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Supported libraries

Libraries that ECTester can test.

  • BouncyCastle
    • 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
    • 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.
  • WolfCrypt(WolfSSL)
    • C + Java
    • Prime field curves only.
    • Jacobian coordinates:
      • Uses sliding window scalar multiplication, (discards b parameter of curve), but validates points.
  • OpenSSL
    • 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
    • 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:
cd ext/boringssl
mkdir build && cd build
cmake -DBUILD_SHARED_LIBS=1 -GNinja ..
ninja

Libraries with ECC support

Popular libraries with at least some ECC support, that ECTester does not yet support:

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