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diff --git a/docs/LIBS.md b/docs/LIBS.md index 4fac57b..d1a68d0 100644 --- a/docs/LIBS.md +++ b/docs/LIBS.md @@ -1,31 +1,89 @@ -# Libraries with ECC +# Libraries with ECC support -Libraries with at least some ECC support: +Popular libraries with at least some ECC support: - - [Crypto++](https://cryptopp.com/) - [libgcrypt](https://www.gnupg.org/related_software/libgcrypt/) - - [mbedTLS](https://tls.mbed.org/) - [Nettle](http://www.lysator.liu.se/~nisse/nettle/) - - [OpenSSL](https://www.openssl.org/) - [OpenSSL (FIPS mode)](https://www.openssl.org/docs/fipsnotes.html) - - - [Microsoft CNG](https://msdn.microsoft.com/en-us/library/windows/desktop/aa376210(v=vs.85).aspx) + - BoringSSL - [Microsoft .NET crypto](https://docs.microsoft.com/en-us/dotnet/standard/security/cryptography-model) - + # Supported libraries - [BouncyCastle](https://bouncycastle.org/java.html) - Java + - Works with the short Weierstrass curve model. + - Works with coordinates: + - Affine + - Projective(Homogenous) + - Jacobian + - Jacobian-Chudnovsky + - Jacobian-Modified + - Lambda-Affine? + - Lambda-Projective? + - Skewed? + - Multiple scalar multiplication algorithms implemented and used: + - Double-and-add always (DoubleAddMultiplier) + - Fixed point comb (FixedPointCombMultiplier) + - GLV (Gallant-Lambert-Vanstone) using endomorphisms (GLVMultiplier): Faster point multiplication on elliptic curves with efficient endomorphisms. <-- default, if available + - Binary NAF right-to-left multiplication(mixed coordinates) (MixedNafR2LMultiplier) + - Montgomery ladder (MontgomeryLadderMultiplier) + - Binary NAF right-to-left multiplication (NafR2LMultiplier) + - Binary NAF left-to-right multiplication (NafL2RMultiplier) + - Double-and-add reference implementation (ReferenceMultiplier) + - Window NAF left-to-right multiplication (WNafL2RMultiplier) <-- default + - Window Tau-NAF multiplication (WTauNafMultiplier): Improved Algorithms for Arithmetic on Anomalous Binary Curves + - Zeroless signed digit binary right-to-left multiplication (ZSignedDigitR2LMultiplier) + - Zeroless signed digit binary left-to-right multiplication (ZSignedDigitL2RMultiplier) + - Has custom field and point arithmetic for: + - Curve25519 (transformed into short Weierstrass model) + - SMP2 curves + - SECG curves - [Sun EC](https://docs.oracle.com/javase/7/docs/technotes/guides/security/SunProviders.html#SunEC) - Java + C - - [Botan](https://botan.randombit.net/), since 2.4.0 (unreleased) + - Uses the short Weierstrass curve model. + - For prime field curves: + - Uses 5-bit window NAF, Uses mixed Modified-Jacobian coordinates + for doubling and Chudnovsky Jacobian coordinates for additions (ecp_jm.c). From: + Brown, Hankerson, Lopez, Menezes: Software Implementation of the NIST Elliptic Curves Over Prime Fields. + - Contains an implementation of scalar multiplication with 4-bit sliding window, using Jacobian coordinates (ecp_jac.c) + - Contains an implementation of IEEE P1363 algorithm A.10.3 using affine coordinates (ecp_aff.c) + - For binary field curves: + - Uses Lopez-Dahab (Montgomery) ladder, XZ coordinates (ec2_mont.c): Fast multiplication on elliptic curves over GF(2^m) without precomputation (Algorithm 2P) + - Contains an implementation of IEEE P1363 algorithm A.10.3 using affine coordinates (ec2_aff.c) + - Has some custom arithmetic for some of the NIST primes. + - [OpenSSL](https://www.openssl.org/) + - C + - For prime field curves: + - Uses Jacobian coordinates, and Montgomery ladder, also uses wNAF-based interleaving multi-exponentiation method(ec_mult.c): http://www.bmoeller.de/pdf/TI-01-08.multiexp.pdf + - Also uses multiplication with precomputation by wNAF splitting(ec_mult.c) + - For binary field curves: + - Uses Jacobian coordinates, and Lopez-Dahab ladder, also uses wNAF-based interleaving multi-exponentiation method(ec2_smpl.c) + - [Botan](https://botan.randombit.net/) - C++ - Uses blinded(randomized) Montgomery ladder. - - https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2 - - https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-1986-cc - - https://eprint.iacr.org/2015/657 + - <https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-1998-cmo-2> + - <https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-1986-cc> + - <https://eprint.iacr.org/2015/657> + - ECTester supports v2.4.0 and up. - [libtomcrypt](http://www.libtom.net/LibTomCrypt/) - C - Uses Jacobian coordinates. - - Sliding window scalar multiplication algorithm.
\ No newline at end of file + - Sliding window scalar multiplication algorithm. + - [Crypto++](https://cryptopp.com/) + - C++ + - For prime field curves: + - Uses projective coordinates and sliding window scalar multiplication algorithm. + - For binary field curves: + - Uses affine coordinates and sliding window scalar multiplication algorithm. + - [Microsoft CNG](https://msdn.microsoft.com/en-us/library/windows/desktop/aa376210(v=vs.85).aspx) + - C API. + - Closed source. + - For prime field curves(only supports): + - Uses Short Weierstrass model. + - Uses Twisted Edwards model. + - Uses Montgomery model. + - Uses fixed window scalar multiplication. + - Uses Wnaf multi-scalar multiplication with interleaving. + - Uses Montgomery ladder.
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