c, 0x1d50d031, 0x97f5e610, 0x4d9c2066, 0x01f6c791, 0xadb52178, 0xe2bd6c88, 0xe89cf012), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x851695d4, 0x9a83f8ef, 0x919bb861, 0x53cbcb16, 0x630fb68a, 0xed0a766a, 0x3ec693d6, 0x8e6afa40, 0xbde70df5, 0x1939b94c, 0x9c24979f, 0xa7dd04eb, 0xd9b3572d, 0xa7802290, 0x438af2a6, 0x81895441), 0, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000001, 0xbde70df5, 0x1939b94c, 0x9c24979f, 0xa7dd04eb, 0xd9b3572d, 0xa7802290, 0x438af2a6, 0x81895441), 3, {SECP256K1_FE_CONST(0xd3779b57, 0x3cb17828, 0xac118cff, 0x74412ab5, 0xb84c86f8, 0xa92f48b8, 0xefcbe4c7, 0x0a675631), SECP256K1_FE_CONST(0xea6f729d, 0xdc884123, 0xf0130aa0, 0x339bda36, 0x2166d034, 0xfe50d9d7, 0x53bf0dde, 0x7721fa3f), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x99a70224, 0xc3062c32, 0x6c45d3c6, 0x46a545e9, 0xb152b75b, 0xee868378, 0x07e47951, 0x9e5b600d, 0x95b6675a, 0x10845b66, 0x37ff96e8, 0xe67f2a75, 0xbbf0f764, 0xc56d26c5, 0x4b2db5eb, 0xb026d7de), 3, {SECP256K1_FE_CONST(0xb74a9552, 0xc5b9b6ed, 0x575d380f, 0xec3df8ed, 0xdb524ed1, 0x80b13607, 0x81e2eec6, 0x7ad06c04), SECP256K1_FE_CONST(0xbb702282, 0x4194fbe4, 0x4a74c4f4, 0xabd01ee3, 0xdac8f4cb, 0x5a0e3a67, 0xd2276039, 0xdd4aac1a), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0xb5902433, 0x3110b310, 0x8625f254, 0x47665c1e, 0xbf10c6a6, 0xbbe9f018, 0xc421f4b0, 0xdcb5a993, 0x43bae2cd, 0xaae9c002, 0xe57ac99a, 0x17926e22, 0x76a66728, 0xf92b11bb, 0x7dc953b9, 0xea6d49b7), 3, {SECP256K1_FE_CONST(0xd5a57c1b, 0x71916606, 0xbfb235f0, 0xce8d880d, 0xe9109a01, 0xb86d58c8, 0x2852b211, 0x0e55ee0f), SECP256K1_FE_CONST(0xca6cf74b, 0x128e1d79, 0x75482bfd, 0xc9e81416, 0x71a5c3e7, 0xe2af854b, 0x23707630, 0x97ba917b), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0xb526749e, 0x35fa04ef, 0x5d20b1d6, 0xcda6f57e, 0x2f3c10c9, 0x85098901, 0xc390da79, 0x31769e34, 0x182093b3, 0xce5883a2, 0x7b834af6, 0x18547fd1, 0x6017cee0, 0x4e9398da, 0x6aaaed2b, 0x87ca0e7c), 0, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x901c52d6, 0xa39718c7, 0x255e94e3, 0x3189cbeb, 0x41f2fa97, 0x95279076, 0xbecd6678, 0x99684c17, 0xf988a838, 0x156cc39f, 0x2182bbc5, 0xf7e4f707, 0x9cf75bfb, 0x58638cff, 0x5b201fd3, 0xcf499fc0), 1, {SECP256K1_FE_CONST(0xa356db31, 0x44b754a3, 0xdafdf2a9, 0x0767b65a, 0xbaea92ca, 0x56c69c3a, 0x31a4ff5b, 0xd7914d9c), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x957d4fd4, 0x4a10f38a, 0x0d0e1e46, 0x2656dd2e, 0x7f2b6b8c, 0x9545ee02, 0x903f28b0, 0x8f9a57e7, 0x3f4bf4de, 0x3731bea3, 0x291627e3, 0x9daa7dac, 0xcdcd4e13, 0xb2418482, 0x488730b7, 0xa7a816b7), 1, {SECP256K1_FE_CONST(0xa761cd3a, 0x58385878, 0x300c6963, 0xe918b545, 0x99eb0254, 0x550f6254, 0xe414628c, 0x2f431bbd), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x0a7b6db2, 0x56f01aea, 0x797a0798, 0x5eaf98d6, 0x64486f82, 0x723758bf, 0x1a5f7b00, 0xb74887e1, 0xe07ce7ec, 0x5f24b6da, 0x199329ff, 0x674788c4, 0x1b7312d4, 0xbb63672f, 0x81ebbfd3, 0x6d962235), 15, {SECP256K1_FE_CONST(0x442e15e3, 0xac31958b, 0x7acdb8b9, 0x7977b6d0, 0x533b1ef0, 0x5094f496, 0x126a04d0, 0xc6d6c327), SECP256K1_FE_CONST(0xc565d637, 0x6c8f4fa4, 0xa22ab5d4, 0xe1c87f5d, 0x6f9beb27, 0x7764a77f, 0x8ebe3796, 0xaa82cba5), SECP256K1_FE_CONST(0x2082a3b7, 0x04d3729c, 0x71a73a0c, 0xd745c7ce, 0x7a7c5e26, 0x77c688e2, 0x772806d1, 0xdd1a849f), SECP256K1_FE_CONST(0xc00c8cc3, 0x5ea8122e, 0xf17b0a8e, 0xc69218d1, 0x8cb45a3f, 0x0227a2c5, 0x68fbd9f9, 0xc6d6d141)}}, + {SECP256K1_GE_CONST(0x770ed6cb, 0xf6d2156b, 0x362523eb, 0xc2908f68, 0x65ab182c, 0x43468bc8, 0x69d6754e, 0x68dc71a0, 0x2a378713, 0x10223129, 0xbaba56c2, 0x0dc4a1e9, 0x634dba32, 0xa034d21f, 0x3104176b, 0x870c9916), 15, {SECP256K1_FE_CONST(0x092c79ab, 0xbbafd66d, 0x58c56208, 0x7ba5c385, 0x9fed6c1b, 0x5f8005af, 0x0087cedb, 0xec7dc084), SECP256K1_FE_CONST(0x3f5c280a, 0x60802515, 0x16dfd84a, 0x4488df47, 0x96198d5f, 0xbce0be21, 0x1ab0ee7d, 0xa456e73e), SECP256K1_FE_CONST(0x94057b6b, 0xd54b13b2, 0xe2b9d322, 0x687569f5, 0xdd16727d, 0x3d912ba3, 0xeb8aa33d, 0x36c15108), SECP256K1_FE_CONST(0x098360ae, 0xcf93979e, 0x7cd6df39, 0x6e8fe2f3, 0x18fa1da3, 0x9efa707a, 0xeab95cd8, 0xcd5dca2a)}}, + {SECP256K1_GE_CONST(0xab01575c, 0x0604c63e, 0xe77d3153, 0x4a5bcfa2, 0x0ce66c9d, 0xf47d6054, 0xb822bfd8, 0x6934f8ec, 0xce488d85, 0xd0875b40, 0x4fb92b6e, 0x8068602a, 0x670ac4f8, 0xd76b78b6, 0xc246b713, 0x595e226b), 12, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x4ab21b18, 0x1009aa48, 0xb8ba5eb9, 0xd373919b, 0xcfcb36a6, 0xf34961b2, 0xc859f5a8, 0x6da8ba41), SECP256K1_FE_CONST(0x9a11c401, 0x9a4ba9fc, 0xf4698a71, 0x2d85c8e4, 0x70028e02, 0x545ef049, 0xf9f3083d, 0x187c5b41)}}, + {SECP256K1_GE_CONST(0x6084cfdd, 0xf8d9736e, 0xa90100eb, 0xdb43338f, 0x65e2ab43, 0xef35a799, 0x926e6ce3, 0x2a89ae17, 0x753998b5, 0x9eaae7a3, 0xdcab34d9, 0xa15dbc71, 0xe539cdff, 0xdcf05927, 0x0eb27c86, 0xab6b62a4), 12, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x18b1f707, 0x3fca3167, 0x04e1b3b8, 0x8cc8ff5a, 0x702d79bc, 0x756e4dea, 0x2ff948cc, 0xdb43a9f4), SECP256K1_FE_CONST(0xca02e589, 0x89eb16d1, 0x520463d2, 0x435745cf, 0x6e69fa52, 0x6b5c7adc, 0x57cea2b3, 0xf5a6441c)}}, + {SECP256K1_GE_CONST(0xc9fbac00, 0x9d8eda5d, 0x25c9aabb, 0x2b6794bc, 0x9a801afd, 0x17adef78, 0x78c65392, 0x04eb0f82, 0x95ed9e51, 0x898b903e, 0xe689e6ed, 0xff2b54bf, 0xed5c2da1, 0x69e2bdd0, 0x415a392e, 0x16b3de2b), 13, {SECP256K1_FE_CONST(0x21a95220, 0x8577e3f0, 0xcc5b4b17, 0xf5e434b2, 0x2bbdbaaa, 0x51cd2659, 0xe37880a6, 0xa25aa7dd), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0xcfd1ca13, 0x2f8d3eae, 0x73a97895, 0x01d2c82a, 0x6f057566, 0x7949fab9, 0x267bc1e8, 0xef9bf5bd), SECP256K1_FE_CONST(0x9cde02aa, 0x3acd2596, 0xdbea4b82, 0xf9f47ad1, 0x994ad567, 0x3c0d4fb2, 0xe8a3dca5, 0xe8e067fb)}}, + {SECP256K1_GE_CONST(0x8dcb38d9, 0x0059d4f1, 0x270455af, 0x6f3dd40e, 0x8d671a34, 0xa1fad81d, 0x2470db8a, 0x13b18f76, 0x603ed5be, 0x7bc3e67f, 0x439067da, 0x29949bcb, 0xd3c96c9f, 0x94da4231, 0x3c9c0feb, 0xe5cdf560), 13, {SECP256K1_FE_CONST(0x3ef4008a, 0x8a190a3f, 0x5c97d211, 0x3bb539e1, 0xf4261a78, 0xf7cd85c4, 0xfd254837, 0xeaacd020), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x0fe7af4f, 0xcab80199, 0x37ee0026, 0x47d55d97, 0x575474b3, 0x4b9cc1bb, 0x133f4261, 0x017124a0), SECP256K1_FE_CONST(0x09dcec3b, 0x93c4ab42, 0x91d01dce, 0xccc19525, 0xc801add3, 0x77170c2c, 0x919f5488, 0xf41d6d3e)}}, + {SECP256K1_GE_CONST(0xf69dfe44, 0x890d2b09, 0x4b749a56, 0xf680e851, 0x50c47c4c, 0xd51e7796, 0x3fec4e6a, 0x09dcd0a1, 0xfb5d321c, 0x1e243b63, 0x6dfb71f3, 0xcf0e8a01, 0x2e52b22c, 0x905cec6d, 0x2f6ae32a, 0x6a4eb7be), 3, {SECP256K1_FE_CONST(0xa17fd528, 0x7276cbf6, 0xc168dcde, 0xb32aba14, 0xe1aeae2f, 0xe7f5bea5, 0xa87d384e, 0xe8046aac), SECP256K1_FE_CONST(0x637f176a, 0xf2fe854a, 0x968ab19b, 0xee010554, 0x313e3eff, 0xc6ff8cb4, 0xcb538a6d, 0xbaedd954), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x043a0631, 0x871a3f67, 0xac03c5f8, 0x406b69a0, 0xdc14bd5b, 0x23e55f27, 0xa5d4462b, 0x0f0a2d23, 0x247b9bcc, 0x0019091c, 0x31eb4b03, 0xe731a0b5, 0xa9b33f75, 0xad9e5e63, 0x39286573, 0xa6439d88), 3, {SECP256K1_FE_CONST(0xd65add13, 0xad3044d9, 0x2ebcd0e6, 0xd42853d8, 0xe5733ff6, 0x5297f544, 0x09a3ce89, 0xfdaffbdc), SECP256K1_FE_CONST(0x7281ad3c, 0x85de3870, 0x84f64e14, 0x42b37154, 0xeab39453, 0x8b1c0753, 0x4b303ae7, 0x37f3973e), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x8855508a, 0xade16ec5, 0x73d21e6a, 0x485dfd0a, 0x7624085c, 0x1a14b5ec, 0xdd6485de, 0x0c6839a4, 0xe50aaeba, 0xa0ceceec, 0xa1bce62e, 0x5f0fac4b, 0xe78ab03a, 0x7b2deaa6, 0xe5c17e88, 0x98e277e9), 1, {SECP256K1_FE_CONST(0x4e96da73, 0xae14fc85, 0x25eccb2d, 0xf4416924, 0x8a7fd269, 0xa065e065, 0x04d315e6, 0x63666b03), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0xc66327bc, 0x5b0b8b90, 0x37adfd63, 0xc2a9f192, 0x2ce2144a, 0xa513b390, 0xd48bc387, 0xae3ebff6, 0x17a1ca89, 0x64eb0b41, 0x162894e6, 0x4fb4112b, 0x638f96ec, 0xe0c6f30d, 0xef7616fe, 0x0e78386a), 1, {SECP256K1_FE_CONST(0x56e8e17e, 0xfaf989d6, 0xa7efb81d, 0x5a602393, 0x6814930e, 0xbc3f6fdf, 0x72ebf472, 0x69ba4c9a), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaa9, 0xfffffd6b, 0xc53feaaf, 0x97e7afc6, 0x9f97550f, 0x3c0dbebb, 0x65d986a9, 0x9677cc2b, 0x7f3fc239, 0x98749460), 4, {SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x4218f20a, 0xe6c646b3, 0x63db6860, 0x5822fb14, 0x264ca8d2, 0x587fdd6f, 0xbc750d58, 0x7e76a7ee), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x9d709c02, 0x74604cb6, 0x3b531fea, 0x35932e2e, 0xc965f4bf, 0x5913e577, 0xff31080b, 0x67727a2e, 0xf2b0b821, 0xa24081a9, 0xd0ca84d9, 0x303068cf, 0x7ea32788, 0x05926b0a, 0xb90b9af7, 0x498efbd5), 3, {SECP256K1_FE_CONST(0xb06abefa, 0x192a6498, 0xbce368ff, 0xacc843fb, 0xb39f8117, 0xa56a1870, 0xf57197ef, 0xd9312f6d), SECP256K1_FE_CONST(0x1263d142, 0xaac9cfc5, 0x64c56650, 0x0fa4a62f, 0x38e727fb, 0xb4dbeaf2, 0x6fdf7d05, 0xfd022c71), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0xb4955dcb, 0x4daaa784, 0x9b421c14, 0x53ec8945, 0xd685d554, 0xf41103f8, 0x12cbfb2f, 0x54a4539b, 0x354d18e4, 0xb1cee7a3, 0xf98b0651, 0xf5544091, 0xe8a00656, 0x0c74750d, 0xaadf460e, 0xc3f620ea), 3, {SECP256K1_FE_CONST(0x6281a8a7, 0x0a3b5745, 0xb897ce4f, 0x58305fb0, 0xd6a0f8ab, 0xa6c5ba18, 0xed278ce1, 0x50f7911c), SECP256K1_FE_CONST(0x5f95a708, 0x2d2f6d69, 0xf7ff9b74, 0x2b88063c, 0x39a3003b, 0xb03f333c, 0x7e3d7c5e, 0xd861fb04), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x6ad63dfd, 0xcd231967, 0xff2508f4, 0x75896976, 0xf8728e40, 0xdd7a2acc, 0x6b5ced37, 0xcada8291, 0xf93e5181, 0x8f5329b8, 0xd520a9af, 0xd72938e1, 0x2e3f8be6, 0x421d2bce, 0x89d7b14e, 0x25bf5336), 1, {SECP256K1_FE_CONST(0x0f050318, 0x622f79f1, 0x5a2b23d9, 0xf76329b7, 0x8e195f1a, 0x4651aae0, 0x65d58bcd, 0xdfa4d3b6), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0xa91b7f2a, 0xb93de821, 0xabeec175, 0x0258e4d4, 0xf5f09831, 0xb0a11dda, 0x47e89ddf, 0x6944d819, 0x22eb9bf6, 0x4a517df2, 0xc27d1c55, 0x1df07609, 0x166fc995, 0xe2b39fee, 0x0473ea46, 0xed14efc1), 1, {SECP256K1_FE_CONST(0x7a01651a, 0x81a7f09e, 0x2733cf34, 0x9e6472a1, 0x18c16780, 0x6f5c880f, 0x534b89a6, 0x52be06a7), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000001, 0x4218f20a, 0xe6c646b3, 0x63db6860, 0x5822fb14, 0x264ca8d2, 0x587fdd6f, 0xbc750d58, 0x7e76a7ee), 3, {SECP256K1_FE_CONST(0x2c8864a8, 0xc34e87d7, 0x53ee7300, 0x8bbed54a, 0x47b37907, 0x56d0b747, 0x10341b37, 0xf598a5fe), SECP256K1_FE_CONST(0x15908d62, 0x2377bedc, 0x0fecf55f, 0xcc6425c9, 0xde992fcb, 0x01af2628, 0xac40f220, 0x88de01f0), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0xa64de96a, 0x6254cefc, 0xffbeaf89, 0x8f2c228a, 0xf6d405f3, 0xbcc6a4cc, 0xe068312a, 0xf7ccf8e1, 0x8f9b3a1b, 0x2d146ea9, 0x54bfc5e2, 0xcdfe861c, 0xcbed8431, 0xc741c5f9, 0xd32f16a3, 0x073ea496), 3, {SECP256K1_FE_CONST(0x4591d33d, 0x1a133a87, 0x94689b1b, 0x0ca445b7, 0x8ada3bce, 0xc2e812b0, 0x8315e2b1, 0x07940ad4), SECP256K1_FE_CONST(0xa763d217, 0x6027d40e, 0x8a8ff34b, 0xd9c639b7, 0x3e2ea045, 0x92274fdc, 0xfa4051c6, 0x6d93a1b6), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x49a0dc06, 0x8c3f117a, 0xefdc842d, 0x3d358153, 0xf677f04c, 0x6dabc9c9, 0x1b09d452, 0xfef27b66, 0x7b944da4, 0x8a175dbc, 0x444ead8d, 0xb82eff66, 0xb081a8aa, 0xe6453fed, 0x2bca9720, 0xb44dd6e5), 3, {SECP256K1_FE_CONST(0x7bf1e2b1, 0x720c1c44, 0x0db64687, 0xf16439fa, 0x41b39833, 0x8095f24e, 0xbeec0cfa, 0x88750dc9), SECP256K1_FE_CONST(0xdc97e26d, 0x3137445d, 0x6c1269b6, 0x1a765501, 0x0c19c36a, 0x2e361066, 0xe31e2bb1, 0x0403470b), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0xd09a4047, 0xf158fe52, 0xf96c661d, 0x02c68657, 0xc4c976ea, 0x96ea85ef, 0x46d6985b, 0xd540756b, 0xe793bfaa, 0xe9300f18, 0xe6f9b55a, 0xae263223, 0x68b61d51, 0xae5022ef, 0xe266c72d, 0x574178bc), 1, {SECP256K1_FE_CONST(0x7e6175fd, 0xfbb9fb4f, 0xaf6e2b92, 0x5ef86c4a, 0x444d819a, 0xaa82dbee, 0x545d3d9b, 0x296375be), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}}, + {SECP256K1_GE_CONST(0x34986625, 0x04b73c7c, 0x8cecb6c3, 0x3cd493bd, 0xfc190e0f, 0x87d913d7, 0xff9ad42e, 0x222bfe95, 0x245b3a61, 0xb8d46997, 0xf14f2fea, 0x28748996, 0x91eb3254, 0x2b9907d6, 0x5eb9d21d, 0x42454021), 1, {SECP256K1_FE_CONST(0x7f556282, 0xc3dd9d26, 0x3390d6bb, 0xddada698, 0xab8fd7c7, 0xd1a06498, 0xf42b3043, 0x7c8361ad), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000), SECP256K1_FE_CONST(0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000)}} +}; + +struct ellsq_enc_test { + unsigned char ell64[64]; + unsigned char pubkey[33]; +}; + +/* Set of (ell64, point) test vectors, selected to maximize branch coverage. + * Created using an independent implementation. */ +static const struct ellsq_enc_test