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# Libraries with ECC support
Popular libraries with at least some ECC support:
- [NSS](https://hg.mozilla.org/projects/nss)
- [mbedTLS](https://tls.mbed.org/)
- [LibreSSL](https://www.libressl.org/)
- [Nettle](http://www.lysator.liu.se/~nisse/nettle/)
- [OpenSSL (FIPS mode)](https://www.openssl.org/docs/fipsnotes.html)
- [Microsoft .NET crypto](https://docs.microsoft.com/en-us/dotnet/standard/security/cryptography-model)
# Supported libraries
Libraries that ECTester can test.
- [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
- 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)
- [BoringSSL](https://boringssl.googlesource.com/boringssl)
- C
- Supports prime field curves only:
- Use Jacobian coordinates, and Montgomery ladder, also uses optimized arithmetic on NIST P-224, P-256.
- Bundled as a git submodule in `ext/boringssl`. To build and use run:
```bash
cd ext/boringssl
mkdir build && cd build
cmake -DBUILD_SHARED_LIBS=1 -GNinja ..
ninja
```
- [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.
- [libtomcrypt](http://www.libtom.net/LibTomCrypt/)
- C
- Uses Jacobian coordinates.
- Sliding window scalar multiplication algorithm.
- [libgcrypt](https://www.gnupg.org/related_software/libgcrypt/)
- C
- Only supports prime field curves.
- Uses short Weierstrass, Montgomery and Twisted Edwards models.
- Uses left-to-right double-and-add always scalar multiplication and Jacobian coordinates in short Weierstrass form.
- Uses Montgomery ladder and X-only in Montgomery form.
- Uses left-to-right double-and-add always scalar multiplication in Twisted Edwards form.
- [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>
- ECTester supports v2.4.0 and up.
- [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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