crrl

This library implements some primitives for purposes of cryptographic research. Its point is to provide efficient, optimized and constant-time implementations that are supposed to be representative of production-ready code, so that realistic performance benchmarks may be performed. Thus, while meant primarily for research, the code here should be fine for production use (though of course I offer no such guarantee; use at your own risks).

So far, only some primitives related to elliptic curve cryptography are implemented:

• A generic type GF255<MQ> for finite fields of integers modulo a prime 2^255-MQ (for a value of MQ between 1 and 32767). The MQ value is provided as a type parameter, i.e. the exact field is known at compile time. This type covers the usual modulus 2^255-19 (used in Curve25519) as well as 2^255-18651 and 2^255-3957 (used in double-odd curves do255e and do255s).

• A generic type ModInt256<M0, M1, M2, M3> for arbitrary finite fields of integers modulo a prime between 2^192 and 2^256. Montgomery representation is internally used. The modulus is provided as type parameters, allowing the compiler to apply optimizations when some parts of the modulus allow them (in particular with the modulus used for NIST curve P-256).

• Type GFsecp256k1 implements the specific base field for curve secp256k1 (integers modulo 2^256-4294968273). The 64-bit backend has a dedicated implementation, while the 32-bit version of this type uses ModInt256.

• The macro define_gfgen allows defining arbitrary finite fields of integers modulo a prime, with a large range of modulus size. It uses Montgomery representation internally.

• Type GF448 implements the specific base field for Curve448. The 64-bit backend has a dedicated implementation, while the 32-bit backend uses define_gfgen.

• Type ed25519::Point provides generic group operations in the twisted Edwards curve Curve25519. Ed25519 signatures (as per RFC 8032) are implemented. Type ed25519::Scalar implements operations on integers modulo the curve subgroup order.

• Type ristretto255::Point provides generic group operations in the ristretto255 group, whose prime order is exactly the size of the interesting subgroup of Curve25519.

• Type ed448::Point provides generic group operations in the Edwards curve edwards448. Ed448 signatures (as per RFC 8032) are implemented. Type ed448::Scalar implements operations on integers modulo the curve subgroup order.

• Type decaf448::Point provides generic group operations in the decaf448 group, whose prime order is exactly the size of the interesting subgroup of Curve448.

• Type p256::Point provides generic group operations in the NIST P-256 curve (aka "secp256r1" aka "prime256v1"). ECDSA signatures are supported. The p256::Scalar type implements the corresponding scalars (integers modulo the curve order).

• Type secp256k1::Point provides generic group operations in the secp256k1 curve (aka "the Bitcoin curve"). ECDSA signatures are supported. The secp256k1::Scalar type implements the corresponding scalars (integers modulo the curve order). The GLV endomorphism is leveraged to speed-up point multiplication (key exchange) and signature verification.

• Types jq255e::Point and jq255s::Point implement the double-odd curves jq255e and jq255s (along with the corresponding scalar types jq255e::Scalar and jq255s::Scalar). Key exchange and Schnorr signatures are implemented. These curves provide a prime-order group abstraction, similar to ristretto255, but with somewhat better performance at the same security level. Moreover, the relevant signatures are both shorter (48 bytes instead of 64) and faster than the usual Ed25519 signatures.

• Function x25519::x25519() implements the X25519 function. An optimized x25519::x2559_base() function is provided when X25519 is applied to the conventional base point. Similarly, x448::x448() and x448::x448_base() provide the same functionality for the X448 function.

• Type gls254::Point implements the GLS254 curve (or, more precisely, a prime-order group homomorphic to a subgroup of that curve), which is defined over a binary field. gls254::Scalar is the type for integers modulo the curve order. gls254::PrivateKey and gls254:PublicKey implement high-level operations such as key exchange and signatures, using that group.

• Module blake2s contains some BLAKE2s implementations, with optional SSE2 and AVX2 optimizations.

Types GF255 and ModInt256 have a 32-bit and a 64-bit implementations each (actually two 64-bit implementations, see later the discussion about the gf255_m51 feature). The code is portable (it was tested on 32-bit and 64-bit x86, 64-bit aarch64, and 64-bit riscv64). Performance is quite decent; e.g. Ed25519 signatures are computed in about 51500 cycles, and verified in about 114000 cycles, on an Intel "Coffee Lake" CPU; this is not too far from the best assembly-optimized implementations. At the same time, use of operator overloading allows to express formulas on points and scalar with about the same syntax as their mathematical description. For instance, the core of the X25519 implementation looks like this:

        let A = x2 + z2;
        let B = x2 - z2;
        let AA = A.square();
        let BB = B.square();
        let C = x3 + z3;
        let D = x3 - z3;
        let E = AA - BB;
        let DA = D * A;
        let CB = C * B;
        x3 = (DA + CB).square();
        z3 = x1 * (DA - CB).square();
        x2 = AA * BB;
        z2 = E * (AA + E.mul_small(121665));

which is quite close to the corresponding description in RFC 7748:

       A = x_2 + z_2
       AA = A^2
       B = x_2 - z_2
       BB = B^2
       E = AA - BB
       C = x_3 + z_3
       D = x_3 - z_3
       DA = D * A
       CB = C * B
       x_3 = (DA + CB)^2
       z_3 = x_1 * (DA - CB)^2
       x_2 = AA * BB
       z_2 = E * (AA + a24 * E)

Optional Features

By default, everything in crrl is compiled, which unfortunately makes for a relatively long compilation time, especially on not-so-fast systems. To only compile support for some primitives, use --no-default-features then add selectively the features you are interested in with -F; e.g. use cargo build --no-default-features -F ed25519 to only compile the Ed25519 support (and the primitives that it needs, such as its base field). The defined primitive-controlling features are the following:

• omnes: enables all of the following.