ellsq_enc_tests[] = { + {{0x54,0xca,0xd2,0x27,0xb2,0xc9,0x8d,0x5f,0x7c,0x78,0x8c,0xfc,0x3d,0xaf,0xd6,0x52,0xf5,0x8f,0x69,0xcf,0xef,0x63,0x2b,0x82,0x2b,0x35,0xd0,0xb0,0xe2,0x4f,0xc0,0x3a,0xd2,0x8c,0xa1,0x4b,0x6f,0x62,0xd4,0x53,0x79,0xc5,0x3f,0x70,0xee,0x40,0x5c,0xa9,0x2c,0xe7,0xb6,0xf9,0x70,0x83,0x13,0x05,0xf2,0x7d,0xc4,0x1e,0xb6,0x9d,0xe0,0x6e}, {0x02,0x11,0x62,0x89,0x03,0x32,0x88,0x91,0xae,0x09,0xd1,0x08,0xd8,0x92,0x43,0xe4,0x7e,0x10,0x9f,0xe7,0xb8,0xbb,0x1e,0x2d,0xf1,0xa3,0xae,0x9b,0x0e,0x78,0x08,0x54,0x9c}}, + {{0xfb,0xe6,0xce,0xab,0x4c,0x5f,0xdf,0xa5,0xfb,0xee,0x8f,0x3d,0x09,0xa2,0xf7,0x23,0x53,0xe7,0x4e,0x5a,0x9c,0xd4,0xab,0x8e,0x6a,0x34,0xd4,0x95,0x23,0xa7,0xd1,0xa2,0xc4,0x50,0xb7,0x45,0xda,0xb1,0xaf,0xa9,0x95,0x4b,0x3a,0x35,0x75,0xe4,0xe8,0xe2,0xdb,0x3d,0xa5,0xcd,0x4d,0x56,0x48,0xea,0xd0,0x0a,0x60,0xb4,0xcd,0xfe,0x84,0xb3}, {0x02,0xc0,0x4c,0x84,0x85,0xf9,0x8d,0x56,0x6c,0x79,0xbf,0x33,0xa7,0x0c,0xb2,0x32,0x54,0x9e,0x3d,0xe1,0xc3,0xe3,0x01,0xe3,0x57,0x1c,0x83,0x68,0x97,0xf0,0x7c,0x5d,0x12}}, + {{0x71,0x7e,0x63,0xd7,0x71,0xdb,0xda,0x67,0x67,0xd5,0x8f,0x26,0xab,0x5f,0x54,0x9b,0xd2,0xd1,0x8a,0xcf,0x59,0xff,0x50,0x77,0x5f,0x4e,0xb5,0x0a,0xc0,0x17,0x4d,0xf1,0x7d,0xd0,0x34,0xc8,0xed,0x08,0x11,0x61,0x5e,0x3e,0xbb,0x36,0xf8,0xf3,0x3e,0x09,0x23,0x8e,0x4d,0xa8,0xf5,0x01,0x9d,0x37,0x00,0x78,0x4f,0x37,0xc1,0x53,0x53,0x94}, {0x02,0x72,0x81,0x15,0x0c,0xeb,0xc3,0xd7,0xb3,0xbb,0xb9,0x92,0xf5,0x81,0xbb,0xcb,0x9e,0x30,0x4f,0x87,0x44,0xf0,0x19,0x98,0xa7,0x1f,0x5d,0xe1,0x14,0xf8,0x22,0x91,0xc4}}, + {{0x01,0xf0,0xbf,0xe4,0xf9,0xbd,0xee,0x52,0x5e,0xb7,0x7c,0x8e,0x35,0x1e,0x1f,0x88,0x3f,0xb9,0xcd,0x37,0x7e,0xf7,0xc5,0xbd,0xde,0xe4,0xf6,0x60,0x64,0x43,0x90,0xf5,0x95,0x3e,0x7d,0x2b,0x6c,0xde,0x36,0x90,0x3e,0xa1,0x34,0x4b,0x0d,0x16,0x33,0x5c,0xc5,0x11,0x5d,0xaa,0x97,0x7c,0x3c,0x2b,0xf9,0x31,0xac,0xde,0x2f,0xf5,0x78,0x9a}, {0x02,0x10,0x44,0x9d,0x7e,0xa0,0x62,0x3e,0x80,0xa5,0x87,0x01,0x9f,0xa5,0x11,0xaf,0xd3,0x94,0xb2,0x55,0xb0,0x8f,0x91,0xb5,0xf7,0x48,0x2a,0xe9,0xd1,0xa1,0xa7,0xfb,0x7c}}, + {{0x82,0xd5,0x87,0x1e,0x18,0x37,0x66,0xbd,0x22,0xe1,0x13,0xa8,0x52,0x79,0xaa,0x61,0x7e,0x6b,0x9f,0x73,0x52,0x2c,0xd4,0x6b,0x90,0x59,0xba,0x51,0x97,0xfa,0x56,0x44,0xaf,0x90,0x41,0x89,0x30,0x98,0x7d,0xb7,0xab,0x4a,0x84,0x0c,0x72,0x64,0x1b,0x58,0xb3,0x66,0xe5,0x7c,0x92,0x8c,0x98,0x3a,0x47,0x37,0x82,0x00,0x3c,0x36,0x10,0xab}, {0x03,0xc8,0xb2,0x62,0xf9,0x31,0x69,0x43,0x75,0x51,0x48,0x3b,0x8a,0x61,0x19,0x83,0x82,0xe3,0x11,0x41,0xaf,0x61,0xbf,0x36,0x10,0x0b,0xd0,0x68,0x46,0x5d,0xdd,0xa8,0x40}}, + {{0xda,0x82,0x53,0xb4,0x3b,0x5a,0xc2,0x3b,0x42,0x36,0x07,0xe9,0x18,0xab,0x5c,0xaa,0x5d,0x7d,0x34,0x3d,0x77,0xa3,0x99,0x6a,0x42,0xeb,0x33,0x2a,0x3b,0x55,0x1d,0x8c,0xda,0x6c,0xb6,0xf9,0x57,0x4c,0xe3,0x60,0x91,0x2c,0xf4,0x5b,0x90,0x9a,0x96,0x2e,0x4d,0xed,0x63,0xae,0x5a,0xac,0xb0,0xab,0x23,0x29,0x45,0xb1,0x01,0xf7,0x2b,0x62}, {0x02,0xe7,0x28,0x34,0x1d,0xf6,0x93,0x48,0x71,0xb3,0x94,0xbb,0x4f,0xb2,0x8b,0xd8,0xd2,0xdf,0x39,0x92,0x55,0xb0,0x30,0x02,0xed,0x6f,0xc3,0x8f,0x28,0xcf,0xbf,0x53,0x56}}, + {{0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00}, {0x03,0x1b,0x41,0x2e,0x7a,0x96,0x6d,0x2c,0x24,0x3d,0xbc,0x5b,0x18,0xb7,0xf9,0xba,0xf1,0x85,0xbc,0xfe,0x41,0x38,0x96,0x04,0x79,0x64,0x1a,0xb1,0xe6,0x3b,0x38,0x1e,0x11}}, + {{0xdc,0x30,0x98,0xe4,0x00,0x61,0x83,0x30,0xf3,0x8b,0x19,0xe9,0x20,0x0a,0xdf,0x7f,0xfb,0x96,0x84,0x3f,0xa8,0x3c,0x49,0x1c,0xf6,0x7f,0x34,0xa7,0x90,0xbb,0xcf,0xe1,0x23,0xdc,0x30,0x07,0xa4,0xfd,0x13,0x3a,0x39,0x44,0x0b,0x06,0x03,0x1e,0x9e,0x2c,0x38,0x8e,0x41,0x47,0xaf,0x0e,0x82,0xbe,0xda,0x6d,0x56,0x4b,0xf8,0xcc,0x37,0xb1}, {0x02,0x5b,0x74,0x48,0x15,0x22,0xd4,0xc2,0x9f,0x2e,0x6a,0x2f,0x11,0x7f,0x9e,0x39,0xf9,0xab,0x01,0xb1,0xe9,0xf2,0xc3,0x4c,0x68,0xbe,0x8f,0x53,0x1b,0xe0,0x1f,0x6e,0xa7}}, + {{0x35,0xd7,0x0a,0x71,0x2c,0xc0,0x85,0x7f,0x8d,0xb1,0xbc,0x55,0x6a,0x6c,0x4e,0xf8,0x66,0x24,0xfd,0x0a,0x47,0x7f,0x96,0x7e,0xed,0xc0,0x32,0xfc,0xda,0xac,0xe7,0x96,0xc6,0x73,0xc5,0x43,0xd0,0x07,0x34,0x32,0x07,0x85,0x5b,0xeb,0xad,0x85,0xe9,0x4b,0xca,0xc7,0x78,0x2b,0x11,0x57,0x9a,0x70,0xdc,0x88,0xe2,0xa4,0x8d,0x9d,0xf2,0xd4}, {0x02,0xdb,0x21,0xb4,0x8f,0xe9,0xf9,0x95,0x08,0x3a,0x1f,0x9c,0x1f,0x3f,0x4b,0x31,0x1d,0x2c,0x43,0xa1,0x28,0xdb,0xb3,0xa4,0xd4,0x78,0x41,0xe4,0xff,0x5d,0xd0,0x2e,0x61}}, + {{0x5f,0xb8,0x07,0xce,0x10,0x0c,0x90,0xd2,0x83,0x7c,0xcf,0xc9,0x4d,0x8f,0x8b,0xa5,0xd3,0x5c,0xd3,0xd6,0xfa,0xfc,0xd2,0xf4,0x1f,0x24,0x5b,0x59,0x6e,0x36,0x00,0x57,0xa0,0x47,0xf8,0x31,0xef,0xf3,0x6f,0x2d,0x7c,0x83,0x30,0x36,0xb2,0x70,0x74,0x5a,0x2c,0xa3,0x2c,0x29,0x05,0x03,0x2d,0x0b,0xe0,0xdb,0xa4,0xa5,0x91,0xc9,0xfb,0xd8}, {0x03,0x41,0x58,0x28,0x65,0x43,0x5e,0xe9,0xc8,0xc9,0x27,0xc3,0x49,0xbd,0x3e,0x43,0x7b,0xce,0x2b,0x5c,0xfc,0xd0,0xc4,0x17,0x77,0xc3,0x4c,0x71,0xc6,0x7b,0x14,0x06,0x93}}, + {{0x1e,0x76,0x57,0x72,0xbf,0x72,0xde,0xb8,0x81,0x54,0x16,0xbd,0x54,0x45,0xdd,0x75,0x50,0xcd,0x86,0x7a,0xa2,0x5a,0xc6,0x3f,0x6f,0xd9,0xaf,0xd3,0x2f,0x92,0x1c,0xc8,0x8a,0x06,0x1a,0xb5,0xf6,0x98,0x1b,0x55,0x92,0x1b,0x90,0x5b,0x6f,0x4f,0x3d,0xf4,0x82,0x5d,0x79,0x72,0xd6,0x99,0xe3,0xb4,0x21,0x4e,0x40,0x44,0xcf,0xbe,0x65,0x34}, {0x03,0x90,0xd2,0x94,0x30,0x92,0xec,0x7e,0xd8,0xff,0x5a,0xf7,0x04,0x43,0x2d,0x0d,0xbe,0xb0,0x33,0x7c,0xbf,0x58,0x22,0x87,0x18,0x32,0x76,0x38,0x68,0x1f,0x70,0xd7,0xf0}}, + {{0x86,0xef,0x92,0xfd,0x28,0x09,0x85,0x4f,0x74,0xf7,0x5a,0xeb,0xbe,0xa1,0x8a,0xee,0xc0,0xee,0xdd,0x4e,0x81,0x92,0xc8,0x8c,0xd7,0xcf,0xf5,0xdf,0xc0,0x8a,0x57,0xdc,0x32,0x73,0xbf,0x6f,0x39,0x2d,0xee,0x48,0x4a,0x72,0x2c,0x3d,0xb0,0x0c,0x0e,0xfb,0x40,0xd5,0x1e,0x8a,0x72,0xfc,0xfb,0x78,0x3f,0xa7,0xeb,0xd4,0x30,0x82,0xdb,0x71}, {0x02,0x31,0x74,0x79,0x29,0x80,0x2d,0x79,0x76,0x02,0x26,0x71,0xb2,0xf7,0x5a,0xc0,0x31,0x18,0x56,0xb3,0x84,0xf4,0xb9,0xa8,0x00,0x0d,0x44,0xa2,0xab,0xc5,0x90,0x3a,0xd4}} +}; + +void run_ellsq_tests(void) { + int i = 0; + /* Verify that secp256k1_ellsq_fe_to_ge_var maps everything to curve points for random inputs. */ + for (i = 0; i < 1000*count; i++) { + int j, matches = 0; + secp256k1_fe t, f; + secp256k1_ge g; + random_field_element_test(&t); + secp256k1_ellsq_fe_to_ge_var(&g, &t); + CHECK(secp256k1_ge_is_valid_var(&g)); + /* t should appear exactly once in preimages */ + for (j = 0; j < 4; j++) { + matches += secp256k1_ellsq_ge_to_fe_var(&f, &g, j) && check_fe_equal(&f, &t); + } + CHECK(matches == 1); + } + /* Verify that secp256k1_ellsq_ge_to_fe_var + fe_to_ge_var roundtrips for random inputs. */ + for (i = 0; i < 1000*count; i++) { + int j, k, nf = 0; + secp256k1_ge g; + secp256k1_fe fs[4]; + random_group_element_test(&g); + for (j = 0; j < 4; j++) { + if (secp256k1_ellsq_ge_to_fe_var(&fs[nf], &g, j)) { + secp256k1_ge g2; + secp256k1_ellsq_fe_to_ge_var(&g2, &fs[nf]); + ge_equals_ge(&g, &g2); + /* Check that all preimages are distinct. */ + for (k = 0; k < nf; ++k) CHECK(!check_fe_equal(&fs[nf], &fs[k])); + ++nf; + } + } + } + /* Verify precomputed test cases. */ + for (i = 0; i < (int)sizeof(ellsq_tests) / (int)sizeof(ellsq_tests[0]); ++i) { + int j; + const struct ellsq_test *test = ellsq_tests + i; + for (j = 0; j < 4; j++) { + secp256k1_fe f; + int ret; + ret = secp256k1_ellsq_ge_to_fe_var(&f, &test->point, j); + CHECK(ret == ((test->enc_bitmap >> j) & 1)); + if (ret) { + secp256k1_ge g; + CHECK(check_fe_equal(&f, &test->encs[j])); + secp256k1_ellsq_fe_to_ge_var(&g, &f); + ge_equals_ge(&test->point, &g); + } + } + } + /* Verify that secp256k1_ellsq_encode + decode roundtrips. */ + for (i = 0; i < 1000*count; i++) { + unsigned char rnd32[32]; + unsigned char ell64[64]; + secp256k1_ge g, g2; + secp256k1_pubkey pubkey, pubkey2; + random_group_element_test(&g); + secp256k1_pubkey_save(&pubkey, &g); + secp256k1_testrand256(rnd32); + secp256k1_ellsq_encode(ctx, ell64, rnd32, &pubkey); + secp256k1_ellsq_decode(ctx, &pubkey2, ell64); + secp256k1_pubkey_load(ctx, &g2, &pubkey2); + ge_equals_ge(&g, &g2); + } + /* Verify decoding of precomputed test cases. */ + for (i = 0; i < (int)sizeof(ellsq_enc_tests) / (int)sizeof(ellsq_enc_tests[0]); ++i) { + secp256k1_pubkey pubkey; + unsigned char pk33[33]; + size_t size = 33; + secp256k1_ellsq_decode(ctx, &pubkey, ellsq_enc_tests[i].ell64); + secp256k1_ec_pubkey_serialize(ctx, pk33, &size, &pubkey, SECP256K1_EC_COMPRESSED); + CHECK(size == 33); + CHECK(secp256k1_memcmp_var(&pk33, ellsq_enc_tests[i].pubkey, size) == 0); + } +} + +#endif diff --git a/src/modules/schnorrsig/tests_impl.h b/src/modules/schnorrsig/tests_impl.h index 2efec8a2b9dc49..7c4321f97a4838 100644 --- a/src/modules/schnorrsig/tests_impl.h +++ b/src/modules/schnorrsig/tests_impl.h @@ -87,7 +87,7 @@ void run_nonce_function_bip340_tests(void) { CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, NULL, 0, NULL) == 0); CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, algo, algolen, NULL) == 1); /* Other algo is fine */ - secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, algo, algolen); + secp256k1_testrand_bytes_test(algo, algolen); CHECK(nonce_function_bip340(nonce, msg, msglen, key, pk, algo, algolen, NULL) == 1); for (i = 0; i < count; i++) { @@ -795,18 +795,18 @@ void test_schnorrsig_sign_verify(void) { /* Flip a few bits in the signature and in the message and check that * verify and verify_batch (TODO) fail */ size_t sig_idx = secp256k1_testrand_int(N_SIGS); - size_t byte_idx = secp256k1_testrand_int(32); + size_t byte_idx = secp256k1_testrand_bits(5); unsigned char xorbyte = secp256k1_testrand_int(254)+1; sig[sig_idx][byte_idx] ^= xorbyte; CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk)); sig[sig_idx][byte_idx] ^= xorbyte; - byte_idx = secp256k1_testrand_int(32); + byte_idx = secp256k1_testrand_bits(5); sig[sig_idx][32+byte_idx] ^= xorbyte; CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk)); sig[sig_idx][32+byte_idx] ^= xorbyte; - byte_idx = secp256k1_testrand_int(32); + byte_idx = secp256k1_testrand_bits(5); msg[sig_idx][byte_idx] ^= xorbyte; CHECK(!secp256k1_schnorrsig_verify(ctx, sig[sig_idx], msg[sig_idx], sizeof(msg[sig_idx]), &pk)); msg[sig_idx][byte_idx] ^= xorbyte; diff --git a/src/precompute_ecmult.c b/src/precompute_ecmult.c new file mode 100644 index 00000000000000..5ccbcb3c5757ca --- /dev/null +++ b/src/precompute_ecmult.c @@ -0,0 +1,96 @@ +/***************************************************************************************************** + * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *****************************************************************************************************/ + +#include +#include + +/* Autotools creates libsecp256k1-config.h, of which ECMULT_WINDOW_SIZE is needed. + ifndef guard so downstream users can define their own if they do not use autotools. */ +#if !defined(ECMULT_WINDOW_SIZE) +#include "libsecp256k1-config.h" +#endif + +#include "../include/secp256k1.h" +#include "assumptions.h" +#include "util.h" +#include "field_impl.h" +#include "group_impl.h" +#include "ecmult.h" +#include "ecmult_compute_table_impl.h" + +static void print_table(FILE *fp, const char *name, int window_g, const secp256k1_ge_storage* table) { + int j; + int i; + + fprintf(fp, "const secp256k1_ge_storage %s[ECMULT_TABLE_SIZE(WINDOW_G)] = {\n", name); + fprintf(fp, " S(%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32 + ",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32")\n", + SECP256K1_GE_STORAGE_CONST_GET(table[0])); + + j = 1; + for(i = 3; i <= window_g; ++i) { + fprintf(fp, "#if WINDOW_G > %d\n", i-1); + for(;j < ECMULT_TABLE_SIZE(i); ++j) { + fprintf(fp, ",S(%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32 + ",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32",%"PRIx32")\n", + SECP256K1_GE_STORAGE_CONST_GET(table[j])); + } + fprintf(fp, "#endif\n"); + } + fprintf(fp, "};\n"); +} + +static void print_two_tables(FILE *fp, int window_g) { + secp256k1_ge_storage* table = malloc(ECMULT_TABLE_SIZE(window_g) * sizeof(secp256k1_ge_storage)); + secp256k1_ge_storage* table_128 = malloc(ECMULT_TABLE_SIZE(window_g) * sizeof(secp256k1_ge_storage)); + + secp256k1_ecmult_compute_two_tables(table, table_128, window_g, &secp256k1_ge_const_g); + + print_table(fp, "secp256k1_pre_g", window_g, table); + print_table(fp, "secp256k1_pre_g_128", window_g, table_128); + + free(table); + free(table_128); +} + +int main(void) { + /* Always compute all tables for window sizes up to 15. */ + int window_g = (ECMULT_WINDOW_SIZE < 15) ? 15 : ECMULT_WINDOW_SIZE; + FILE* fp; + + fp = fopen("src/precomputed_ecmult.c","w"); + if (fp == NULL) { + fprintf(stderr, "Could not open src/precomputed_ecmult.h for writing!\n"); + return -1; + } + + fprintf(fp, "/* This file was automatically generated by precompute_ecmult. */\n"); + fprintf(fp, "/* This file contains an array secp256k1_pre_g with odd multiples of the base point G and\n"); + fprintf(fp, " * an array secp256k1_pre_g_128 with odd multiples of 2^128*G for accelerating the computation of a*P + b*G.