ElligatorSwift + integrated x-only DH

CMakeLists.txt

@@ -71,6 +71,11 @@ if(SECP256K1_ENABLE_MODULE_EXTRAKEYS)
   add_compile_definitions(ENABLE_MODULE_EXTRAKEYS=1)
 endif()
 
+option(SECP256K1_ENABLE_MODULE_ELLSWIFT "Enable ElligatorSwift module." ON)
+if(SECP256K1_ENABLE_MODULE_ELLSWIFT)
+  add_compile_definitions(ENABLE_MODULE_ELLSWIFT=1)
+endif()
+
 option(SECP256K1_USE_EXTERNAL_DEFAULT_CALLBACKS "Enable external default callback functions." OFF)
 if(SECP256K1_USE_EXTERNAL_DEFAULT_CALLBACKS)
   add_compile_definitions(USE_EXTERNAL_DEFAULT_CALLBACKS=1)
@@ -270,6 +275,7 @@ message("  ECDH ................................ ${SECP256K1_ENABLE_MODULE_ECDH}
 message("  ECDSA pubkey recovery ............... ${SECP256K1_ENABLE_MODULE_RECOVERY}")
 message("  extrakeys ........................... ${SECP256K1_ENABLE_MODULE_EXTRAKEYS}")
 message("  schnorrsig .......................... ${SECP256K1_ENABLE_MODULE_SCHNORRSIG}")
+message("  ElligatorSwift ...................... ${SECP256K1_ENABLE_MODULE_ELLSWIFT}")
 message("Parameters:")
 message("  ecmult window size .................. ${SECP256K1_ECMULT_WINDOW_SIZE}")
 message("  ecmult gen precision bits ........... ${SECP256K1_ECMULT_GEN_PREC_BITS}")

Makefile.am

@@ -267,3 +267,7 @@ endif
 if ENABLE_MODULE_SCHNORRSIG
 include src/modules/schnorrsig/Makefile.am.include
 endif
+
+if ENABLE_MODULE_ELLSWIFT
+include src/modules/ellswift/Makefile.am.include
+endif

configure.ac

@@ -190,6 +190,10 @@ AC_ARG_ENABLE(module_schnorrsig,
     AS_HELP_STRING([--enable-module-schnorrsig],[enable schnorrsig module [default=yes]]), [],
     [SECP_SET_DEFAULT([enable_module_schnorrsig], [yes], [yes])])
 
+AC_ARG_ENABLE(module_ellswift,
+    AS_HELP_STRING([--enable-module-ellswift],[enable ElligatorSwift module [default=yes]]), [],
+    [SECP_SET_DEFAULT([enable_module_ellswift], [yes], [yes])])
+
 AC_ARG_ENABLE(external_default_callbacks,
     AS_HELP_STRING([--enable-external-default-callbacks],[enable external default callback functions [default=no]]), [],
     [SECP_SET_DEFAULT([enable_external_default_callbacks], [no], [no])])
@@ -402,6 +406,10 @@ if test x"$enable_module_schnorrsig" = x"yes"; then
   enable_module_extrakeys=yes
 fi
 
+if test x"$enable_module_ellswift" = x"yes"; then
+  AC_DEFINE(ENABLE_MODULE_ELLSWIFT, 1, [Define this symbol to enable the ElligatorSwift module])
+fi
+
 # Test if extrakeys is set after the schnorrsig module to allow the schnorrsig
 # module to set enable_module_extrakeys=yes
 if test x"$enable_module_extrakeys" = x"yes"; then
@@ -444,6 +452,7 @@ 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_ELLSWIFT], [test x"$enable_module_ellswift" = x"yes"])
 AM_CONDITIONAL([USE_EXTERNAL_ASM], [test x"$enable_external_asm" = x"yes"])
 AM_CONDITIONAL([USE_ASM_ARM], [test x"$set_asm" = x"arm32"])
 AM_CONDITIONAL([BUILD_WINDOWS], [test "$build_windows" = "yes"])
@@ -465,6 +474,7 @@ 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 ellswift         = $enable_module_ellswift"
 echo
 echo "  asm                     = $set_asm"
 echo "  ecmult window size      = $set_ecmult_window"