• decaf448: decaf448 prime-order group (based on edwards448)

• ed25519: edwards25519 curve and signatures (RFC 8032: Ed25519)

• ed448: edwards448 curve and signatures (RFC 8032: Ed448)

• frost: FROST threshold signatures (support macros + standard ciphersuites, but only for the curves which are also enabled in this build)

• jq255e: jq255e prime-order group and signatures

• jq255s: jq255s prime-order group and signatures

• lms: LMS support (hash-based signatures)

• p256: NIST P-256 curve and signatures (ECDSA)

• ristretto255: ristretto255 prime-order group (based on edwards25519)

• secp256k1: secp256k1 curve and signatures (ECDSA)

• x25519: X25519 key exchange primitive (RFC 7748)

• x448: X448 key exchange primitive (RFC 7748)

• modint256: generic finite field implementation (prime order of up to 256 bits)

• gf255: generic finite field implementation (for prime order q = 2^255 - MQ with MQ < 2^15)

• gfgen: generic finite field implementation (generating macro; prime modulus of arbitrary length)

• gls254: GLS254 prime-order group and signatures

• gls254bench: additional benchmarking code for GLS254

• blake2s: BLAKE2s hash function

Some operations have multiple backends. An appropriate backend is selected at compile-time, but this can be overridden by enabling some features:

• w32_backend: enforce use of the 32-bit code, even on 64-bit systems.

• w64_backend: enforce use of the 64-bit code, even on 32-bit systems.

• gf255_m64: enforce use of 64-bit limbs for GF255<MQ>; this is the default on 64-bit machines, except RISC-V (riscv64) where 51-bit limbs are used by default. This feature has no effect if the 32-bit code is used.

• gf255_m51: encode use of 51-bit limbs for GF255<MQ>; this is the default on 64-bit RISC-V targets (riscv64), but not on other 64-bit architectures where 64-bit limbs are normally preferred. This feature has no effect if the 32-bit code is used.

• gfb254_m64: enforce use of the generic implementation of the binary field GF(2^254). This feature has no effect if the 32-bit code is used.

• gfb254_x86clmul: enforce use of the AVX2+pclmulqdq implementation of the binary field GF(2^254). This code is used automatically if the compilation target is an x86 with the relevant hardware support; this feature bypasses the automatic detection. This feature has no effect if the 32-bit code is used.

• gfb254_arm64pmull: enforce use of the NEON+pmull implementation of the binary field GF(2^254). This code is used automatically if the compilation target is an aarch64 system; this feature bypasses the automatic detection. This feature has no effect if the 32-bit code is used.

Security and Compliance

All the code is strict, both in terms of timing-based side-channels (everything is constant-time, except if explicitly stated otherwise, e.g. in a function whose name includes vartime) and in compliance to relevant standards. For instance, the Ed25519 signature support applies and enforces canonical encodings of both points and scalars.

There is no attempt at "zeroizing memory" anywhere in the code. In general, such memory cleansing is a fool's quest. Note that since most of the library use no_std rules, dynamic allocation happens only on the stack, thereby limiting the risk of leaving secret information lingering all over the RAM. The only functions that use heap allocation only store public data there.

WARNING: I reiterate what was written above: although all of the code aims at being representative of optimized production-ready code, it is still fairly recent and some bugs might still lurk, however careful I am when writing code. Any assertion of suitability to any purpose is explcitly denied. The primary purpose is to help with "trying out stuff" in cryptographic research, by offering an easy-to-use API backed by performance close enough to what can be done in actual applications.

Truncated Signatures

Support for truncated signatures is implemented for Ed25519 and ECDSA/P-256. Standard signatures can be shortened by 8 to 32 bits (i.e. the size may shrink from 64 down to 60 bytes), and the verifier rebuilds the original signature during verification (at some computational cost). This is not a ground-breaking feature, but it can be very convenient in some situations with tight constraints on bandwidth and a requirement to work with standard signature formats. See ed25519::PublicKey::verify_trunc_raw() and p256::PublicKey::verify_trunc_hash() for details.

FROST Threshold Schnorr Signatures

The FROST protocol for a distributed Schnorr signature generation scheme has been implemented, as per the v14 draft specification: draft-irtf-cfrg-frost-14. Four ciphersuites are provided, with similar APIs, in the frost::ed25519, frost::ristretto255, frost::ed448, frost::p256 and frost::secp256k1 modules. A sample code showing how to use the API is provided in the frost-sample.rs file.

While FROST is inherently a distributed scheme, the implementation can also be used in a single signer mode by using the "group" private key directly.

Benchmarks

cargo bench runs some benchmarks, but there are a few caveats:

• The cycle counter is used on x86. If frequency scaling ("TurboBoost") is not disabled, then you'll get wrong and meaningless results.

• On aarch64, the cycle counter is also accessed directly, which will in general fail with some CPU exception. Access to the counter must first be enabled, which requires (on Linux) a specific kernel module. This one works for me.

• On riscv64gc, the cycle counter is accessed directly. In general, that counter is not enabled and all benches return zero; to enable the cycle counter, run the benchmark binary inside the perf tool (which comes with the linux-tools).

• On architectures other than i386, x86-64, aarch64 and riscv64gc, benchmark code will simply not compile.

TODO

In general, about anything related to cryptography may show up here, if there is a use case for it.