\n"); + fprintf(fp, " */\n"); + fprintf(fp, "#if defined HAVE_CONFIG_H\n"); + fprintf(fp, "# include \"libsecp256k1-config.h\"\n"); + fprintf(fp, "#endif\n"); + fprintf(fp, "#include \"../include/secp256k1.h\"\n"); + fprintf(fp, "#include \"group.h\"\n"); + fprintf(fp, "#include \"ecmult.h\"\n"); + fprintf(fp, "#include \"precomputed_ecmult.h\"\n"); + fprintf(fp, "#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)\n"); + fprintf(fp, "#if ECMULT_WINDOW_SIZE > %d\n", window_g); + fprintf(fp, " #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting precomputed_ecmult.c before the build.\n"); + fprintf(fp, "#endif\n"); + fprintf(fp, "#ifdef EXHAUSTIVE_TEST_ORDER\n"); + fprintf(fp, "# error Cannot compile precomputed_ecmult.c in exhaustive test mode\n"); + fprintf(fp, "#endif /* EXHAUSTIVE_TEST_ORDER */\n"); + fprintf(fp, "#define WINDOW_G ECMULT_WINDOW_SIZE\n"); + + print_two_tables(fp, window_g); + + fprintf(fp, "#undef S\n"); + fclose(fp); + + return 0; +} diff --git a/src/gen_ecmult_gen_static_prec_table.c b/src/precompute_ecmult_gen.c similarity index 61% rename from src/gen_ecmult_gen_static_prec_table.c rename to src/precompute_ecmult_gen.c index 22923df3134b1c..7c6359c402f641 100644 --- a/src/gen_ecmult_gen_static_prec_table.c +++ b/src/precompute_ecmult_gen.c @@ -1,8 +1,8 @@ -/*********************************************************************** - * Copyright (c) 2013, 2014, 2015 Thomas Daede, Cory Fields * - * Distributed under the MIT software license, see the accompanying * - * file COPYING or https://www.opensource.org/licenses/mit-license.php.* - ***********************************************************************/ +/********************************************************************************* + * Copyright (c) 2013, 2014, 2015, 2021 Thomas Daede, Cory Fields, Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *********************************************************************************/ #include #include @@ -12,10 +12,10 @@ #include "util.h" #include "group.h" #include "ecmult_gen.h" -#include "ecmult_gen_prec_impl.h" +#include "ecmult_gen_compute_table_impl.h" int main(int argc, char **argv) { - const char outfile[] = "src/ecmult_gen_static_prec_table.h"; + const char outfile[] = "src/precomputed_ecmult_gen.c"; FILE* fp; int bits; @@ -28,21 +28,20 @@ int main(int argc, char **argv) { return -1; } - fprintf(fp, "/* This file was automatically generated by gen_ecmult_gen_static_prec_table. */\n"); + fprintf(fp, "/* This file was automatically generated by precompute_ecmult_gen. */\n"); fprintf(fp, "/* See ecmult_gen_impl.h for details about the contents of this file. */\n"); - fprintf(fp, "#ifndef SECP256K1_ECMULT_GEN_STATIC_PREC_TABLE_H\n"); - fprintf(fp, "#define SECP256K1_ECMULT_GEN_STATIC_PREC_TABLE_H\n"); - + fprintf(fp, "#if defined HAVE_CONFIG_H\n"); + fprintf(fp, "# include \"libsecp256k1-config.h\"\n"); + fprintf(fp, "#endif\n"); + fprintf(fp, "#include \"../include/secp256k1.h\"\n"); fprintf(fp, "#include \"group.h\"\n"); - - fprintf(fp, "#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) " - "SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u," - "0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)\n"); - + fprintf(fp, "#include \"ecmult_gen.h\"\n"); + fprintf(fp, "#include \"precomputed_ecmult_gen.h\"\n"); fprintf(fp, "#ifdef EXHAUSTIVE_TEST_ORDER\n"); - fprintf(fp, "static secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)];\n"); - fprintf(fp, "#else\n"); - fprintf(fp, "static const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)] = {\n"); + fprintf(fp, "# error Cannot compile precomputed_ecmult_gen.c in exhaustive test mode\n"); + fprintf(fp, "#endif /* EXHAUSTIVE_TEST_ORDER */\n"); + fprintf(fp, "#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u)\n"); + fprintf(fp, "const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)] = {\n"); for (bits = 2; bits <= 8; bits *= 2) { int g = ECMULT_GEN_PREC_G(bits); @@ -50,7 +49,7 @@ int main(int argc, char **argv) { int inner, outer; secp256k1_ge_storage* table = checked_malloc(&default_error_callback, n * g * sizeof(secp256k1_ge_storage)); - secp256k1_ecmult_gen_create_prec_table(table, &secp256k1_ge_const_g, bits); + secp256k1_ecmult_gen_compute_table(table, &secp256k1_ge_const_g, bits); fprintf(fp, "#if ECMULT_GEN_PREC_BITS == %d\n", bits); for(outer = 0; outer != n; outer++) { @@ -74,9 +73,7 @@ int main(int argc, char **argv) { } fprintf(fp, "};\n"); - fprintf(fp, "#endif /* EXHAUSTIVE_TEST_ORDER */\n"); - fprintf(fp, "#undef SC\n"); - fprintf(fp, "#endif /* SECP256K1_ECMULT_GEN_STATIC_PREC_TABLE_H */\n"); + fprintf(fp, "#undef S\n"); fclose(fp); return 0; diff --git a/src/ecmult_static_pre_g.h b/src/precomputed_ecmult.c similarity index 99% rename from src/ecmult_static_pre_g.h rename to src/precomputed_ecmult.c index 9072fb268860c9..3e67f37b747dc3 100644 --- a/src/ecmult_static_pre_g.h +++ b/src/precomputed_ecmult.c @@ -1,187 +1,38 @@ -/* This file was automatically generated by gen_ecmult_static_pre_g. */ +/* This file was automatically generated by precompute_ecmult. */ /* This file contains an array secp256k1_pre_g with odd multiples of the base point G and * an array secp256k1_pre_g_128 with odd multiples of 2^128*G for accelerating the computation of a*P + b*G. */ -#ifndef SECP256K1_ECMULT_STATIC_PRE_G_H -#define SECP256K1_ECMULT_STATIC_PRE_G_H -#include "group.h" -#ifdef S - #error macro identifier S already in use. +#if defined HAVE_CONFIG_H +# include "libsecp256k1-config.h" #endif +#include "../include/secp256k1.h" +#include "group.h" +#include "ecmult.h" +#include "precomputed_ecmult.h" #define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u) -#if ECMULT_TABLE_SIZE(ECMULT_WINDOW_SIZE) > 8192 - #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting ecmult_static_pre_g.h before the build. +#if ECMULT_WINDOW_SIZE > 15 + #error configuration mismatch, invalid ECMULT_WINDOW_SIZE. Try deleting precomputed_ecmult.c before the build. #endif -#if defined(EXHAUSTIVE_TEST_ORDER) -#if EXHAUSTIVE_TEST_ORDER == 13 -#define WINDOW_G 4 -static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = { - S(c3459c3d,35326167,cd86cce8,7a2417f,5b8bd567,de8538ee,d507b0c,d128f5bb,8e467fec,cd30000a,6cc1184e,25d382c2,a2f4494e,2fbe9abc,8b64abac,d005fb24) -,S(ae64a1bd,38872f22,f637b457,125cc859,e4c7a31b,cf553cf5,b96e7096,cc61cc10,8e467fec,cd30000a,6cc1184e,25d382c2,a2f4494e,2fbe9abc,8b64abac,d005fb24) -,S(851695d4,9a83f8ef,919bb861,53cbcb16,630fb68a,ed0a766a,3ec693d6,8e6afa40,3c915051,a5fb60b4,fec49de6,e4385101,59f30035,b6502bc0,f5edba86,9753a96c) -,S(0,0,0,0,0,0,0,1,c36eafae,5a049f4b,13b6219,1bc7aefe,a60cffca,49afd43f,a124578,68ac52c3) -}; -static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)] = { - S(8e55c205,92466f75,3c417ec0,e600f626,bfac877c,52258a1c,3941145a,62753693,8e467fec,cd30000a,6cc1184e,25d382c2,a2f4494e,2fbe9abc,8b64abac,d005fb24) -,S(c3459c3d,35326167,cd86cce8,7a2417f,5b8bd567,de8538ee,d507b0c,d128f5bb,8e467fec,cd30000a,6cc1184e,25d382c2,a2f4494e,2fbe9abc,8b64abac,d005fb24) -,S(0,0,0,0,0,0,0,1,3c915051,a5fb60b4,fec49de6,e4385101,59f30035,b6502bc0,f5edba86,9753a96c) -,S(7ae96a2b,657c0710,6e64479e,ac3434e9,9cf04975,12f58995,c1396c28,719501ee,c36eafae,5a049f4b,13b6219,1bc7aefe,a60cffca,49afd43f,a124578,68ac52c3) -}; -#elif EXHAUSTIVE_TEST_ORDER == 199 -#define WINDOW_G 8 -static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = { - S(226e653f,c8df7744,9bacbf12,7d1dcbf9,87f05b2a,e7edbd28,1f564575,c48dcf18,a13872c2,e933bb17,5d9ffd5b,b5b6e10c,57fe3c00,baaaa15a,e003ec3e,9c269bae) -,S(ff1755e,623c8369,f55edda4,2a5deef0,b32c57f4,80c5884f,d2a2dde1,b1c078c4,640db9f3,9dda2f51,ee3ef3db,775315aa,c06346f1,e31ff76f,83a24bb0,8fc93242) 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-,S(929effed,d3b91ccb,a985ab23,bef45c16,6d5ffaa3,22562529,b84d051c,f94044a1,640db9f3,9dda2f51,ee3ef3db,775315aa,c06346f1,e31ff76f,83a24bb0,8fc93242) -,S(1ea4ff3b,5a0a78a9,fda9d73a,ea5f0629,886b083a,6d3beea4,d6bc96e1,b50da944,9edf1300,7f2b7fb2,92301e8c,77ddb63e,5f2d23c4,315118c1,8b1b6273,86bba11a) -,S(86fef7a7,b4d3b079,2c83a223,d1c929d6,6ca15202,f4b956a1,cf7ed2cb,83dba7c4,61b51308,ac8643f0,7c18eda7,ef9a4196,aa66221,1b809acc,2b2cb538,23010ef8) -,S(c979de1c,1318f60f,a9929ff3,a6621b9,d15226e8,2883556e,36a5f77b,28e3b585,d7bd974a,b40a1bd3,a35a1ee9,16d32768,48e7bcfc,be70851d,8ba758b9,996d2099) -,S(2cdce338,ae1f5aa0,55c76cb5,acbd084e,3284bb5d,b8cf9b4a,141cc8ee,1aa61e59,17e98bbd,6e144db,959b7aea,cd766958,7be26db5,445ea19d,dab8bc90,1f527cb4) -,S(80c5672b,3f773975,b5829101,6fa9de9b,33863263,8a978db,934f04c1,3a909b85,55ebf47c,6835f232,5ea232b3,8af64478,65cbdce1,2f2c5a79,abc445fd,518ab677) -,S(521e20fc,9c7c0514,47f31e74,5bb81662,dac66374,9b891a6f,d9681cb6,21e3155c,61b51308,ac8643f0,7c18eda7,ef9a4196,aa66221,1b809acc,2b2cb538,23010ef8) -,S(b084fee5,5da62ee0,ebdebf3b,245e0d4e,def46aac,bfdc9f43,261d3e2b,eed946a0,80f3b79c,ba5f8457,3f2aa473,1d10c1f,9b6543e1,b8cec5e0,e89cd6df,868cc2aa) -,S(d8a3fd95,b7ed8e8a,674da307,94911393,303917c2,60944d1f,76261274,fba45757,5ec78d3d,16cc44e8,a26002a4,4a491ef3,a801c3ff,45555ea5,1ffc13c0,63d96081) -,S(c2d4b350,75ee5eb,3e2c8d3c,f33649dc,dd4f4c29,728bbdae,3f3ff02d,f3dc7415,6120ecff,80d4804d,6dcfe173,882249c1,a0d2dc3b,ceaee73e,74e49d8b,79445b15) -,S(9fa3c7bd,6b8544f2,df48309,596ea267,8f8537e1,dc406ec7,cf2c67d1,ae5f1e8a,c8268dfc,2da263eb,ac7d81d8,6b8b504d,6d6bc20f,745eef75,bc9bb378,1193744b) -,S(0,0,0,0,0,0,0,1,34b8595b,6ecec7d7,fc92428,9be8c5bf,b8c2c696,a33b88a7,aee2f57d,4524f93e) -,S(969360d2,54e2dba9,e79d0789,c339250d,c438330a,a66addf9,f27e2ee8,fc9036ac,99bb92f2,4fe59864,a6504cb5,d4407301,f5bb78f,f1f8b31,875ae5c8,644408f3) -,S(318f2c1f,3dc109ad,ed9d8958,e2e6eb8c,e26eec32,f2725ad1,68e116c7,497e7044,75b3371,ac71e480,9d8398ec,8376914e,3aab7ea6,bcb96a5,15c6b39b,a6d2ba60) -,S(bcea96e9,4ff1b11e,6e8a09d6,ec594b00,597e2b0a,37b0e581,50a58d59,33220419,7f0c4863,45a07ba8,c0d55b8c,fe2ef3e0,649abc1e,47313a1f,1763291f,79733985) -,S(4ed9d2a,7f32fa30,fd059de5,ee512073,47d68d12,b77df5b8,6a83a814,3fcdd5c0,5ec78d3d,16cc44e8,a26002a4,4a491ef3,a801c3ff,45555ea5,1ffc13c0,63d96081) -,S(875c93a1,8ac5a86e,9e85e4aa,3c5ad0ac,3d697192,6384b05b,568604b3,8fee8fb6,3738dc95,97add4e5,c0a39af1,b98ccba2,7bb43333,e35ab481,54c52779,9191144b) -,S(47a7cc2e,1cbd64c8,301443ed,be1ab328,85dce80e,a6d8c847,4eb9be09,6db5fecf,d160b834,5807531a,327a7269,3627dab6,f9770a12,14eb182d,fa73ad15,41b57ff0) -,S(3e8a6608,17f28243,f363d67e,b874856f,1fc9810a,9da6c3f3,a72dd23f,ec45513e,8a8d4c8f,37d2572,6ca66369,59c9eca3,82bd076e,867092a0,b428ad99,2c54a63b) -,S(9556e393,974bcd02,c6356a53,fce819d4,887b188c,99b8de16,1e5d3697,d595cdce,23575727,9da3d12b,c0004d12,e06a9cda,8405c91e,b8118260,2793e62f,16c2a29e) -,S(5245e215,52c6f785,2cccef32,e9f54774,cfb6bb9b,c363ae72,71174df4,6d77fdcc,ca78f1f0,894a6670,19609169,78c251dc,64f969e,c25be4b4,202508d3,22d07f3b) -,S(5d6f8ab3,ca0a5fca,611b7738,16adb4f8,df73ad68,5ce45286,75101d00,54ff3eca,640db9f3,9dda2f51,ee3ef3db,775315aa,c06346f1,e31ff76f,83a24bb0,8fc93242) -,S(a4465b18,b7f702e2,a8165184,834ce490,68fb0a51,6658734b,6229eda0,605911a2,c8c7236a,68522b1a,3f5c650e,4673345d,844bcccc,1ca54b7e,ab3ad885,6e6ee7e4) -,S(d49b0640,1e240c43,21b2b173,3b640c6a,e2c4b389,2d3f4f73,8faac78b,9995cf2e,75b3371,ac71e480,9d8398ec,8376914e,3aab7ea6,bcb96a5,15c6b39b,a6d2ba60) -,S(599db82f,8229ad47,7a662726,d2d351a6,f76cefd7,8fc376b1,ef6e344e,4e4dae3a,284268b5,4bf5e42c,5ca5e116,e92cd897,b7184303,418f7ae2,7458a745,6692db96) -,S(a0627644,ebc6a423,1f3e113b,eedbf9d8,21d9374a,af2e7c55,14ee7395,aa9992b7,859f03d8,1b54f459,158e3fc9,ad47c3a3,a54a2537,15bc213d,7b8e6072,9283bfae) -}; -static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)] = { - S(ec823227,1d0e875a,8e1cf7e6,f9a35a15,749be650,1cc885c4,f383060b,46bd3d33,aa140b83,97ca0dcd,a15dcd4c,7509bb87,9a34231e,d0d3a586,543bba01,ae7545b8) -,S(66abbf18,f58dd1c9,4b6072c,eb182abe,c31d3af9,6d91060b,d233f462,5716f289,d380d231,1bde27ad,2c400971,66c3744b,3e762c41,42b05998,95a6605f,739c5fdf) -,S(4d756b2,e61d9806,e02ec830,f1fd44f8,46438689,c528346,15a1addf,ac864bcd,36f8fb36,708d2741,9c75c923,178976f6,5386de3,23ab2ceb,f76044c0,9256faa5) -,S(875c93a1,8ac5a86e,9e85e4aa,3c5ad0ac,3d697192,6384b05b,568604b3,8fee8fb6,c8c7236a,68522b1a,3f5c650e,4673345d,844bcccc,1ca54b7e,ab3ad885,6e6ee7e4) -,S(f3a864ac,edc7852f,f4dfae93,5f8588a6,96ff17bf,7233134e,6704ceb,16f3b74c,39cfeb15,665f371f,535d56c1,317a8d62,29ea2827,943a98f1,cee7f685,86e47eec) -,S(3e8a6608,17f28243,f363d67e,b874856f,1fc9810a,9da6c3f3,a72dd23f,ec45513e,8a8d4c8f,37d2572,6ca66369,59c9eca3,82bd076e,867092a0,b428ad99,2c54a63b) -,S(47bbafcd,f612ca3e,703f7721,623bde14,926fc00d,a6bf9e9,41ddb2d5,587626e3,d160b834,5807531a,327a7269,3627dab6,f9770a12,14eb182d,fa73ad15,41b57ff0) -,S(709c8403,ed2fd0f9,5fac44f0,dfa96ec2,e7b357e4,4ebb3dcf,6f688f20,39d3d67d,2e9f47cb,a7f8ace5,cd858d96,c9d82549,688f5ed,eb14e7d2,58c52e9,be4a7c3f) -,S(66fd0ada,7159c2df,fdd925e7,2eb70772,743e39e3,4c10d5cf,f58eac4e,a30e4157,8a8d4c8f,37d