SymCrypt

Version: 103.1.0 (tag v103.1.0)

Repository: https://github.com/microsoft/SymCrypt

Docs:

Primitives

Supports ECDH and ECDSA with NIST curves (192, 224, 256, 384, 521) and Twisted Edwards NUMS curves (NumsP256t1, NumsP384t1, NumsP512t1). Also custom curves. Supports X25519.

ECDH

KeyGen:

• (signed) Fixed-window via SymCryptEcpointGenericSetRandom -> SymCryptEcpointScalarMul -> SymCryptEcpointScalarMulFixedWindow. Algorithm 1 in Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis.

• NIST (Short-Weierstrass) use Jacobian.

  • dbl-2007-bl for generic double via SymCryptEcpointDouble or a tweak of dbl-2007-bl/dbl-2001-b formulae via SymCryptShortWeierstrassDoubleSpecializedAm3 for a=-3.

  • add-2007-bl via SymCryptEcpointAddDiffNonZero. It also has side-channel unsafe version SymCryptShortWeierstrassAddSideChannelUnsafe and a generic wrapper for both via SymCryptEcpointAdd.

• NUMS (Twisted-Edwards) curves use Extended projective.

  • dbl-2008-hwcd via SymCryptTwistedEdwardsDouble.

  • add-2008-hwcd via SymCryptTwistedEdwardsAdd or SymCryptTwistedEdwardsAddDiffNonZero.

Derive:

• (signed) Fixed-window via SymCryptEcDhSecretAgreement -> SymCryptEcpointScalarMul -> SymCryptEcpointScalarMulFixedWindow. Algorithm 1 in Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis.

• Same coordinates and formulas as KeyGen.

ECDSA

KeyGen:

• Short-Weierstrass

• (signed) Fixed-window via SymCryptEcpointGenericSetRandom -> SymCryptEcpointScalarMul -> SymCryptEcpointScalarMulFixedWindow. Algorithm 1 in Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis.

• NIST (Short-Weierstrass) use Jacobian.

  • dbl-2007-bl for generic double via SymCryptEcpointDouble or a tweak of dbl-2007-bl/dbl-2001-b formulae via SymCryptShortWeierstrassDoubleSpecializedAm3 for a=-3.

  • add-2007-bl via SymCryptEcpointAddDiffNonZero. It also has side-channel unsafe version SymCryptShortWeierstrassAddSideChannelUnsafe and a generic wrapper for both via SymCryptEcpointAdd.

• NUMS (Twisted-Edwards) curves use Extended projective.

  • dbl-2008-hwcd via SymCryptTwistedEdwardsDouble.

  • add-2008-hwcd via SymCryptTwistedEdwardsAdd or SymCryptTwistedEdwardsAddDiffNonZero.

Sign:

• Short-Weierstrass

• (signed) Fixed-window via SymCryptEcDsaSignEx -> SymCryptEcpointScalarMul -> SymCryptEcpointScalarMulFixedWindow. Algorithm 1 in Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis.

• Same coordinates and formulas as KeyGen.

Verify:

• Short-Weierstrass

• Double-scalar multiplication using the width-w NAF with interleaving via SymCryptEcDsaVerify > SymCryptEcpointMultiScalarMul -> SymCryptEcpointMultiScalarMulWnafWithInterleaving. Algorithm 9 in Selecting Elliptic Curves for Cryptography: An Efficiency and Security Analysis.

• Same coordinates and formulas as KeyGen.

X25519

KeyGen:

• Montgomery

• Ladder via SymCryptMontgomeryPointScalarMul.

• xz.

• ladd-1987-m-3 via SymCryptMontgomeryDoubleAndAdd.

Derive:

• Same as Keygen.