include/secp256k1_ellswift.h

@@ -0,0 +1,185 @@
+#ifndef SECP256K1_ELLSWIFT_H
+#define SECP256K1_ELLSWIFT_H
+
+#include "secp256k1.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+/* This module provides an implementation of ElligatorSwift as well as a
+ * version of x-only ECDH using it.
+ *
+ * ElligatorSwift is described in https://eprint.iacr.org/2022/759 by
+ * Chavez-Saab, Rodriguez-Henriquez, and Tibouchi. It permits encoding
+ * uniformly chosen public keys as 64-byte arrays which are indistinguishable
+ * from uniformly random arrays.
+ *
+ * Let f be the function from pairs of field elements to point X coordinates,
+ * defined as follows (all operations modulo p = 2^256 - 2^32 - 977)
+ * f(u,t):
+ * - Let C = 0xa2d2ba93507f1df233770c2a797962cc61f6d15da14ecd47d8d27ae1cd5f852,
+ *   a square root of -3.
+ * - If u=0, set u=1 instead.
+ * - If t=0, set t=1 instead.
+ * - If u^3 + t^2 + 7 = 0, multiply t by 2.
+ * - Let X = (u^3 + 7 - t^2) / (2 * t)
+ * - Let Y = (X + t) / (C * u)
+ * - Return the first in [u + 4 * Y^2, (-X/Y - u) / 2, (X/Y - u) / 2] that is an
+ *   X coordinate on the curve (at least one of them is, for any u and t).
+ *
+ * Then an ElligatorSwift encoding of x consists of the 32-byte big-endian
+ * encodings of field elements u and t concatenated, where f(u,t) = x.
+ * The encoding algorithm is described in the paper, and effectively picks a
+ * uniformly random pair (u,t) among those which encode x.
+ *
+ * If the Y coordinate is relevant, it is given the same parity as t.
+ *
+ * Changes w.r.t. the the paper:
+ * - The u=0, t=0, and u^3+t^2+7=0 conditions result in decoding to the point
+ *   at infinity in the paper. Here they are remapped to finite points.
+ * - The paper uses an additional encoding bit for the parity of y. Here the
+ *   parity of t is used (negating t does not affect the decoded x coordinate,
+ *   so this is possible).
+ */
+
+/** A pointer to a function used by secp256k1_ellswift_xdh to hash the shared X
+ *  coordinate along with the encoded public keys to a uniform shared secret.
+ *
+ *  Returns: 1 if a shared secret was successfully computed.
+ *           0 will cause secp256k1_ellswift_xdh to fail and return 0.
+ *           Other return values are not allowed, and the behaviour of
+ *           secp256k1_ellswift_xdh is undefined for other return values.
+ *  Out:     output:     pointer to an array to be filled by the function
+ *  In:      x32:        pointer to the 32-byte serialized X coordinate
+ *                       of the resulting shared point (will not be NULL)
+ *           ell_a64:    pointer to the 64-byte encoded public key of party A
+ *                       (will not be NULL)
+ *           ell_b64:    pointer to the 64-byte encoded public key of party B
+ *                       (will not be NULL)
+ *           data:       arbitrary data pointer that is passed through
+ */
+typedef int (*secp256k1_ellswift_xdh_hash_function)(
+    unsigned char *output,
+    const unsigned char *x32,
+    const unsigned char *ell_a64,
+    const unsigned char *ell_b64,
+    void *data
+);
+
+/** Construct a 64-byte ElligatorSwift encoding of a given pubkey.
+ *
+ *  Returns: 1 always.
+ *  Args:    ctx:        pointer to a context object
+ *  Out:     ell64:      pointer to a 64-byte array to be filled
+ *  In:      pubkey:     a pointer to a secp256k1_pubkey containing an
+ *                       initialized public key
+ *           rnd32:      pointer to 32 bytes of randomness
+ *
+ * It is recommended that rnd32 consists of 32 uniformly random bytes, not
+ * known to any adversary trying to detect whether public keys are being
+ * encoded, though 16 bytes of randomness (padded to an array of 32 bytes,
+ * e.g., with zeros) suffice to make the result indistinguishable from
+ * uniform. The randomness in rnd32 must not be a deterministic function of
+ * the pubkey (it can be derived from the private key, though).
+ *
+ * It is not guaranteed that the computed encoding is stable across versions
+ * of the library, even if all arguments to this function (including rnd32)
+ * are the same.
+ *
+ * This function runs in variable time.
+ */
+SECP256K1_API int secp256k1_ellswift_encode(
+    const secp256k1_context *ctx,
+    unsigned char *ell64,
+    const secp256k1_pubkey *pubkey,