2572,6ca66369,59c9eca3,82bd076e,867092a0,b428ad99,2c54a63b) -,S(60d5d771,4e1e7589,e0b1e68c,ed7f881,73fca809,eae35685,65334942,79962dc2,99bb92f2,4fe59864,a6504cb5,d4407301,f5bb78f,f1f8b31,875ae5c8,644408f3) -,S(3d98fe85,5d42f661,e35d8ce3,cfee5f17,57bc3de9,ecec02fa,11a2d90,378ac0e8,bdc6dc52,8a55814e,da6bcb58,e2a73b96,9d975c7,a3270483,b419b29b,5263f45) -,S(2f63a396,4d14ca73,2167e033,306863d8,f75605c7,4ea6c917,890dd50d,fc20f53b,1dd6a38e,deb870ad,f2b2e755,8d327d51,e66a2c81,910d1fa5,b215911c,9c8e004c) -,S(bcea96e9,4ff1b11e,6e8a09d6,ec594b00,597e2b0a,37b0e581,50a58d59,33220419,80f3b79c,ba5f8457,3f2aa473,1d10c1f,9b6543e1,b8cec5e0,e89cd6df,868cc2aa) -,S(ae3796a4,823f3eb4,ea4bd677,110dc3fb,45537c3c,4d10d2e8,e758a3be,4875db83,ef2b477b,a9c921df,5ff65b6e,7c6f96a8,627743ff,a53e3858,cd9d7673,f7435ac4) -,S(5245e215,52c6f785,2cccef32,e9f54774,cfb6bb9b,c363ae72,71174df4,6d77fdcc,ca78f1f0,894a6670,19609169,78c251dc,64f969e,c25be4b4,202508d3,22d07f3b) -,S(26e2e75b,aeb04a72,8b893f67,d27ebfc6,b8984a88,6fbd8eee,5719107d,5a413f0f,61b51308,ac8643f0,7c18eda7,ef9a4196,aa66221,1b809acc,2b2cb538,23010ef8) -,S(e0089ec9,4b25ac6,ff44b5da,2dfedb37,9fdaedf1,6bc8cecd,b1a95fa0,32431c73,e8167442,f91ebb24,6a648515,328996a7,841d924a,bba15e62,2547436e,e0ad7f7b) -,S(f8f16642,266d8dc6,abfdbbc6,f6c47711,a192c051,7f00a633,b78076a7,a7884e72,4f6d0e5,148ce7e1,772f84c,b08903b8,71d2beb5,d0934488,8ab1c75d,42232790) -,S(23082df9,a86b80fc,5185ee3c,6493763b,14a6e237,baf686aa,f589b649,8573d04c,bdc6dc52,8a55814e,da6bcb58,e2a73b96,9d975c7,a3270483,b419b29b,5263f45) -,S(76dac07e,bc240289,791e6a9a,56abdc7,bdf2fac1,e7a0100b,5a0ee09e,3455cc33,8b4502cd,420d4202,39a5ad3c,fa10b0b2,6ccd084d,5faed560,7de07a6,fb7b4093) -,S(8735fb32,6950ae71,31cd03f7,cc1511d8,65c87e84,748c9824,8ccc576e,5480ed8,c63014ea,99a0c8e0,aca2a93e,ce85729d,d615d7d8,6bc5670e,31180979,791b7d43) -,S(969360d2,54e2dba9,e79d0789,c339250d,c438330a,a66addf9,f27e2ee8,fc9036ac,66446d0d,b01a679b,59afb34a,2bbf8cfe,f0a44870,f0e074ce,78a51a36,9bbbf33c) -,S(74f5ba33,89d075d3,eebaa54d,73e9f038,881b7329,5623e833,b5e87beb,29ba3246,74bafd32,bdf2bdfd,c65a52c3,5ef4f4d,9332f7b2,a0512a9f,f821f858,484bb9c) -,S(a4465b18,b7f702e2,a8165184,834ce490,68fb0a51,6658734b,6229eda0,605911a2,c8c7236a,68522b1a,3f5c650e,4673345d,844bcccc,1ca54b7e,ab3ad885,6e6ee7e4) -,S(eac612b0,84cb452a,35d49c60,c0d0c0bd,359eb909,68a80186,92a028f,ece4c331,23575727,9da3d12b,c0004d12,e06a9cda,8405c91e,b8118260,2793e62f,16c2a29e) -,S(f31a7dfe,4d2e4a98,aaf3dd70,25441c7a,2da056b0,db6795e8,3a39d76f,b316bd92,e8167442,f91ebb24,6a648515,328996a7,841d924a,bba15e62,2547436e,e0ad7f7b) -,S(470ce05d,53f77ff0,c5ab8770,a4c11a3e,23f7d4fe,f5c0ab36,1b940a8a,6b8cf7b9,57d6adb1,5f0b1daa,1fce91d7,ccf75d45,9480b056,6f81ff8a,85612173,1cd8f2b8) -,S(d9fbce92,515652cf,3714f87b,e16e505,91a28eb4,1bf7053,2ab42ebd,be900212,2d7d0b7e,4fb4131d,9f21966a,4a73b0f2,639ede1f,26b0ba25,a2580eb,30100c96) -,S(1ea4ff3b,5a0a78a9,fda9d73a,ea5f0629,886b083a,6d3beea4,d6bc96e1,b50da944,9edf1300,7f2b7fb2,92301e8c,77ddb63e,5f2d23c4,315118c1,8b1b6273,86bba11a) -,S(3d303d12,f8eb67d0,ecaee514,bdd90e57,b58b6d6a,c896a26f,78c06103,52225b04,2d7d0b7e,4fb4131d,9f21966a,4a73b0f2,639ede1f,26b0ba25,a2580eb,30100c96) -,S(9fa3c7bd,6b8544f2,df48309,596ea267,8f8537e1,dc406ec7,cf2c67d1,ae5f1e8a,37d97203,d25d9c14,53827e27,9474afb2,92943df0,8ba1108a,43644c86,ee6c87e4) -,S(92906a31,52682000,a59736ed,ef48a7b0,c78d6a49,8727b3b,893d3478,de04ada5,80f3b79c,ba5f8457,3f2aa473,1d10c1f,9b6543e1,b8cec5e0,e89cd6df,868cc2aa) -,S(599db82f,8229ad47,7a662726,d2d351a6,f76cefd7,8fc376b1,ef6e344e,4e4dae3a,284268b5,4bf5e42c,5ca5e116,e92cd897,b7184303,418f7ae2,7458a745,6692db96) -,S(ee534645,42ff07e2,8cf783ee,1da96e00,b81f531,9b9a4885,27f92302,acd12cac,c90704c9,8f72d8be,638a36dc,e8768909,fac7921c,dc54d314,89fbb3e,6da9018a) -,S(7fe309bb,e3e8edd3,3f5f94b,4247256e,41e62e69,fd9f2063,d878c6d6,3d85675f,dca8a8d8,625c2ed4,3fffb2ed,1f956325,7bfa36e1,47ee7d9f,d86c19cf,e93d5991) -,S(64eaaad1,9c7e9d01,5cc997ff,c2f23022,c59805d,48a48e1,970b8847,10211659,fb092f1a,eb73181e,f88d07b3,4f76fc47,8e2d414a,2f6cbb77,754e38a1,bddcd49f) -,S(59e10f43,eb4b2fb0,94f2f66d,1404dd08,ab9c2442,50bd16e0,21feb78f,e0380d01,e2295c71,21478f52,d4d18aa,72cd82ae,1995d37e,6ef2e05a,4dea6ee2,6371fbe3) -,S(c979de1c,1318f60f,a9929ff3,a6621b9,d15226e8,2883556e,36a5f77b,28e3b585,d7bd974a,b40a1bd3,a35a1ee9,16d32768,48e7bcfc,be70851d,8ba758b9,996d2099) -,S(64dd1439,5d19a544,a7a1e81b,b9d079b3,593e7022,6bcd444e,6dc8197a,1a6dc3e6,d380d231,1bde27ad,2c400971,66c3744b,3e762c41,42b05998,95a6605f,739c5fdf) -,S(d8a3fd95,b7ed8e8a,674da307,94911393,303917c2,60944d1f,76261274,fba45757,a13872c2,e933bb17,5d9ffd5b,b5b6e10c,57fe3c00,baaaa15a,e003ec3e,9c269bae) -,S(acee4285,57fc32a1,d3d14199,30cadaf0,613a630a,7a7e8c14,d08d05df,19143c3a,ca78f1f0,894a6670,19609169,78c251dc,64f969e,c25be4b4,202508d3,22d07f3b) -,S(5d771e5d,6dc6c87,5ede8bae,4b27a9d4,3c5f8da2,8e84f5c3,501299c8,db16484c,859f03d8,1b54f459,158e3fc9,ad47c3a3,a54a2537,15bc213d,7b8e6072,9283bfae) -,S(e8d3f45a,b5be455f,dc3c2270,34100ca2,b8d203e1,35a9ed3d,5c8b703c,ef4d9b48,2d7d0b7e,4fb4131d,9f21966a,4a73b0f2,639ede1f,26b0ba25,a2580eb,30100c96) -,S(9963e528,754cbba8,29622664,1aec11b0,3fba2739,40f61cbd,5d4c0478,5429f40,298f1c0e,f903dc7d,b940cdc0,ed8183eb,a891c59b,a2a3be25,bf0dd4d5,b03574c3) -,S(cbdb65,553cd5d8,ff61cf33,e53fdd9a,cf0ee159,c21dc578,be5bac2b,7973c229,ca78f1f0,894a6670,19609169,78c251dc,64f969e,c25be4b4,202508d3,22d07f3b) -,S(5029bff6,d4c80347,738230c8,cb252906,471b5bc1,3d26a533,304f5f0d,808f756c,97682462,a5c276b7,1568f961,f218a99e,4e528b1b,d4e255b0,acc27744,98ec84fe) -,S(80c5672b,3f773975,b5829101,6fa9de9b,33863263,8a978db,934f04c1,3a909b85,55ebf47c,6835f232,5ea232b3,8af64478,65cbdce1,2f2c5a79,abc445fd,518ab677) -,S(226e653f,c8df7744,9bacbf12,7d1dcbf9,87f05b2a,e7edbd28,1f564575,c48dcf18,5ec78d3d,16cc44e8,a26002a4,4a491ef3,a801c3ff,45555ea5,1ffc13c0,63d96081) -,S(521e20fc,9c7c0514,47f31e74,5bb81662,dac66374,9b891a6f,d9681cb6,21e3155c,9e4aecf7,5379bc0f,83e71258,1065be69,f5599dde,e47f6533,d4d34ac6,dcfeed37) -,S(5472b5d0,4ba1ca80,236183b1,46e596e5,4b20b83b,248988c8,bbe8460e,3666f262,a829524e,a0f4e255,e0316e28,3308a2ba,6b7f4fa9,907e0075,7a9ede8b,e3270977) -,S(2ecd421e,47399e76,60d10143,1789a437,89b54d23,31d1cb78,49cabda2,bc5174f9,c8268dfc,2da263eb,ac7d81d8,6b8b504d,6d6bc20f,745eef75,bc9bb378,1193744b) -,S(4097892c,5478baea,62e8da20,6d17fcd8,b8eed45f,24fb7648,fe742508,8da60a4e,10d4b884,5636de20,a009a491,83906957,9d88bc00,5ac1c7a7,3262898b,8bca16b) -,S(eb5c4120,4917d176,6fea883b,e680dfd9,233d9654,97fac48b,76f5d0d4,7f6dbf73,6897db9d,5a3d8948,ea97069e,de75661,b1ad74e4,2b1daa4f,533d88ba,67137731) -,S(92b866ad,a37a3f2f,bc607717,96b2c74f,57dde74c,da8e015f,792df531,7eb21fa6,55ebf47c,6835f232,5ea232b3,8af64478,65cbdce1,2f2c5a79,abc445fd,518ab677) -,S(a78dab,f2f2ef7f,4d424752,aa1aeaf5,50bec241,bf9ad129,3b9fe680,32b6141b,9de02272,226d60c0,97e5907c,407f9e07,d4bc6959,a2079419,139a9578,4e48cb7f) -,S(b084fee5,5da62ee0,ebdebf3b,245e0d4e,def46aac,bfdc9f43,261d3e2b,eed946a0,80f3b79c,ba5f8457,3f2aa473,1d10c1f,9b6543e1,b8cec5e0,e89cd6df,868cc2aa) -,S(ff1755e,623c8369,f55edda4,2a5deef0,b32c57f4,80c5884f,d2a2dde1,b1c078c4,640db9f3,9dda2f51,ee3ef3db,775315aa,c06346f1,e31ff76f,83a24bb0,8fc93242) -,S(2cdce338,ae1f5aa0,55c76cb5,acbd084e,3284bb5d,b8cf9b4a,141cc8ee,1aa61e59,e8167442,f91ebb24,6a648515,328996a7,841d924a,bba15e62,2547436e,e0ad7f7b) -,S(3faf6744,2aebb675,c6b75911,e3d34f4c,a8f5b669,a4c438f2,2c163659,3e36c1ea,fc0b579e,cbaf2c74,7b5c792d,7b66abf2,dfb1a44d,2ed6a417,7e1fc6bd,a989b623) -,S(34772cad,ad5888f2,53a810b7,5b175b8d,e3a454e4,26a1b5a5,c003f222,8e7b45c0,d380d231,1bde27ad,2c400971,66c3744b,3e762c41,42b05998,95a6605f,739c5fdf) -,S(853cffd4,4cb0a29e,390ad886,455566cc,2776ab74,55210e57,9bf1fcc0,c8d767ed,621fdd8d,dd929f3f,681a6f83,bf8061f8,2b4396a6,5df86be6,ec656a86,b1b730b0) -,S(1130e02f,29480660,b2cb4f68,81da3f2c,1bdaf64,8df3b6ce,1a333738,29e4165e,10d4b884,5636de20,a009a491,83906957,9d88bc00,5ac1c7a7,3262898b,8bca16b) -,S(a0627644,ebc6a423,1f3e113b,eedbf9d8,21d9374a,af2e7c55,14ee7395,aa9992b7,7a60fc27,e4ab0ba6,ea71c036,52b83c5c,5ab5dac8,ea43dec2,84719f8c,6d7c3c81) -,S(1e864d74,9e96a16a,c4299b88,226aaff9,9a45ab9c,203853ac,ea0378ef,5715ded6,6120ecff,80d4804d,6dcfe173,882249c1,a0d2dc3b,ceaee73e,74e49d8b,79445b15) -}; -#else - #error No known generator for the specified exhaustive test group order. -#endif -#else /* !defined(EXHAUSTIVE_TEST_ORDER) */ +#ifdef EXHAUSTIVE_TEST_ORDER +# error Cannot compile precomputed_ecmult.c in exhaustive test mode +#endif /* EXHAUSTIVE_TEST_ORDER */ #define WINDOW_G ECMULT_WINDOW_SIZE -static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = { +const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = { S(79be667e,f9dcbbac,55a06295,ce870b07,29bfcdb,2dce28d9,59f2815b,16f81798,483ada77,26a3c465,5da4fbfc,e1108a8,fd17b448,a6855419,9c47d08f,fb10d4b8) -#if ECMULT_TABLE_SIZE(WINDOW_G) > 1 +#if WINDOW_G > 2 ,S(f9308a01,9258c310,49344f85,f89d5229,b531c845,836f99b0,8601f113,bce036f9,388f7b0f,632de814,fe337e6,2a37f356,6500a999,34c2231b,6cb9fd75,84b8e672) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 2 +#if WINDOW_G > 3 ,S(2f8bde4d,1a072093,55b4a725,a5c5128,e88b84bd,dc619ab7,cba8d569,b240efe4,d8ac2226,36e5e3d6,d4dba9dd,a6c9c426,f788271b,ab0d6840,dca87d3a,a6ac62d6) ,S(5cbdf064,6e5db4ea,a398f365,f2ea7a0e,3d419b7e,330e39c,e92bdded,cac4f9bc,6aebca40,ba255960,a3178d6d,861a54db,a813d0b8,13fde7b5,a5082628,87264da) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 4 +#if WINDOW_G > 4 ,S(acd484e2,f0c7f653,9ad178a,9f559abd,e0979697,4c57e714,c35f110d,fc27ccbe,cc338921,b0a7d9fd,64380971,763b61e9,add888a4,375f8e0f,5cc262a,c64f9c37) ,S(774ae7f8,58a9411e,5ef4246b,70c65aac,5649980b,e5c17891,bbec1789,5da008cb,d984a032,eb6b5e19,243dd56,d7b7b365,372db1e2,dff9d6a8,301d74c9,c953c61b) ,S(f28773c2,d975288b,c7d1d205,c3748651,b075fbc6,610e58cd,deeddf8f,19405aa8,ab0902e,8d880a89,758212eb,65cdaf47,3a1a06da,521fa91f,29b5cb52,db03ed81) ,S(d7924d4f,7d43ea96,5a465ae3,95ff411,31e5946f,3c85f79e,44adbcf8,e27e080e,581e2872,a86c72a6,83842ec2,28cc6def,ea40af2b,d896d3a5,c504dc9f,f6a26b58) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 8 +#if WINDOW_G > 5 ,S(defdea4c,db677750,a420fee8,7eacf21,eb9898ae,79b97687,66e4faa0,4a2d4a34,4211ab06,94635168,e997b0ea,d2a93dae,ced1f4a0,4a95c0f6,cfb199f6,9e56eb77) ,S(2b4ea0a7,97a443d2,93ef5cff,444f4979,f06acfeb,d7e86d27,74756561,38385b6c,85e89bc0,37945d93,b343083b,5a1c8613,1a01f60c,50269763,b570c854,e5c09b7a) ,S(352bbf4a,4cdd1256,4f93fa33,2ce33330,1d9ad402,71f81071,81340aef,25be59d5,321eb407,5348f534,d59c1825,9dda3e1f,4a1b3b2e,71b1039c,67bd3d8b,cf81998c) @@ -191,7 +42,7 @@ static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = ,S(c44d12c7,65d812e,8acf28d7,cbb19f90,11ecd9e9,fdf281b0,e6a3b5e8,7d22e7db,2119a460,ce326cdc,76c45926,c982fdac,e106e86,1edf61c5,a039063f,e0e6482) ,S(6a245bf6,dc698504,c89a20cf,ded60853,152b6953,36c28063,b61c65cb,d269e6b4,e022cf42,c2bd4a70,8b3f5126,f16a24ad,8b33ba48,d0423b6e,fd5e6348,100d8a82) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 16 +#if WINDOW_G > 6 ,S(1697ffa6,fd9de627,c077e3d2,fe541084,ce13300b,bec1146,f95ae57f,d0bd6a5,b9c398f1,86806f5d,27561506,e4557433,a2cf1500,9e498ae7,adee9d63,d01b2396) ,S(605bdb01,9981718b,986d0f07,e834cb0d,9deb8360,ffb7f61d,f982345e,f27a7479,2972d2d,e4f8d206,81a78d93,ec96fe23,c26bfae8,4fb14db4,3b01e1e9,56b8c49) ,S(62d14dab,4150bf49,7402fdc4,5a215e10,dcb01c35,4959b10c,fe31c7e9,d87ff33d,80fc06bd,8cc5b010,98088a19,50eed0db,1aa1329,67ab4722,35f56424,83b25eaf) @@ -209,7 +60,7 @@ static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = ,S(754e3239,f325570c,dbbf4a87,deee8a66,b7f2b334,79d468fb,c1a50743,bf56cc18,673fb86,e5bda30f,b3cd0ed3,4ea49a0,23ee33d0,197a695d,c5d9809,3c536683) ,S(e3e6bd10,71a1e96a,ff57859c,82d570f0,33080066,1d1c952f,9fe26946,91d9b9e8,59c9e0bb,a394e76f,40c0aa58,379a3cb6,a5a22839,93e90c41,67002af4,920e37f5) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 32 +#if WINDOW_G > 7 ,S(186b483d,56a0338,26ae73d8,8f732985,c4ccb1f3,2ba35f4b,4cc47fdc,f04aa6eb,3b952d32,c67cf77e,2e17446e,204180ab,21fb8090,895138b4,a4a797f8,6e80888b) ,S(df9d70a6,b9876ce5,44c98561,f4be4f72,5442e6d2,b737d9c9,1a832172,4ce0963f,55eb2daf,d84d6ccd,5f862b78,5dc39d4a,b1572227,20ef9da2,17b8c45c,f2ba2417) ,S(5edd5cc2,3c51e87a,497ca815,d5dce0f8,ab52554f,849ed899,5de64c5f,34ce7143,efae9c8d,bc141306,61e8cec0,30c89ad0,c13c66c0,d17a2905,cdc706ab,7399a868) @@ -243,7 +94,7 @@ static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = ,S(c4191636,5abb2b5d,9192f5f,2dbeafec,208f020f,12570a18,4dbadc3e,58595997,4f14351,d0087efa,49d245b3,28984989,d5caf945,f34bfc0,ed16e96b,58fa9913) ,S(841d6063,a586fa47,5a724604,da03bc5b,92a2e0d2,e0a36acf,e4c73a55,14742881,73867f5,9c0659e8,1904f9a1,c7543698,e62562d6,744c169c,e7a36de0,1a8d6154) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 