constantine/constantine/config/curves_declaration.nim

# Constantine
# Copyright (c) 2018-2019    Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
#   * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
#   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.

import
  # Internal
  ./curves_parser

export CurveFamily

# ############################################################
#
#           Configuration of finite fields
#
# ############################################################

# Curves & their corresponding finite fields are preconfigured in this file

# Note, in the past the convention was to name a curve by its conjectured security level.
# as this might change with advances in research, the new convention is
# to name curves according to the length of the prime bit length.
# i.e. the BN254 was previously named BN128.

# Curves security level were significantly impacted by
# advances in the Tower Number Field Sieve.
# in particular BN254 curve security dropped
# from estimated 128-bit to estimated 100-bit
# Barbulescu, R. and S. Duquesne, "Updating Key Size Estimations for Pairings",
# Journal of Cryptology, DOI 10.1007/s00145-018-9280-5, January 2018.

# Generates public:
# - type Curve* = enum
# - proc Mod*(curve: static Curve): auto
#   which returns the field modulus of the curve
# - proc Family*(curve: static Curve): CurveFamily
#   which returns the curve family

declareCurves:
  # -----------------------------------------------------------------------------
  # Curves added when passed "-d:testingCurves"
  curve Fake101:
    testingCurve: true
    bitwidth: 7
    modulus: "0x65" # 101 in hex
  curve Fake103: # 103 ≡ 3 (mod 4)
    testingCurve: true
    bitwidth: 7
    modulus: "0x67" # 103 in hex
  curve Fake10007: # 10007 ≡ 3 (mod 4)
    testingCurve: true
    bitwidth: 14
    modulus: "0x2717" # 10007 in hex
  curve Fake65519: # 65519 ≡ 3 (mod 4)
    testingCurve: true
    bitwidth: 16
    modulus: "0xFFEF" # 65519 in hex
  curve Mersenne61:
    testingCurve: true
    bitwidth: 61
    modulus: "0x1fffffffffffffff" # 2^61 - 1
  curve Mersenne127:
    testingCurve: true
    bitwidth: 127
    modulus: "0x7fffffffffffffffffffffffffffffff" # 2^127 - 1
  # -----------------------------------------------------------------------------
  curve P224: # NIST P-224
    bitwidth: 224
    modulus: "0xffffffff_ffffffff_ffffffff_ffffffff_00000000_00000000_00000001"
  curve BN254_Nogami: # Integer Variable χ–Based Ate Pairing, 2008, Nogami et al
    bitwidth: 254
    modulus: "0x2523648240000001ba344d80000000086121000000000013a700000000000013"
    family: BarretoNaehrig
    # Equation: Y^2 = X^3 + 2
    # u: -(2^62 + 2^55 + 1)

    order: "0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d"
    orderBitwidth: 254
    cofactor: 1
    eq_form: ShortWeierstrass
    coef_a: 0
    coef_b: 2
    nonresidue_quad_fp: -1       #      -1   is not a square in 𝔽p
    nonresidue_cube_fp2: (1, 1)  # 1+𝑖   1+𝑖  is not a cube in 𝔽p²

    sexticTwist: D_Twist
    sexticNonResidue_fp2: (1, 1) # 1+𝑖

  curve BN254_Snarks: # Zero-Knowledge proofs curve (SNARKS, STARKS, Ethereum)
    bitwidth: 254
    modulus: "0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47"
    family: BarretoNaehrig

    # G1 Equation: Y^2 = X^3 + 3
    # G2 Equation: Y^2 = X^3 + 3/(9+𝑖)
    order: "0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001"
    orderBitwidth: 254
    cofactor: 1
    eq_form: ShortWeierstrass
    coef_a: 0
    coef_b: 3
    nonresidue_quad_fp: -1       #      -1   is not a square in 𝔽p
    nonresidue_cube_fp2: (9, 1)  # 9+𝑖   9+𝑖  is not a cube in 𝔽p²

    sexticTwist: D_Twist
    sexticNonResidue_fp2: (9, 1) # 9+𝑖

  curve Curve25519: # Bernstein curve
    bitwidth: 255
    modulus: "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed"
  curve P256: # secp256r1 / NIST P-256
    bitwidth: 256
    modulus: "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff"
  curve Secp256k1: # Bitcoin curve
    bitwidth: 256
    modulus: "0xFFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F"
  curve BLS12_377:
    # Zexe curve
    # (p41) https://eprint.iacr.org/2018/962.pdf
    # https://github.com/ethereum/EIPs/blob/41dea9615/EIPS/eip-2539.md
    bitwidth: 377
    modulus: "0x01ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001"
    family: BarretoLynnScott
    # u: 3 * 2^46 * (7 * 13 * 499) + 1
    # u: 0x8508c00000000001

    # G1 Equation: y² = x³ + 1
    # G2 Equation: y² = x³ + 1/ with 𝑗 = √-5
    order: "0x12ab655e9a2ca55660b44d1e5c37b00159aa76fed00000010a11800000000001"
    orderBitwidth: 253
    eq_form: ShortWeierstrass
    coef_a: 0
    coef_b: 1
    nonresidue_quad_fp: -5       #      -5   is not a square in 𝔽p
    nonresidue_cube_fp2: (0, 1)  # √-5  √-5  is not a cube in 𝔽p²

    sexticTwist: D_Twist
    sexticNonResidue_fp2: (0, 1) # √-5

  curve BLS12_381:
    bitwidth: 381
    modulus: "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
    family: BarretoLynnScott
    # u: -(2^63 + 2^62 + 2^60 + 2^57 + 2^48 + 2^16)

    # G1 Equation: y² = x³ + 4
    # G2 Equation: y² = x³ + 4 (1+i)
    order: "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001"
    orderBitwidth: 255
    cofactor: "0x396c8c005555e1568c00aaab0000aaab"
    eq_form: ShortWeierstrass
    coef_a: 0
    coef_b: 4
    nonresidue_quad_fp: -1       #      -1   is not a square in 𝔽p
    nonresidue_cube_fp2: (1, 1)  # 1+𝑖   1+𝑖  is not a cube in 𝔽p²

    sexticTwist: M_Twist
    sexticNonResidue_fp2: (1, 1) # 1+𝑖