+    const unsigned char *rnd32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4);
+
+/** Decode a 64-bytes ElligatorSwift 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_ellswift_decode(
+    const secp256k1_context *ctx,
+    secp256k1_pubkey *pubkey,
+    const unsigned char *ell64
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Compute an ElligatorSwift public key for a secret key.
+ *
+ *  Returns: 1: secret was valid, public key was stored.
+ *           0: secret was invalid, try again.
+ *  Args:    ctx:        pointer to a context object
+ *  Out:     ell64:      pointer to a 64-byte array to receive the ElligatorSwift
+ *                       public key
+ *  In:      seckey32:   pointer to a 32-byte secret key
+ *           auxrnd32:   (optional) pointer to 32 bytes of randomness
+ *
+ * Constant time in seckey and auxrnd32, but not in the resulting public key.
+ *
+ * It is recommended that auxrnd32 contains 32 uniformly random bytes, though
+ * it is optional (and does result in encodings that are indistinguishable from
+ * uniform even without any auxrnd32). It differs from the (mandatory) rnd32
+ * argument to secp256k1_ellswift_encode in this regard.
+ *
+ * This function can be used instead of calling secp256k1_ec_pubkey_create
+ * followed by secp256k1_ellswift_encode. It is safer, as it uses the secret
+ * key as entropy for the encoding (supplemented with auxrnd32, if provided).
+ *
+ * Like secp256k1_ellswift_encode, this function does not guarantee that the
+ * computed encoding is stable across versions of the library, even if all
+ * arguments (including auxrnd32) are the same.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ellswift_create(
+    const secp256k1_context *ctx,
+    unsigned char *ell64,
+    const unsigned char *seckey32,
+    const unsigned char *auxrnd32
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3);
+
+/** Given a private key, and ElligatorSwift public keys sent in both directions,
+ *  compute a shared secret using x-only Elliptic Curve Diffie-Hellman (ECDH).
+ *
+ *  Returns: 1: shared secret was succesfully computed
+ *           0: secret was invalid or hashfp returned 0
+ *  Args:    ctx:       pointer to a context object.
+ *  Out:     output:    pointer to an array to be filled by hashfp.
+ *  In:      ell_a64:   pointer to the 64-byte encoded public key of party A
+ *                      (will not be NULL)
+ *           ell_b64:   pointer to the 64-byte encoded public key of party B
+ *                      (will not be NULL)
+ *           seckey32:  a pointer to our 32-byte secret key
+ *           party:     boolean indicating which party we are: zero if we are
+ *                      party A, non-zero if we are party B. seckey32 must be
+ *                      the private key corresponding to that party's ell_?64.
+ *                      This correspondence is not checked.
+ *           hashfp:    pointer to a hash function.
+ *           data:      arbitrary data pointer passed through to hashfp.
+ *
+ * Constant time in seckey32.
+ *
+ * This function is more efficient than decoding the public keys, and performing
+ * ECDH on them.
+ */
+SECP256K1_API SECP256K1_WARN_UNUSED_RESULT int secp256k1_ellswift_xdh(
+  const secp256k1_context *ctx,
+  unsigned char *output,
+  const unsigned char *ell_a64,
+  const unsigned char *ell_b64,
+  const unsigned char *seckey32,
+  int party,
+  secp256k1_ellswift_xdh_hash_function hashfp,
+  void *data
+) SECP256K1_ARG_NONNULL(1) SECP256K1_ARG_NONNULL(2) SECP256K1_ARG_NONNULL(3) SECP256K1_ARG_NONNULL(4) SECP256K1_ARG_NONNULL(5) SECP256K1_ARG_NONNULL(7);
+
+#ifdef __cplusplus
+}
+#endif
+
+#endif /* SECP256K1_ELLSWIFT_H */

src/CMakeLists.txt

@@ -132,6 +132,9 @@ if(SECP256K1_INSTALL)
   if(SECP256K1_ENABLE_MODULE_SCHNORRSIG)
     list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_schnorrsig.h")
   endif()
+  if(SECP256K1_ENABLE_MODULE_ELLSWIFT)
+    list(APPEND ${PROJECT_NAME}_headers "${PROJECT_SOURCE_DIR}/include/secp256k1_ellswift.h")
+  endif()
   install(FILES ${${PROJECT_NAME}_headers}
     DESTINATION ${CMAKE_INSTALL_INCLUDEDIR}
   )

src/modules/ellswift/Makefile.am.include

@@ -0,0 +1,2 @@
+include_HEADERS += include/secp256k1_ellswift.h
+noinst_HEADERS += src/modules/ellswift/main_impl.h