64 +#if WINDOW_G > 8 ,S(5e95bb39,9a6971d3,76026947,f89bde2f,282b3381,928be4d,ed112ac4,d70e20d5,39f23f36,6809085b,eebfc711,81313775,a99c9aed,7d8ba38b,161384c7,46012865) ,S(36e4641a,53948fd4,76c39f8a,99fd974e,5ec07564,b5315d8b,f99471bc,a0ef2f66,d2424b1b,1abe4eb8,164227b0,85c9aa94,56ea1349,3fd563e0,6fd51cf5,694c78fc) ,S(336581e,a7bfbbb2,90c191a2,f507a41c,f5643842,170e914f,aeab27c2,c579f726,ead12168,595fe1be,99252129,b6e56b33,91f7ab14,10cd1e0e,f3dcdcab,d2fda224) @@ -309,7 +160,7 @@ static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = ,S(809a20c6,7d64900f,fb698c4c,825f6d5f,2310fb04,51c86934,5b7319f6,45605721,9e994980,d9917e22,b76b0619,27fa0414,3d096ccc,54963e6a,5ebfa5f3,f8e286c1) ,S(1b38903a,43f7f114,ed4500b4,eac7083f,defece1c,f29c6352,8d563446,f972c180,4036edc9,31a60ae8,89353f77,fd53de4a,2708b26b,6f5da72a,d3394119,daf408f9) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 128 +#if WINDOW_G > 9 ,S(90a80db6,eb294b9e,ab0b4e8d,dfa3efe7,263458ce,2d07566d,f4e6c588,68feef23,753c8b9f,9754f18d,87f21145,d9e2936b,5ee050b2,7bbd9681,442c76e9,2fcf91e6) ,S(c2c80f84,4b705998,12d62546,f60340e,3e6f3605,4a14546e,6dc25d47,376bea9b,86ca160d,68f4d4e7,18b495b8,91d3b1b5,73b871a7,2b4cf61,23abd448,3aa79c64) ,S(9cf60674,4cf4b5f3,fdf989d3,f19fb265,2d00cfe1,d5fcd692,a323ce11,a28e7553,8147cbf7,b973fcc1,5b57b6a3,cfad6863,edd0f30e,3c45b85d,c300c513,c247759d) @@ -439,7 +290,7 @@ static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = ,S(367807c9,a3606b4e,1b8c2616,ad528030,1dfcf686,40eddf02,fc59317c,230e9a86,1f023f2f,a2bbece7,3dba14c,124095cb,fdc4f92f,281a14,8304a412,c16ecae6) ,S(8ec4fdc3,9891f6af,1374e06f,c44b815,1b82541,75fc4909,acba5941,201af62b,2dc6cae5,cac2d887,83dca0e5,3c798f8,fe067bcf,5fc29751,13756cf7,ef4e5f1b) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 256 +#if WINDOW_G > 10 ,S(5cc24a6d,4c5b24f9,14542f91,e5fa937f,ffa08551,51b8b842,8729b06a,9178a263,b1da8635,81531a1f,bfb38a4e,419fa1fe,ca8d55a8,3ddbcb98,da19d5cf,fb7da472) ,S(83905926,c03905c3,a9644a6c,da810dd2,92602a50,50c52a21,9134fc4d,e3599e9f,4293260f,e8af6792,a20b115e,aa837638,9094298b,21d9de16,cf20e0c5,7a46089a) ,S(944b097e,4721e9dd,f8204ac3,d3878fa,e8fa6c14,34ae4822,481b2985,6589b6c7,5fc47565,30e9b095,f8b79643,1e745b99,1525bd4c,4764e8e,e8af4b96,9bd6ddf6) @@ -697,7 +548,7 @@ static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = ,S(d9a0c689,95283291,972d6a72,897181b2,6b4ae317,4e98a676,f75bbfbf,81be876e,d36ae886,a0acbc9a,d1564d97,4d3f0309,e9039b93,bb350d92,2b7f8c7a,c6bfa042) ,S(c7a36324,6aeb7c8c,991b2aa7,10abdf5c,fff29912,30b3a69f,be2dd481,7c7c3e0a,1298fdd7,e448d2d,79986302,6b4b2d49,2b32148,d6d1e5f8,15f5b0c0,5c9e21f) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 512 +#if WINDOW_G > 11 ,S(635cd7a0,5064d3bc,66535a0,4dbf563a,640d2464,c7fe0ac4,8304214f,e4985a86,e40265,913e77f6,46735cfc,af9e2f30,e8d5f047,f3281a4c,e0453e27,e9e3ae1f) ,S(5da624f,38edea25,37f5b632,695b481a,eca54bb7,2169cadc,c5b91e10,989ee5f5,d3ea6dba,a1080300,fffaeeb2,43a5256e,48c28822,37b16505,a220d771,ca721779) ,S(aa4f64a2,b19775ec,92c1f687,1fe4b6d5,ce05278c,2976c80e,fe19284f,e87d4d5e,f39f117e,95fce0fb,6976e949,9583a66c,224ea028,8396518e,293793dc,3ed4f240) @@ -1211,7 +1062,7 @@ static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = ,S(dd879eba,f870ee3d,f6e3f03,60833e12,fbdf844c,d6a5b76c,19802485,6649bbc1,e7bb04c3,a99a5c11,dd7a324c,1d5696c8,b041a12a,c6a538f7,3094716c,9943c55a) ,S(7aa4afbe,29b06a1e,da9319d5,72572b13,1df68f74,1b5f8d8e,d00ccc04,80f8016e,15f79a9f,b77b8587,7f02e3c1,3202b972,423fd00d,937c0d2d,c9d94b17,53fe7130) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 1024 +#if WINDOW_G > 12 ,S(9145f3f5,876a3265,5d7fee64,f2d6e660,c34354e9,1571d68b,a19e4cc5,8c39f890,45e0a95d,cf369fd0,5bc9ba7f,da108d6f,37650c1d,5766b6c9,98ecda28,b285d8ff) ,S(5450b752,36fb010d,1ef37afa,2077f3dc,a5a7f6c8,91a21317,13df740f,4511ac9e,a7c7ed57,62bef86d,4de1084d,3ded2d7b,13ff563a,67109ef0,8b6f0180,fe6ba175) ,S(ba6c0d72,5e48de2c,cb8256d6,7417d075,bbf2766f,d13501b8,4c32cf88,c0666a0f,cd2a9132,7137299f,50eda669,3a599032,bdecd64b,91bcc640,5ed186f3,e525e442) @@ -2237,7 +2088,7 @@ static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = ,S(6d109d8c,2505808f,7b4052d6,b170ec80,c68373bb,e02f2b62,1cd29773,a96acb3e,c8dea0de,511f6e40,5141088e,cb023bff,200c870b,9cb952ad,c5038b28,eadc9a57) ,S(9c219898,6d202467,c055c734,73557505,6105b3e,2874dbf2,8f7f0c39,66e1af88,8637496c,8eddff12,f9dd4146,36565e0f,efddf5cd,52d48455,ec9fb2d,8dd0914a) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 2048 +#if WINDOW_G > 13 ,S(22ca5039,e660f60,1036dd75,2bb973b,dcd104b5,dcb8f2e7,4de8edc6,c292b03a,86fd4471,1ef6b81e,4416449a,708fa0c9,cb6731ba,c403e58e,da5e915f,646b11e8) ,S(cfc18f02,cc004640,f2116fdd,1f6ca202,2e39be25,df75e27c,80bde842,e6b6f938,d62b58df,4f79d0e5,97ba2923,f708cbe5,c09236a4,d9d01398,6451d684,6290df7d) ,S(3388bcc2,3425458e,991f46ca,6235c50a,57490556,becbaf25,9d3c14f9,9a80a087,7d4aa2f8,6f65783,1c22316,6958fbf3,6c3dca5,d4ac413b,3102e13e,a645c016) @@ -4287,7 +4138,7 @@ static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = ,S(d5acff71,e82a455c,3a1ce292,689e8686,f441ce1b,e644e79a,bd6d0efe,29270865,aac6d48f,1b46e970,a044971a,ad13f033,ca8cde96,958d870e,dc7d80,1d26d5e8) ,S(5cf51c1b,2210d85,9d765e17,32109514,8f03fc57,51004b6a,91f098e2,e2711596,1eeb19e0,610df459,2c31e58e,aa2a2148,17fe9ee,a3995838,f395bdcf,26d5c3b3) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 4096 +#if WINDOW_G > 14 ,S(21456873,b58e3687,52c75800,8d3bcae,9efaf1f5,c5727842,25e3d854,8fd421cb,a2f2d10,c85e8a0f,4a136ad0,5df991ce,7d3c5585,a263d5cf,da50a4f4,3db76cb0) ,S(c10de5c0,51ae2d73,28ac06ca,cca840b4,ed7ab204,21c6122f,1d68fe7f,7893d38d,ee30e086,a891484,2ad4041,f9ab9c57,cff1a315,f0642d31,b31c2914,faac99e0) ,S(be778032,f12c1b77,9bba3d9e,d290ca90,30ac7050,bdd77a2,7eac09be,eea65c0b,8657348b,a1e27a63,1dd2a54b,e2d5270f,4cca817a,219c5378,4d4f73ba,2c932e63) @@ -8386,22 +8237,22 @@ static const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)] = ,S(1e70619c,381a6adc,e5d925e0,c9c74f97,3c02ff64,ff2662d7,34efc485,d2bce895,c923f771,f543ffed,42935c28,8474aaaf,80a46ad4,3c579ce0,bb5e663d,668b24b3) #endif }; -static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)] = { +const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)] = { S(8f68b9d2,f63b5f33,9239c1ad,981f162e,e88c5678,723ea335,1b7b444c,9ec4c0da,662a9f2d,ba063986,de1d90c2,b6be215d,bbea2cfe,95510bfd,f23cbf79,501fff82) -#if ECMULT_TABLE_SIZE(WINDOW_G) > 1 +#if WINDOW_G > 2 ,S(38381dbe,2e509f22,8ba93363,f2451f08,fd845cb3,51d954be,18e2b8ed,d23809fa,e4a32d0a,fb917dc,b09405a5,520eb1cc,3681fccb,32d8f24d,bd707518,331fed52) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 2 +#if WINDOW_G > 3 ,S(49262724,e4372ae6,f6921b82,aa4699a1,f186aea5,40122630,3ea42648,97c2a310,1337e773,bca7abf9,5a2cfa56,9714303b,6d163612,a75ff8ce,c41b681,5e27ded0) ,S(e306568c,1a240c90,d5e253b3,e477e2f8,4dcc1a56,ff06db8d,1384b079,cebd2d31,eac6fe3,78934260,888f2b10,7f7d0db6,ffbc8042,be373826,692b4083,92546e44) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 4 +#if WINDOW_G > 4 ,S(3b9e100e,2428cefc,271b0e76,23fbd633,74ebf8d9,aab41dd9,c530c39e,363136b0,fafb9815,2d16bb71,df1533eb,8f475b26,a2ae28a3,3ad31f81,953ec16f,6cdbbc8a) ,S(bb0aad49,712ac9a9,2b76ca80,f5dedef7,17ca0768,8107beee,9608f047,2f485d3f,ea699c53,c5835479,8ecd201f,7297da34,895a5afa,31670bff,e7939250,3ca2f975) ,S(79090ac8,e4eefcc0,d4e8eb19,7afe0113,e1e58b4d,b01123de,4aeed33a,36718dc9,eaab722b,91905b8f,13d816cb,cd9aaa56,dd36afb7,ba9008b,963322b1,1cfae7c5) ,S(e77c81ad,e9f97b55,1c03dbbc,e549ba66,8dd71de7,cd775ad2,a269694c,7f60c7d1,3acf1478,eef81321,c5fc3b32,3ea81543,631470f7,1c2986d3,4ec581f2,82d72449) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 8 +#if WINDOW_G > 5 ,S(de2b5ce9,dbce511c,f2d8878e,3ded87cc,3d633dae,a2d45341,501fb3a4,55ccf6b0,f10576f3,d3c3e0e1,bbf717e9,8b1a3744,65b8c45a,c66318bb,34829eb7,11100666) ,S(d07bddff,d491a2fe,1ea59fbd,7c121217,29659ca5,de46658b,26b1460b,13c03c56,b2ad4708,cd3c97dd,f9c40e2,a1de04d5,61d963ff,8cc2eea7,6be3f60c,2b405ce7) ,S(82403e7c,5d3016af,3765ec4c,396ce8e1,f8da45c,434b8257,10edab41,bb6a4d51,d09661b,e27cb767,4456badd,b3e84051,99ab6ccc,4ec67c1b,11e92ead,7b463b19) @@ -8411,7 +8262,7 @@ static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G ,S(1f56f096,b18a7499,a153a5ae,acf8be05,8496dd23,da8e6c19,215628fb,c0567ed0,fef22b8a,3b52f490,83004436,b65cd69,c94189f4,1a93c0d5,1fc13cb4,379dff58) ,S(1d9f69b1,a4a47432,e386f525,234aa30,79e947cf,cf203297,4e0fc05b,638e213b,d898ec17,949c0761,b38500c3,a2b1da24,5438d5b3,d3f6f720,41f15d6e,e4d4ccbb) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 16 +#if WINDOW_G > 6 ,S(128c913,4d9dcb78,12fc4361,5c67ad0,55213354,dc8008b1,aeb5a9dc,fb629efd,fee3e54a,dd152610,d9725936,99d662,c160c8e4,ec6f76e4,5ff41818,be67c96) ,S(21ec012f,5a95b94d,244b8d51,9756075c,301f2854,8e2c51fc,49c0e3d9,d1a9685,2def2105,77af497f,4c7fef71,6949f28e,7418eda6,fd5fc162,d128de19,3cde08ae) ,S(688f5202,fb9d8bc0,9e480e89,4c7cfc74,761c3be7,7dafb11c,58422836,3e331cc5,96ba7d59,63b541a7,2ec7cabd,92403434,1a393eaf,89eebd94,62d9c218,c7302cd3) @@ -8429,7 +8280,7 @@ static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G ,S(144e88f6,3e73abff,72cac11e,7ddccf79,19e744e6,278941ae,18d1b797,e098e4e5,63cdbf3,5df3c655,c58197f,ea54633d,158705cf,7dc2eb3b,4e09f83c,3021837c) ,S(9436e3dc,489ecd8e,2d16a739,c9c73e3d,60e5bc93,68157039,75b8efbd,5c3a9081,1460531f,50cb6ebf,d1aa7806,ea84e7f7,8e8d76b2,b3a66d5e,3a0bf60,39a7e59c) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 32 +#if WINDOW_G > 7 ,S(9d3c2561,7a56d10b,46d9b01a,1710d193,e840e005,df669e76,1936c275,20890db9,6bbdc0bc,4c4ae9bc,c2dfee9b,82da9b94,1f89ffcd,e8af2aca,4467ce3,78521ea3) ,S(29f98e50,f51b7f8b,e18c6ae0,b453c4f2,d0aca5a8,b0e61d2d,dda8506,3fdb76c8,daf3bcdc,ae8e031c,73eb8b21,14058063,58a6ec30,ad379186,df80e3c7,f0e5d28f) ,S(d67d30c2,c71daa36,1805e31,1dd6046e,17a89752,94d76e1a,538af074,4dc22c94,48b9b0e7,12c807b0,b92e690a,a2e068cc,e87ebbbe,aaf4bd96,9c1114bb,a54f670c) @@ -8463,7 +8314,7 @@ static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G ,S(6f97ac0f,27b87905,6b442d13,e566978e,91f0cc1d,d6ac1e64,e9764a35,325dd1b7,83c6e70c,fac6c707,226ce1cc,691b38a0,7e937f5a,5f2d9c81,4dd0d3ff,9f433d32) ,S(72c5d60f,eb014e2d,ba8265ca,d454f261,2d6abcd4,b2236bad,c94c4801,561dce1f,e3119a19,7ef91963,b3b28216,3c5d3acb,97b281b6,d246cbf0,690b40da,63978fe2) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 64 +#if WINDOW_G > 8 ,S(a96d2da0,1b10186,6998659d,f441a1b0,2af32b94,aae8c6ea,707d9ed0,d5f33825,660d7d83,5da5235,9f7cfd41,28c370aa,5659ea71,16a91690,6c0e8108,a513f9f) ,S(2cce6f63,4d815ecc,1981d200,87616677,d906aa27,990c4875,17314dc5,5be3c4fa,615210dd,bd599e91,1b6f997a,fd05475,b33cb274,c9ecb6e5,d3c23323,beba4b50) ,S(992b0084,525dd399,d98602d9,8b8d53b2,4558fafc,758a2f46,60e89bd6,a645f0c4,83ca98d2,26545a29,8c45f40b,11420602,f5a5c70e,595eea57,2da64d61,a4e2f98d) @@ -8529,7 +8380,7 @@ static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G ,S(7590a4a,627d5e90,e42a4b0f,6be6497a,f906182d,d2dddc48,a8b6bbfd,f56c0504,d611e21a,b5498760,5c97e878,baa464bc,cc5bd875,353b69f8,1f93ce2a,a6c38587) ,S(94b1da0f,b310e056,db0dff72,81db3362,1fcc555d,bf3c973b,76097908,7fe19d6a,8318893d,d5b41a56,33a2ab4,ae4b953c,45c42e9c,8f2fd159,85286de3,fd4fc217) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 128 +#if WINDOW_G > 9 ,S(b5af4299,bcdacef1,e07d081,daec2cfa,d6f8f821,38e151a5,f20e6d52,84c9a6cb,c0984407,8a7db82d,f572987e,b137dc09,c8cf65fd,aedcb20,43b2479b,ab95448d) ,S(5f49ad43,70744587,3980a153,c851829b,f8ef6141,9889bb0c,3c476847,6939c3e3,5c40d385,20f56c3d,ba08ae1,b40fc24a,2ae25c94,45cae0f7,d01d1800,747e04eb) ,S(f6bb067f,88ccc11c,64e30d1a,e6893942,16bea3bf,26ec9c64,5cde1b9e,487da385,315a476d,7268978c,d89d4ec8,adde4a83,28dbfdd9,f2bf44fe,ad4ed721,78288f55) @@ -8659,7 +8510,7 @@ static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G ,S(8ac79852,75673818,69fe93c9,6141493e,72ca344,790487b,d5425ed6,9f5c5c18,bb314248,fcbfc867,d1972e04,b9ef1f90,775375f9,9d25bcec,684c72c9,bdd1c08e) ,S(560e9711,88cbc7ce,c61f3bf4,45f0ade3,6f3f174d,219a160,5f9c8692,3f848b9d,9e92dace,6775cc67,bfbbf21f,c64e6e9d,4d133f8a,c18ee277,bc80ef6d,d1b9cd2f) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 256 +#if WINDOW_G > 10 ,S(8c464204,4b95eb66,cc95ca08,8469a1c0,28eea52f,7f709fe,e6d90700,f5fb943a,bf10fc5d,7bc25181,301b3a61,5ebea597,a3492025,953c3aa5,1a11271e,689d0223) ,S(d293f74c,f3578b71,35377247,cd8b0367,7f2245da,f87453cb,4d8d1cc2,871eb5aa,86c2013a,61dfea14,63e45931,eb09050f,f080e3d4,ae357423,ba7afbed,a64a6f26) ,S(35997241,ae757b1f,c767611e,c76eb935,fefbf7a7,33666aff,4c6bd744,d7687d35,bcbea61f,246bcd4c,c3c7fd35,7bd393da,2f36e0ef,cca0df9c,5994f96f,c44b2aa0) @@ -8917,7 +8768,7 @@ static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G ,S(6ca7e032,8bf5d67a,b804d431,e5f709e,bd3156e0,1d4511da,1dc67394,24d2e659,c428b133,f3683909,6551c2ff,2f870d80,d80aaaf4,6d2b1a69,7722057,5eca2647) ,S(60df19a9,83e9086c,4cbd20ba,fbafa8b2,346ae4ee,9c1ad4dd,99959e91,2df530d3,dae7b854,29f817a0,421c2f1e,e4e8e4d,a09d60f8,84701e31,d7a8b7b0,3b79cc48) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 512 +#if WINDOW_G > 11 ,S(6f18d50e,5ef5f2ad,bad80ea1,c59a3847,5c22ff05,6ba52c7,e1d26d6d,d3686bce,d1d7ea0f,a166efd0,facf5c83,bc3786e0,d3f3405d,5b4578f5,13a336ad,f0d7d7a9) ,S(b634dc9d,5ed51336,4ac9569a,8ddee9d9,fcdfe00e,65e59233,b3be8a07,2fd949e0,d72e46e2,c61b2575,f25a505c,bdc3456e,fdf18976,6562a1a7,e86d036,eb31db69) ,S(5a37fcf0,2dba24f3,e6646171,43dbc5ab,40d91983,69f5cf0e,4fc566fd,97445910,a960d1d8,13f8746c,662a9582,614c7847,33e6153d,2975cb59,c3342463,75c69d1e) @@ -9431,7 +9282,7 @@ static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G ,S(edc9e8b1,3c61a1e0,8f93be12,495084ed,b5a90eca,4f11dc03,cd217b1a,56285a2c,66c2fd21,7e8fac7,4fd43b1b,58c80661,b0e8df85,a2fddfda,5e9f99fe,621e1f3d) ,S(dd94295f,8388a498,2aaa4164,927b81ba,cae9d002,b3ddb6b6,97082c70,f1e2c66e,838c060c,d409c1ea,9bcd9e8c,b1fac83f,3b08c2b2,482d8f4b,fd3ebc18,8d6706b) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 1024 +#if WINDOW_G > 12 ,S(7e068e04,dfc0be48,e5c0d3b3,5bfc734e,96e96ddd,d0ac4876,92f74535,685ab7e,df2cd146,90d225c8,d04052e6,93f14bf,69351e08,79883646,2c88401e,4ec70d0a) ,S(73a9bfcf,d10aac9b,46e659f,76c439a0,b7c2a073,7dec217a,21f43f39,949a5052,73b91529,3ea7b052,682062c,8f86cbf,bf379df6,91a9cec2,4a1424a9,b3be10dd) ,S(efddff84,c8cc754,e6e34678,d85809bc,55cc224b,f69be05a,daa847ec,d408c55b,65dd8f41,8264aab2,efe6ed7e,c45b4ac,8aac218a,3b6713fc,1736dd6d,c2f188d5) @@ -10457,7 +10308,7 @@ static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G ,S(8a663e7,40cad237,12dad6f9,1bb5d266,30542933,853e02eb,665e198d,a5c6e53b,e206b399,51175d15,daccf711,63b0918c,786a8fe,2077812,c0c1eee6,bb5c1e99) ,S(2b0956cb,e0ca91ee,f44fac0a,76cc0b00,5f4a5ae8,27e63696,fe1aa8b4,a92941a1,a31e6fa8,dd454eaf,90ee1e11,62627e3,3f84b8fe,da29f423,ddf2a962,386cffd2) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 2048 +#if WINDOW_G > 13 ,S(e0144151,7a2ac970,eb6381df,7e11fb4c,6b009980,6a0d330,d5429126,e662c3bd,8238ce9b,a691c80c,21563934,18d18dbf,aeb3fd34,48863a1e,7f4ba360,408dfcee) ,S(be3213e,8b062f33,caf16c53,5a0b666,f344e0d7,1e28aeba,8b215a3,7ec86c37,552523ba,eaca38a4,cd795683,852a2643,550fb83d,d1db0adc,3f1b29c9,7d51cd1f) ,S(623393b6,bfbfbd64,fc7aa1db,9e58e274,1c18eb6d,b5eb30ab,c4fe167e,a9e8ff2b,7c0e4174,f0fd5bf2,a025e316,fa3b7b97,1339a197,b52b0b50,bad4dfe,34e42cd3) @@ -12507,7 +12358,7 @@ static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G ,S(4beaa213,3c6161d0,c7da6d7c,8eb09cba,2e8ca505,a790a7d3,9d0c16b,8053bb52,da4c083c,9cbdda2e,c6626d8f,e4b2ee13,703496c,c298bffa,db1acdca,99d4f6d5) ,S(a8d31ec6,53ce1834,a78de363,c5f9abd1,8594b34,4d34f5fc,8a10e81f,5804831,b4d6a9cd,7cbbe370,9edb5601,cb7c8ba4,8c462c18,594a4bce,64f4c286,dac5cff9) #endif -#if ECMULT_TABLE_SIZE(WINDOW_G) > 4096 +#if WINDOW_G > 14 ,S(a8f11586,f3df4945,a753c485,ee0fd4d,e410771d,bddc1b26,c9ff10e0,77b915b7,a4ad6f16,dbd741bc,71b2dfd2,dd2d340,3816bf73,4e73cc10,abcfa6bb,d0f161a4) ,S(13e697c3,812d4772,254082da,372892d4,e1a66e1a,eb16bbd4,f7a0d531,c979cb2,87fa7baa,f6def12d,31e42c14,f672c0d6,a9d0e2e1,ceee2546,d65bd01,c18df57f) ,S(3cae4590,821a9697,a5963269,b44f0222,98f60021,b6048b3f,49c6fd4d,8650c7a,e03f8745,60418449,ad97f28,41664745,349329d,268c1c43,86e25147,6e44b234) @@ -16606,6 +16457,4 @@ static const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G ,S(1b9a142f,fc4d03ea,4b079f2d,b05fad98,8ddb2d32,b359967f,c173801f,63320825,59bda7ed,5b691c20,4fc8f8ac,f53be298,ae628954,a8134d0f,dd097e67,be9ff9b6) #endif }; -#endif #undef S -#endif diff --git a/src/precomputed_ecmult.h b/src/precomputed_ecmult.h new file mode 100644 index 00000000000000..949b62c874b308 --- /dev/null +++ b/src/precomputed_ecmult.h @@ -0,0 +1,35 @@ +/***************************************************************************************************** + * Copyright (c) 2013, 2014, 2017, 2021 Pieter Wuille, Andrew Poelstra, Jonas Nick, Russell O'Connor * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *****************************************************************************************************/ + +#ifndef SECP256K1_PRECOMPUTED_ECMULT_H +#define SECP256K1_PRECOMPUTED_ECMULT_H + +#ifdef __cplusplus +extern "C" { +#endif + +#include "group.h" +#if defined(EXHAUSTIVE_TEST_ORDER) +#if EXHAUSTIVE_TEST_ORDER == 13 +# define WINDOW_G 4 +# elif EXHAUSTIVE_TEST_ORDER == 199 +# define WINDOW_G 8 +# else +# error No known generator for the specified exhaustive test group order. +# endif +static secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)]; +static secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; +#else /* !defined(EXHAUSTIVE_TEST_ORDER) */ +# define WINDOW_G ECMULT_WINDOW_SIZE +extern const secp256k1_ge_storage secp256k1_pre_g[ECMULT_TABLE_SIZE(WINDOW_G)]; +extern const secp256k1_ge_storage secp256k1_pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; +#endif /* defined(EXHAUSTIVE_TEST_ORDER) */ + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_PRECOMPUTED_ECMULT_H */ diff --git a/src/ecmult_gen_static_prec_table.h b/src/precomputed_ecmult_gen.c similarity index 99% rename from src/ecmult_gen_static_prec_table.h rename to src/precomputed_ecmult_gen.c index bf4e5ea248f312..d67291fcf505a1 100644 --- a/src/ecmult_gen_static_prec_table.h +++ b/src/precomputed_ecmult_gen.c @@ -1,13 +1,17 @@ -/* This file was automatically generated by gen_ecmult_gen_static_prec_table. */ +/* This file was automatically generated by precompute_ecmult_gen. */ /* See ecmult_gen_impl.h for details about the contents of this file. */ -#ifndef SECP256K1_ECMULT_GEN_STATIC_PREC_TABLE_H -#define SECP256K1_ECMULT_GEN_STATIC_PREC_TABLE_H +#if defined HAVE_CONFIG_H +# include "libsecp256k1-config.h" +#endif +#include "../include/secp256k1.h" #include "group.h" -#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u) +#include "ecmult_gen.h" +#include "precomputed_ecmult_gen.h" #ifdef EXHAUSTIVE_TEST_ORDER -static secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)]; -#else -static const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)] = { +# error Cannot compile precomputed_ecmult_gen.c in exhaustive test mode +#endif /* EXHAUSTIVE_TEST_ORDER */ +#define S(a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p) SECP256K1_GE_STORAGE_CONST(0x##a##u,0x##b##u,0x##c##u,0x##d##u,0x##e##u,0x##f##u,0x##g##u,0x##h##u,0x##i##u,0x##j##u,0x##k##u,0x##l##u,0x##m##u,0x##n##u,0x##o##u,0x##p##u) +const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)] = { #if ECMULT_GEN_PREC_BITS == 2 {S(3a9ed373,6eed3eec,9aeb5ac0,21b54652,56817b1f,8de6cd0,fbcee548,ba044bb5,7bcc5928,bdc9c023,dfc663b8,9e4f6969,ab751798,8e600ec1,d242010c,45c7974a), S(e44d7675,c3cb2857,4e133c01,a74f4afc,5ce684f8,4a789711,603f7c4f,50abef58,25bcb62f,fe2e2ce2,196ad86c,a006e20,8c64d21b,b25320a3,b5574b9c,1e1bfb4b), @@ -9743,6 +9747,4 @@ S(244b87a4,fcecef37,76c16c5c,24c7785,be3b3c13,46595363,b8c066ec,45bfe561,9642f5f S(9de52b81,157165cc,aef44485,4c2b3535,a599a79,80d024de,5334b385,ecbb2e91,74fca165,26fe2f87,a41ce510,4dd5634,5cf98c11,803c0392,3eb4b8b7,60240c02)} #endif }; -#endif /* EXHAUSTIVE_TEST_ORDER */ -#undef SC -#endif /* SECP256K1_ECMULT_GEN_STATIC_PREC_TABLE_H */ +#undef S diff --git a/src/precomputed_ecmult_gen.h b/src/precomputed_ecmult_gen.h new file mode 100644 index 00000000000000..7256ad2e3049e4 --- /dev/null +++ b/src/precomputed_ecmult_gen.h @@ -0,0 +1,26 @@ +/********************************************************************************* + * Copyright (c) 2013, 2014, 2015, 2021 Thomas Daede, Cory Fields, Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or https://www.opensource.org/licenses/mit-license.php. * + *********************************************************************************/ + +#ifndef SECP256K1_PRECOMPUTED_ECMULT_GEN_H +#define SECP256K1_PRECOMPUTED_ECMULT_GEN_H + +#ifdef __cplusplus +extern "C" { +#endif + +#include "group.h" +#include "ecmult_gen.h" +#ifdef EXHAUSTIVE_TEST_ORDER +static secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)]; +#else +extern const secp256k1_ge_storage secp256k1_ecmult_gen_prec_table[ECMULT_GEN_PREC_N(ECMULT_GEN_PREC_BITS)][ECMULT_GEN_PREC_G(ECMULT_GEN_PREC_BITS)]; +#endif /* defined(EXHAUSTIVE_TEST_ORDER) */ + +#ifdef __cplusplus +} +#endif + +#endif /* SECP256K1_PRECOMPUTED_ECMULT_GEN_H */ diff --git a/src/secp256k1.c b/src/secp256k1.c index 36fde24c3d1477..270490f207a422 100644 --- a/src/secp256k1.c +++ b/src/secp256k1.c @@ -423,8 +423,12 @@ static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *m unsigned int offset = 0; secp256k1_rfc6979_hmac_sha256 rng; unsigned int i; + secp256k1_scalar msg; + unsigned char msgmod32[32]; + secp256k1_scalar_set_b32(&msg, msg32, NULL); + secp256k1_scalar_get_b32(msgmod32, &msg); /* We feed a byte array to the PRNG as input, consisting of: - * - the private key (32 bytes) and message (32 bytes), see RFC 6979 3.2d. + * - the private key (32 bytes) and reduced message (32 bytes), see RFC 6979 3.2d. * - optionally 32 extra bytes of data, see RFC 6979 3.6 Additional Data. * - optionally 16 extra bytes with the algorithm name. * Because the arguments have distinct fixed lengths it is not possible for @@ -432,7 +436,7 @@ static int nonce_function_rfc6979(unsigned char *nonce32, const unsigned char *m * nonces. */ buffer_append(keydata, &offset, key32, 32); - buffer_append(keydata, &offset, msg32, 32); + buffer_append(keydata, &offset, msgmod32, 32); if (data != NULL) { buffer_append(keydata, &offset, data, 32); } @@ -761,3 +765,7 @@ int secp256k1_tagged_sha256(const secp256k1_context* ctx, unsigned char *hash32, #ifdef ENABLE_MODULE_SCHNORRSIG # include "modules/schnorrsig/main_impl.h" #endif + +#ifdef ENABLE_MODULE_ELLSQ +# include "modules/ellsq/main_impl.h" +#endif diff --git a/src/testrand.h b/src/testrand.h index 667d1867bd6154..bd149bb1b486c9 100644 --- a/src/testrand.h +++ b/src/testrand.h @@ -17,11 +17,14 @@ SECP256K1_INLINE static void secp256k1_testrand_seed(const unsigned char *seed16); /** Generate a pseudorandom number in the range [0..2**32-1]. */ -static uint32_t secp256k1_testrand32(void); +SECP256K1_INLINE static uint32_t secp256k1_testrand32(void); + +/** Generate a pseudorandom number in the range [0..2**64-1]. */ +SECP256K1_INLINE static uint64_t secp256k1_testrand64(void); /** Generate a pseudorandom number in the range [0..2**bits-1]. Bits must be 1 or * more. */ -static uint32_t secp256k1_testrand_bits(int bits); +SECP256K1_INLINE static uint64_t secp256k1_testrand_bits(int bits); /** Generate a pseudorandom number in the range [0..range-1]. */ static uint32_t secp256k1_testrand_int(uint32_t range); diff --git a/src/testrand_impl.h b/src/testrand_impl.h index c8d30ef6a814ba..e9b9d7ded44bc2 100644 --- a/src/testrand_impl.h +++ b/src/testrand_impl.h @@ -14,37 +14,64 @@ #include "testrand.h" #include "hash.h" -static secp256k1_rfc6979_hmac_sha256 secp256k1_test_rng; -static uint32_t secp256k1_test_rng_precomputed[8]; -static int secp256k1_test_rng_precomputed_used = 8; +static uint64_t secp256k1_test_state[4]; static uint64_t secp256k1_test_rng_integer; static int secp256k1_test_rng_integer_bits_left = 0; SECP256K1_INLINE static void secp256k1_testrand_seed(const unsigned char *seed16) { - secp256k1_rfc6979_hmac_sha256_initialize(&secp256k1_test_rng, seed16, 16); + static const unsigned char PREFIX[19] = "secp256k1 test init"; + unsigned char out32[32]; + secp256k1_sha256 hash; + int i; + + /* Use SHA256(PREFIX || seed16) as initial state. */ + secp256k1_sha256_initialize(&hash); + secp256k1_sha256_write(&hash, PREFIX, sizeof(PREFIX)); + secp256k1_sha256_write(&hash, seed16, 16); + secp256k1_sha256_finalize(&hash, out32); + for (i = 0; i < 4; ++i) { + uint64_t s = 0; + int j; + for (j = 0; j < 8; ++j) s = (s << 8) | out32[8*i + j]; + secp256k1_test_state[i] = s; + } + secp256k1_test_rng_integer_bits_left = 0; } -SECP256K1_INLINE static uint32_t secp256k1_testrand32(void) { - if (secp256k1_test_rng_precomputed_used == 8) { - secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, (unsigned char*)(&secp256k1_test_rng_precomputed[0]), sizeof(secp256k1_test_rng_precomputed)); - secp256k1_test_rng_precomputed_used = 0; - } - return secp256k1_test_rng_precomputed[secp256k1_test_rng_precomputed_used++]; +SECP256K1_INLINE static uint64_t rotl(const uint64_t x, int k) { + return (x << k) | (x >> (64 - k)); +} + +SECP256K1_INLINE static uint64_t secp256k1_testrand64(void) { + /* Test-only Xoshiro256++ RNG. See https://prng.di.unimi.it/ */ + const uint64_t result = rotl(secp256k1_test_state[0] + secp256k1_test_state[3], 23) + secp256k1_test_state[0]; + const uint64_t t = secp256k1_test_state[1] << 17; + secp256k1_test_state[2] ^= secp256k1_test_state[0]; + secp256k1_test_state[3] ^= secp256k1_test_state[1]; + secp256k1_test_state[1] ^= secp256k1_test_state[2]; + secp256k1_test_state[0] ^= secp256k1_test_state[3]; + secp256k1_test_state[2] ^= t; + secp256k1_test_state[3] = rotl(secp256k1_test_state[3], 45); + return result; } -static uint32_t secp256k1_testrand_bits(int bits) { - uint32_t ret; +SECP256K1_INLINE static uint64_t secp256k1_testrand_bits(int bits) { + uint64_t ret; if (secp256k1_test_rng_integer_bits_left < bits) { - secp256k1_test_rng_integer |= (((uint64_t)secp256k1_testrand32()) << secp256k1_test_rng_integer_bits_left); - secp256k1_test_rng_integer_bits_left += 32; + secp256k1_test_rng_integer = secp256k1_testrand64(); + secp256k1_test_rng_integer_bits_left = 64; } ret = secp256k1_test_rng_integer; secp256k1_test_rng_integer >>= bits; secp256k1_test_rng_integer_bits_left -= bits; - ret &= ((~((uint32_t)0)) >> (32 - bits)); + ret &= ((~((uint64_t)0)) >> (64 - bits)); return ret; } +SECP256K1_INLINE static uint32_t secp256k1_testrand32(void) { + return secp256k1_testrand_bits(32); +} + static uint32_t secp256k1_testrand_int(uint32_t range) { /* We want a uniform integer between 0 and range-1, inclusive. * B is the smallest number such that range <= 2**B. @@ -85,7 +112,19 @@ static uint32_t secp256k1_testrand_int(uint32_t range) { } static void secp256k1_testrand256(unsigned char *b32) { - secp256k1_rfc6979_hmac_sha256_generate(&secp256k1_test_rng, b32, 32); + int i; + for (i = 0; i < 4; ++i) { + uint64_t val = secp256k1_testrand64(); + b32[0] = val; + b32[1] = val >> 8; + b32[2] = val >> 16; + b32[3] = val >> 24; + b32[4] = val >> 32; + b32[5] = val >> 40; + b32[6] = val >> 48; + b32[7] = val >> 56; + b32 += 8; + } } static void secp256k1_testrand_bytes_test(unsigned char *bytes, size_t len) { @@ -109,7 +148,7 @@ static void secp256k1_testrand256_test(unsigned char *b32) { } static void secp256k1_testrand_flip(unsigned char *b, size_t len) { - b[secp256k1_testrand_int(len)] ^= (1 << secp256k1_testrand_int(8)); + b[secp256k1_testrand_int(len)] ^= (1 << secp256k1_testrand_bits(3)); } static void secp256k1_testrand_init(const char* hexseed) { diff --git a/src/tests.c b/src/tests.c index 712fc655fa135d..69934b8a027348 100644 --- a/src/tests.c +++ b/src/tests.c @@ -28,6 +28,8 @@ #include "modinv64_impl.h" #endif +#define CONDITIONAL_TEST(cnt, nam) if (count < (cnt)) { printf("Skipping %s (iteration count too low)\n", nam); } else + static int count = 64; static secp256k1_context *ctx = NULL; @@ -100,6 +102,12 @@ void random_group_element_jacobian_test(secp256k1_gej *gej, const secp256k1_ge * gej->infinity = ge->infinity; } +void random_gej_test(secp256k1_gej *gej) { + secp256k1_ge ge; + random_group_element_test(&ge); + random_group_element_jacobian_test(gej, &ge); +} + void random_scalar_order_test(secp256k1_scalar *num) { do { unsigned char b32[32]; @@ -790,7 +798,7 @@ void signed30_to_uint16(uint16_t* out, const secp256k1_modinv32_signed30* in) { void mutate_sign_signed30(secp256k1_modinv32_signed30* x) { int i; for (i = 0; i < 16; ++i) { - int pos = secp256k1_testrand_int(8); + int pos = secp256k1_testrand_bits(3); if (x->v[pos] > 0 && x->v[pos + 1] <= 0x3fffffff) { x->v[pos] -= 0x40000000; x->v[pos + 1] += 1; @@ -811,12 +819,32 @@ void test_modinv32_uint16(uint16_t* out, const uint16_t* in, const uint16_t* mod uint16_to_signed30(&x, in); nonzero = (x.v[0] | x.v[1] | x.v[2] | x.v[3] | x.v[4] | x.v[5] | x.v[6] | x.v[7] | x.v[8]) != 0; uint16_to_signed30(&m.modulus, mod); - mutate_sign_signed30(&m.modulus); /* compute 1/modulus mod 2^30 */ m.modulus_inv30 = modinv2p64(m.modulus.v[0]) & 0x3fffffff; CHECK(((m.modulus_inv30 * m.modulus.v[0]) & 0x3fffffff) == 1); + /* Test secp256k1_jacobi32_maybe_var. */ + { + int jac; + uint16_t sqr[16], negone[16]; + mulmod256(sqr, in, in, mod); + uint16_to_signed30(&x, sqr); + /* Compute jacobi symbol of in^2, which must be 0 or 1 (or uncomputable). */ + jac = secp256k1_jacobi32_maybe_var(&x, &m); + CHECK(jac == -2 || jac == nonzero); + /* Then compute the jacobi symbol of -(in^2). x and -x have opposite + * jacobi symbols if and only if (mod % 4) == 3. */ + negone[0] = mod[0] - 1; + for (i = 1; i < 16; ++i) negone[i] = mod[i]; + mulmod256(sqr, sqr, negone, mod); + uint16_to_signed30(&x, sqr); + jac = secp256k1_jacobi32_maybe_var(&x, &m); + CHECK(jac == -2 || jac == (1 - (mod[0] & 2)) * nonzero); + } + + uint16_to_signed30(&x, in); + mutate_sign_signed30(&m.modulus); for (vartime = 0; vartime < 2; ++vartime) { /* compute inverse */ (vartime ? secp256k1_modinv32_var : secp256k1_modinv32)(&x, &m); @@ -862,7 +890,7 @@ void mutate_sign_signed62(secp256k1_modinv64_signed62* x) { static const int64_t M62 = (int64_t)(UINT64_MAX >> 2); int i; for (i = 0; i < 8; ++i) { - int pos = secp256k1_testrand_int(4); + int pos = secp256k1_testrand_bits(2); if (x->v[pos] > 0 && x->v[pos + 1] <= M62) { x->v[pos] -= (M62 + 1); x->v[pos + 1] += 1; @@ -884,12 +912,32 @@ void test_modinv64_uint16(uint16_t* out, const uint16_t* in, const uint16_t* mod uint16_to_signed62(&x, in); nonzero = (x.v[0] | x.v[1] | x.v[2] | x.v[3] | x.v[4]) != 0; uint16_to_signed62(&m.modulus, mod); - mutate_sign_signed62(&m.modulus); /* compute 1/modulus mod 2^62 */ m.modulus_inv62 = modinv2p64(m.modulus.v[0]) & M62; CHECK(((m.modulus_inv62 * m.modulus.v[0]) & M62) == 1); + /* Test secp256k1_jacobi64_maybe_var. */ + { + int jac; + uint16_t sqr[16], negone[16]; + mulmod256(sqr, in, in, mod); + uint16_to_signed62(&x, sqr); + /* Compute jacobi symbol of in^2, which must be 0 or 1 (or uncomputable). */ + jac = secp256k1_jacobi64_maybe_var(&x, &m); + CHECK(jac == -2 || jac == nonzero); + /* Then compute the jacobi symbol of -(in^2). x and -x have opposite + * jacobi symbols if and only if (mod % 4) == 3. */ + negone[0] = mod[0] - 1; + for (i = 1; i < 16; ++i) negone[i] = mod[i]; + mulmod256(sqr, sqr, negone, mod); + uint16_to_signed62(&x, sqr); + jac = secp256k1_jacobi64_maybe_var(&x, &m); + CHECK(jac == -2 || jac == (1 - (mod[0] & 2)) * nonzero); + } + + uint16_to_signed62(&x, in); + mutate_sign_signed62(&m.modulus); for (vartime = 0; vartime < 2; ++vartime) { /* compute inverse */ (vartime ? secp256k1_modinv64_var : secp256k1_modinv64)(&x, &m); @@ -2451,13 +2499,16 @@ void run_field_convert(void) { CHECK(secp256k1_memcmp_var(&fes2, &fes, sizeof(fes)) == 0); } -int fe_secp256k1_memcmp_var(const secp256k1_fe *a, const secp256k1_fe *b) { - secp256k1_fe t = *b; +/* Returns true if two field elements have the same representation. */ +int fe_identical(const secp256k1_fe *a, const secp256k1_fe *b) { + int ret = 1; #ifdef VERIFY - t.magnitude = a->magnitude; - t.normalized = a->normalized; + ret &= (a->magnitude == b->magnitude); + ret &= (a->normalized == b->normalized); #endif - return secp256k1_memcmp_var(a, &t, sizeof(secp256k1_fe)); + /* Compare the struct member that holds the limbs. */ + ret &= (secp256k1_memcmp_var(a->n, b->n, sizeof(a->n)) == 0); + return ret; } void run_field_misc(void) { @@ -2483,13 +2534,13 @@ void run_field_misc(void) { CHECK(x.normalized && x.magnitude == 1); #endif secp256k1_fe_cmov(&x, &x, 1); - CHECK(fe_secp256k1_memcmp_var(&x, &z) != 0); - CHECK(fe_secp256k1_memcmp_var(&x, &q) == 0); + CHECK(!fe_identical(&x, &z)); + CHECK(fe_identical(&x, &q)); secp256k1_fe_cmov(&q, &z, 1); #ifdef VERIFY CHECK(!q.normalized && q.magnitude == z.magnitude); #endif - CHECK(fe_secp256k1_memcmp_var(&q, &z) == 0); + CHECK(fe_identical(&q, &z)); secp256k1_fe_normalize_var(&x); secp256k1_fe_normalize_var(&z); CHECK(!secp256k1_fe_equal_var(&x, &z)); @@ -2659,8 +2710,10 @@ void run_sqrt(void) { for (j = 0; j < count; j++) { random_fe(&x); secp256k1_fe_sqr(&s, &x); + CHECK(secp256k1_fe_jacobi_var(&s) == 1); test_sqrt(&s, &x); secp256k1_fe_negate(&t, &s, 1); + CHECK(secp256k1_fe_jacobi_var(&t) == -1); test_sqrt(&t, NULL); secp256k1_fe_mul(&t, &s, &ns); test_sqrt(&t, NULL); @@ -3338,6 +3391,37 @@ void run_ge(void) { test_intialized_inf(); } +void test_gej_cmov(const secp256k1_gej *a, const secp256k1_gej *b) { + secp256k1_gej t = *a; + secp256k1_gej_cmov(&t, b, 0); + CHECK(gej_xyz_equals_gej(&t, a)); + secp256k1_gej_cmov(&t, b, 1); + CHECK(gej_xyz_equals_gej(&t, b)); +} + +void run_gej(void) { + int i; + secp256k1_gej a, b; + + /* Tests for secp256k1_gej_cmov */ + for (i = 0; i < count; i++) { + secp256k1_gej_set_infinity(&a); + secp256k1_gej_set_infinity(&b); + test_gej_cmov(&a, &b); + + random_gej_test(&a); + test_gej_cmov(&a, &b); + test_gej_cmov(&b, &a); + + b = a; + test_gej_cmov(&a, &b); + + random_gej_test(&b); + test_gej_cmov(&a, &b); + test_gej_cmov(&b, &a); + } +} + void test_ec_combine(void) { secp256k1_scalar sum = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); secp256k1_pubkey data[6]; @@ -4052,6 +4136,174 @@ void test_ecmult_multi(secp256k1_scratch *scratch, secp256k1_ecmult_multi_func e } } +int test_ecmult_multi_random(secp256k1_scratch *scratch) { + /* Large random test for ecmult_multi_* functions which exercises: + * - Few or many inputs (0 up to 128, roughly exponentially distributed). + * - Few or many 0*P or a*INF inputs (roughly uniformly distributed). + * - Including or excluding an nonzero a*G term (or such a term at all). + * - Final expected result equal to infinity or not (roughly 50%). + * - ecmult_multi_var, ecmult_strauss_single_batch, ecmult_pippenger_single_batch + */ + + /* These 4 variables define the eventual input to the ecmult_multi function. + * g_scalar is the G scalar fed to it (or NULL, possibly, if g_scalar=0), and + * scalars[0..filled-1] and gejs[0..filled-1] are the scalars and points + * which form its normal inputs. */ + int filled = 0; + secp256k1_scalar g_scalar = SECP256K1_SCALAR_CONST(0, 0, 0, 0, 0, 0, 0, 0); + secp256k1_scalar scalars[128]; + secp256k1_gej gejs[128]; + /* The expected result, and the computed result. */ + secp256k1_gej expected, computed; + /* Temporaries. */ + secp256k1_scalar sc_tmp; + secp256k1_ge ge_tmp; + /* Variables needed for the actual input to ecmult_multi. */ + secp256k1_ge ges[128]; + ecmult_multi_data data; + + int i; + /* Which multiplication function to use */ + int fn = secp256k1_testrand_int(3); + secp256k1_ecmult_multi_func ecmult_multi = fn == 0 ? secp256k1_ecmult_multi_var : + fn == 1 ? secp256k1_ecmult_strauss_batch_single : + secp256k1_ecmult_pippenger_batch_single; + /* Simulate exponentially distributed num. */ + int num_bits = 2 + secp256k1_testrand_int(6); + /* Number of (scalar, point) inputs (excluding g). */ + int num = secp256k1_testrand_int((1 << num_bits) + 1); + /* Number of those which are nonzero. */ + int num_nonzero = secp256k1_testrand_int(num + 1); + /* Whether we're aiming to create an input with nonzero expected result. */ + int nonzero_result = secp256k1_testrand_bits(1); + /* Whether we will provide nonzero g multiplicand. In some cases our hand + * is forced here based on num_nonzero and nonzero_result. */ + int g_nonzero = num_nonzero == 0 ? nonzero_result : + num_nonzero == 1 && !nonzero_result ? 1 : + (int)secp256k1_testrand_bits(1); + /* Which g_scalar pointer to pass into ecmult_multi(). */ + const secp256k1_scalar* g_scalar_ptr = (g_nonzero || secp256k1_testrand_bits(1)) ? &g_scalar : NULL; + /* How many EC multiplications were performed in this function. */ + int mults = 0; + /* How many randomization steps to apply to the input list. */ + int rands = (int)secp256k1_testrand_bits(3); + if (rands > num_nonzero) rands = num_nonzero; + + secp256k1_gej_set_infinity(&expected); + secp256k1_gej_set_infinity(&gejs[0]); + secp256k1_scalar_set_int(&scalars[0], 0); + + if (g_nonzero) { + /* If g_nonzero, set g_scalar to nonzero value r. */ + random_scalar_order_test(&g_scalar); + if (!nonzero_result) { + /* If expected=0 is desired, add a (a*r, -(1/a)*g) term to compensate. */ + CHECK(num_nonzero > filled); + random_scalar_order_test(&sc_tmp); + secp256k1_scalar_mul(&scalars[filled], &sc_tmp, &g_scalar); + secp256k1_scalar_inverse_var(&sc_tmp, &sc_tmp); + secp256k1_scalar_negate(&sc_tmp, &sc_tmp); + secp256k1_ecmult_gen(&ctx->ecmult_gen_ctx, &gejs[filled], &sc_tmp); + ++filled; + ++mults; + } + } + + if (nonzero_result && filled < num_nonzero) { + /* If a nonzero result is desired, and there is space, add a random nonzero term. */ + random_scalar_order_test(&scalars[filled]); + random_group_element_test(&ge_tmp); + secp256k1_gej_set_ge(&gejs[filled], &ge_tmp); + ++filled; + } + + if (nonzero_result) { + /* Compute the expected result using normal ecmult. */ + CHECK(filled <= 1); + secp256k1_ecmult(&expected, &gejs[0], &scalars[0], &g_scalar); + mults += filled + g_nonzero; + } + + /* At this point we have expected = scalar_g*G + sum(scalars[i]*gejs[i] for i=0..filled-1). */ + CHECK(filled <= 1 + !nonzero_result); + CHECK(filled <= num_nonzero); + + /* Add entries to scalars,gejs so that there are num of them. All the added entries + * either have scalar=0 or point=infinity, so these do not change the expected result. */ + while (filled < num) { + if (secp256k1_testrand_bits(1)) { + secp256k1_gej_set_infinity(&gejs[filled]); + random_scalar_order_test(&scalars[filled]); + } else { + secp256k1_scalar_set_int(&scalars[filled], 0); + random_group_element_test(&ge_tmp); + secp256k1_gej_set_ge(&gejs[filled], &ge_tmp); + } + ++filled; + } + + /* Now perform cheapish transformations on gejs and scalars, for indices + * 0..num_nonzero-1, which do not change the expected result, but may + * convert some of them to be both non-0-scalar and non-infinity-point. */ + for (i = 0; i < rands; ++i) { + int j; + secp256k1_scalar v, iv; + /* Shuffle the entries. */ + for (j = 0; j < num_nonzero; ++j) { + int k = secp256k1_testrand_int(num_nonzero - j); + if (k != 0) { + secp256k1_gej gej = gejs[j]; + secp256k1_scalar sc = scalars[j]; + gejs[j] = gejs[j + k]; + scalars[j] = scalars[j + k]; + gejs[j + k] = gej; + scalars[j + k] = sc; + } + } + /* Perturb all consecutive pairs of inputs: + * a*P + b*Q -> (a+b)*P + b*(Q-P). */ + for (j = 0; j + 1 < num_nonzero; j += 2) { + secp256k1_gej gej; + secp256k1_scalar_add(&scalars[j], &scalars[j], &scalars[j+1]); + secp256k1_gej_neg(&gej, &gejs[j]); + secp256k1_gej_add_var(&gejs[j+1], &gejs[j+1], &gej, NULL); + } + /* Transform the last input: a*P -> (v*a) * ((1/v)*P). */ + CHECK(num_nonzero >= 1); + random_scalar_order_test(&v); + secp256k1_scalar_inverse(&iv, &v); + secp256k1_scalar_mul(&scalars[num_nonzero - 1], &scalars[num_nonzero - 1], &v); + secp256k1_ecmult(&gejs[num_nonzero - 1], &gejs[num_nonzero - 1], &iv, NULL); + ++mults; + } + + /* Shuffle all entries (0..num-1). */ + for (i = 0; i < num; ++i) { + int j = secp256k1_testrand_int(num - i); + if (j != 0) { + secp256k1_gej gej = gejs[i]; + secp256k1_scalar sc = scalars[i]; + gejs[i] = gejs[i + j]; + scalars[i] = scalars[i + j]; + gejs[i + j] = gej; + scalars[i + j] = sc; + } + } + + /* Compute affine versions of all inputs. */ + secp256k1_ge_set_all_gej_var(ges, gejs, filled); + /* Invoke ecmult_multi code. */ + data.sc = scalars; + data.pt = ges; + CHECK(ecmult_multi(&ctx->error_callback, scratch, &computed, g_scalar_ptr, ecmult_multi_callback, &data, filled)); + mults += num_nonzero + g_nonzero; + /* Compare with expected result. */ + secp256k1_gej_neg(&computed, &computed); + secp256k1_gej_add_var(&computed, &computed, &expected, NULL); + CHECK(secp256k1_gej_is_infinity(&computed)); + return mults; +} + void test_ecmult_multi_batch_single(secp256k1_ecmult_multi_func ecmult_multi) { secp256k1_scalar szero; secp256k1_scalar sc; @@ -4093,7 +4345,7 @@ void test_secp256k1_pippenger_bucket_window_inv(void) { * for a given scratch space. */ void test_ecmult_multi_pippenger_max_points(void) { - size_t scratch_size = secp256k1_testrand_int(256); + size_t scratch_size = secp256k1_testrand_bits(8); size_t max_size = secp256k1_pippenger_scratch_size(secp256k1_pippenger_bucket_window_inv(PIPPENGER_MAX_BUCKET_WINDOW-1)+512, 12); secp256k1_scratch *scratch; size_t n_points_supported; @@ -4242,6 +4494,7 @@ void test_ecmult_multi_batching(void) { void run_ecmult_multi_tests(void) { secp256k1_scratch *scratch; + int64_t todo = (int64_t)320 * count; test_secp256k1_pippenger_bucket_window_inv(); test_ecmult_multi_pippenger_max_points(); @@ -4252,6 +4505,9 @@ void run_ecmult_multi_tests(void) { test_ecmult_multi_batch_single(secp256k1_ecmult_pippenger_batch_single); test_ecmult_multi(scratch, secp256k1_ecmult_strauss_batch_single); test_ecmult_multi_batch_single(secp256k1_ecmult_strauss_batch_single); + while (todo > 0) { + todo -= test_ecmult_multi_random(scratch); + } secp256k1_scratch_destroy(&ctx->error_callback, scratch); /* Run test_ecmult_multi with space for exactly one point */ @@ -4347,7 +4603,7 @@ void test_constant_wnaf(const secp256k1_scalar *number, int w) { secp256k1_scalar_add(&x, &x, &t); } /* Skew num because when encoding numbers as odd we use an offset */ - secp256k1_scalar_set_int(&scalar_skew, 1 << (skew == 2)); + secp256k1_scalar_set_int(&scalar_skew, skew); secp256k1_scalar_add(&num, &num, &scalar_skew); CHECK(secp256k1_scalar_eq(&x, &num)); } @@ -4540,8 +4796,8 @@ void test_ecmult_accumulate(secp256k1_sha256* acc, const secp256k1_scalar* x, se } } -void test_ecmult_constants(void) { - /* Test ecmult_gen for: +void test_ecmult_constants_2bit(void) { + /* Using test_ecmult_accumulate, test ecmult for: * - For i in 0..36: * - Key i * - Key -i @@ -4584,8 +4840,81 @@ void test_ecmult_constants(void) { secp256k1_scratch_space_destroy(ctx, scratch); } +void test_ecmult_constants_sha(uint32_t prefix, size_t iter, const unsigned char* expected32) { + /* Using test_ecmult_accumulate, test ecmult for: + * - Key 0 + * - Key 1 + * - Key -1 + * - For i in range(iter): + * - Key SHA256(LE32(prefix) || LE16(i)) + */ + secp256k1_scalar x; + secp256k1_sha256 acc; + unsigned char b32[32]; + unsigned char inp[6]; + size_t i; + secp256k1_scratch_space *scratch = secp256k1_scratch_space_create(ctx, 65536); + + inp[0] = prefix & 0xFF; + inp[1] = (prefix >> 8) & 0xFF; + inp[2] = (prefix >> 16) & 0xFF; + inp[3] = (prefix >> 24) & 0xFF; + secp256k1_sha256_initialize(&acc); + secp256k1_scalar_set_int(&x, 0); + test_ecmult_accumulate(&acc, &x, scratch); + secp256k1_scalar_set_int(&x, 1); + test_ecmult_accumulate(&acc, &x, scratch); + secp256k1_scalar_negate(&x, &x); + test_ecmult_accumulate(&acc, &x, scratch); + + for (i = 0; i < iter; ++i) { + secp256k1_sha256 gen; + inp[4] = i & 0xff; + inp[5] = (i >> 8) & 0xff; + secp256k1_sha256_initialize(&gen); + secp256k1_sha256_write(&gen, inp, sizeof(inp)); + secp256k1_sha256_finalize(&gen, b32); + secp256k1_scalar_set_b32(&x, b32, NULL); + test_ecmult_accumulate(&acc, &x, scratch); + } + secp256k1_sha256_finalize(&acc, b32); + CHECK(secp256k1_memcmp_var(b32, expected32, 32) == 0); + + secp256k1_scratch_space_destroy(ctx, scratch); +} + void run_ecmult_constants(void) { - test_ecmult_constants(); + /* Expected hashes of all points in the tests below. Computed using an + * independent implementation. */ + static const unsigned char expected32_6bit20[32] = { + 0x68, 0xb6, 0xed, 0x6f, 0x28, 0xca, 0xc9, 0x7f, + 0x8e, 0x8b, 0xd6, 0xc0, 0x61, 0x79, 0x34, 0x6e, + 0x5a, 0x8f, 0x2b, 0xbc, 0x3e, 0x1f, 0xc5, 0x2e, + 0x2a, 0xd0, 0x45, 0x67, 0x7f, 0x95, 0x95, 0x8e + }; + static const unsigned char expected32_8bit8[32] = { + 0x8b, 0x65, 0x8e, 0xea, 0x86, 0xae, 0x3c, 0x95, + 0x90, 0xb6, 0x77, 0xa4, 0x8c, 0x76, 0xd9, 0xec, + 0xf5, 0xab, 0x8a, 0x2f, 0xfd, 0xdb, 0x19, 0x12, + 0x1a, 0xee, 0xe6, 0xb7, 0x6e, 0x05, 0x3f, 0xc6 + }; + /* For every combination of 6 bit positions out of 256, restricted to + * 20-bit windows (i.e., the first and last bit position are no more than + * 19 bits apart), all 64 bit patterns occur in the input scalars used in + * this test. */ + CONDITIONAL_TEST(1, "test_ecmult_constants_sha 1024") { + test_ecmult_constants_sha(4808378u, 1024, expected32_6bit20); + } + + /* For every combination of 8 consecutive bit positions, all 256 bit + * patterns occur in the input scalars used in this test. */ + CONDITIONAL_TEST(3, "test_ecmult_constants_sha 2048") { + test_ecmult_constants_sha(1607366309u, 2048, expected32_8bit8); + } + + CONDITIONAL_TEST(35, "test_ecmult_constants_2bit") { + test_ecmult_constants_2bit(); + } } void test_ecmult_gen_blind(void) { @@ -5851,14 +6180,14 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly /* We generate two classes of numbers: nlow==1 "low" ones (up to 32 bytes), nlow==0 "high" ones (32 bytes with 129 top bits set, or larger than 32 bytes) */ nlow[n] = der ? 1 : (secp256k1_testrand_bits(3) != 0); /* The length of the number in bytes (the first byte of which will always be nonzero) */ - nlen[n] = nlow[n] ? secp256k1_testrand_int(33) : 32 + secp256k1_testrand_int(200) * secp256k1_testrand_int(8) / 8; + nlen[n] = nlow[n] ? secp256k1_testrand_int(33) : 32 + secp256k1_testrand_int(200) * secp256k1_testrand_bits(3) / 8; CHECK(nlen[n] <= 232); /* The top bit of the number. */ nhbit[n] = (nlow[n] == 0 && nlen[n] == 32) ? 1 : (nlen[n] == 0 ? 0 : secp256k1_testrand_bits(1)); /* The top byte of the number (after the potential hardcoded 16 0xFF characters for "high" 32 bytes numbers) */ nhbyte[n] = nlen[n] == 0 ? 0 : (nhbit[n] ? 128 + secp256k1_testrand_bits(7) : 1 + secp256k1_testrand_int(127)); /* The number of zero bytes in front of the number (which is 0 or 1 in case of DER, otherwise we extend up to 300 bytes) */ - nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_testrand_int(3) : secp256k1_testrand_int(300 - nlen[n]) * secp256k1_testrand_int(8) / 8); + nzlen[n] = der ? ((nlen[n] == 0 || nhbit[n]) ? 1 : 0) : (nlow[n] ? secp256k1_testrand_int(3) : secp256k1_testrand_int(300 - nlen[n]) * secp256k1_testrand_bits(3) / 8); if (nzlen[n] > ((nlen[n] == 0 || nhbit[n]) ? 1 : 0)) { *certainly_not_der = 1; } @@ -5867,7 +6196,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly nlenlen[n] = nlen[n] + nzlen[n] < 128 ? 0 : (nlen[n] + nzlen[n] < 256 ? 1 : 2); if (!der) { /* nlenlen[n] max 127 bytes */ - int add = secp256k1_testrand_int(127 - nlenlen[n]) * secp256k1_testrand_int(16) * secp256k1_testrand_int(16) / 256; + int add = secp256k1_testrand_int(127 - nlenlen[n]) * secp256k1_testrand_bits(4) * secp256k1_testrand_bits(4) / 256; nlenlen[n] += add; if (add != 0) { *certainly_not_der = 1; @@ -5881,7 +6210,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly CHECK(tlen <= 856); /* The length of the garbage inside the tuple. */ - elen = (der || indet) ? 0 : secp256k1_testrand_int(980 - tlen) * secp256k1_testrand_int(8) / 8; + elen = (der || indet) ? 0 : secp256k1_testrand_int(980 - tlen) * secp256k1_testrand_bits(3) / 8; if (elen != 0) { *certainly_not_der = 1; } @@ -5889,7 +6218,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly CHECK(tlen <= 980); /* The length of the garbage after the end of the tuple. */ - glen = der ? 0 : secp256k1_testrand_int(990 - tlen) * secp256k1_testrand_int(8) / 8; + glen = der ? 0 : secp256k1_testrand_int(990 - tlen) * secp256k1_testrand_bits(3) / 8; if (glen != 0) { *certainly_not_der = 1; } @@ -5904,7 +6233,7 @@ static void random_ber_signature(unsigned char *sig, size_t *len, int* certainly } else { int tlenlen = tlen < 128 ? 0 : (tlen < 256 ? 1 : 2); if (!der) { - int add = secp256k1_testrand_int(127 - tlenlen) * secp256k1_testrand_int(16) * secp256k1_testrand_int(16) / 256; + int add = secp256k1_testrand_int(127 - tlenlen) * secp256k1_testrand_bits(4) * secp256k1_testrand_bits(4) / 256; tlenlen += add; if (add != 0) { *certainly_not_der = 1; @@ -6401,6 +6730,10 @@ void run_ecdsa_edge_cases(void) { # include "modules/schnorrsig/tests_impl.h" #endif +#ifdef ENABLE_MODULE_ELLSQ +# include "modules/ellsq/tests_impl.h" +#endif + void run_secp256k1_memczero_test(void) { unsigned char buf1[6] = {1, 2, 3, 4, 5, 6}; unsigned char buf2[sizeof(buf1)]; @@ -6633,6 +6966,7 @@ int main(int argc, char **argv) { /* group tests */ run_ge(); + run_gej(); run_group_decompress(); /* ecmult tests */ @@ -6685,6 +7019,10 @@ int main(int argc, char **argv) { run_schnorrsig_tests(); #endif +#ifdef ENABLE_MODULE_ELLSQ + run_ellsq_tests(); +#endif + /* util tests */ run_secp256k1_memczero_test(); diff --git a/src/tests_exhaustive.c b/src/tests_exhaustive.c index 6bae7a47780c6b..6a4e2340f2856b 100644 --- a/src/tests_exhaustive.c +++ b/src/tests_exhaustive.c @@ -22,7 +22,8 @@ #include "assumptions.h" #include "group.h" #include "testrand_impl.h" -#include "ecmult_gen_prec_impl.h" +#include "ecmult_compute_table_impl.h" +#include "ecmult_gen_compute_table_impl.h" static int count = 2; @@ -389,8 +390,9 @@ int main(int argc, char** argv) { printf("running tests for core %lu (out of [0..%lu])\n", (unsigned long)this_core, (unsigned long)num_cores - 1); } - /* Recreate the ecmult_gen table using the right generator (as selected via EXHAUSTIVE_TEST_ORDER) */ - secp256k1_ecmult_gen_create_prec_table(&secp256k1_ecmult_gen_prec_table[0][0], &secp256k1_ge_const_g, ECMULT_GEN_PREC_BITS); + /* Recreate the ecmult{,_gen} tables using the right generator (as selected via EXHAUSTIVE_TEST_ORDER) */ + secp256k1_ecmult_gen_compute_table(&secp256k1_ecmult_gen_prec_table[0][0], &secp256k1_ge_const_g, ECMULT_GEN_PREC_BITS); + secp256k1_ecmult_compute_two_tables(secp256k1_pre_g, secp256k1_pre_g_128, WINDOW_G, &secp256k1_ge_const_g); while (count--) { /* Build context */