mirror of
https://github.com/logos-storage/constantine.git
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d84edcd217
* Pairing - initial commit - line functions - sparse Fp12 functions * Small fixes: - Line parametrized by twist for generic algorithm - Add a conjugate operator for quadratic extensions - Have frobenius use it - Create an Affine coordinate type for elliptic curve * Implement (failing) pairing test * Stash pairing debug session, temp switch Fp12 over Fp4 * Proper naive pairing on BLS12-381 * Frobenius map * Implement naive pairing for BN curves * Add pairing tests to CI + reduce time spent on lower-level tests * Test without assembler in Github Actions + less base layers test iterations
225 lines
8.9 KiB
Nim
225 lines
8.9 KiB
Nim
# Constantine
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# Copyright (c) 2018-2019 Status Research & Development GmbH
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# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
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# Licensed and distributed under either of
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# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
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# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
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# at your option. This file may not be copied, modified, or distributed except according to those terms.
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import
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# Internal
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./curves_parser
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export CurveFamily
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# ############################################################
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#
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# Configuration of finite fields
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#
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# ############################################################
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# Curves & their corresponding finite fields are preconfigured in this file
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# Note, in the past the convention was to name a curve by its conjectured security level.
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# as this might change with advances in research, the new convention is
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# to name curves according to the length of the prime bit length.
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# i.e. the BN254 was previously named BN128.
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# Curves security level were significantly impacted by
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# advances in the Tower Number Field Sieve.
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# in particular BN254 curve security dropped
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# from estimated 128-bit to estimated 100-bit
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# Barbulescu, R. and S. Duquesne, "Updating Key Size Estimations for Pairings",
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# Journal of Cryptology, DOI 10.1007/s00145-018-9280-5, January 2018.
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# Generates public:
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# - type Curve* = enum
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# - proc Mod*(curve: static Curve): auto
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# which returns the field modulus of the curve
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# - proc Family*(curve: static Curve): CurveFamily
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# which returns the curve family
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# - proc get_BN_param_u_BE*(curve: static Curve): array[N, byte]
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# which returns the "u" parameter of a BN curve
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# as a big-endian canonical integer representation
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# if it's a BN curve and u is positive
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# - proc get_BN_param_6u_minus1_BE*(curve: static Curve): array[N, byte]
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# which returns the "6u-1" parameter of a BN curve
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# as a big-endian canonical integer representation
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# if it's a BN curve and u is positive.
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# This is used for optimized field inversion for BN curves
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declareCurves:
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# -----------------------------------------------------------------------------
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# Curves added when passed "-d:testingCurves"
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curve Fake101:
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testingCurve: true
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bitwidth: 7
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modulus: "0x65" # 101 in hex
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curve Fake103: # 103 ≡ 3 (mod 4)
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testingCurve: true
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bitwidth: 7
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modulus: "0x67" # 103 in hex
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curve Fake10007: # 10007 ≡ 3 (mod 4)
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testingCurve: true
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bitwidth: 14
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modulus: "0x2717" # 10007 in hex
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curve Fake65519: # 65519 ≡ 3 (mod 4)
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testingCurve: true
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bitwidth: 16
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modulus: "0xFFEF" # 65519 in hex
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curve Mersenne61:
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testingCurve: true
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bitwidth: 61
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modulus: "0x1fffffffffffffff" # 2^61 - 1
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curve Mersenne127:
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testingCurve: true
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bitwidth: 127
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modulus: "0x7fffffffffffffffffffffffffffffff" # 2^127 - 1
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# -----------------------------------------------------------------------------
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curve P224: # NIST P-224
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bitwidth: 224
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modulus: "0xffffffff_ffffffff_ffffffff_ffffffff_00000000_00000000_00000001"
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curve BN254_Nogami: # Integer Variable χ–Based Ate Pairing, 2008, Nogami et al
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bitwidth: 254
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modulus: "0x2523648240000001ba344d80000000086121000000000013a700000000000013"
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family: BarretoNaehrig
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# Equation: Y^2 = X^3 + 2
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# u: -(2^62 + 2^55 + 1)
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order: "0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d"
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orderBitwidth: 254
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cofactor: 1
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eq_form: ShortWeierstrass
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coef_a: 0
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coef_b: 2
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nonresidue_quad_fp: -1 # -1 is not a square in 𝔽p
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nonresidue_cube_fp2: (1, 1) # 1+𝑖 1+𝑖 is not a cube in 𝔽p²
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sexticTwist: D_Twist
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sexticNonResidue_fp2: (1, 1) # 1+𝑖
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curve BN254_Snarks: # Zero-Knowledge proofs curve (SNARKS, STARKS, Ethereum)
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bitwidth: 254
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modulus: "0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47"
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family: BarretoNaehrig
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bn_u_bitwidth: 63
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bn_u: "0x44E992B44A6909F1" # u: 4965661367192848881
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cubicRootOfUnity_modP: "0x30644e72e131a0295e6dd9e7e0acccb0c28f069fbb966e3de4bd44e5607cfd48"
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# For sanity checks
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cubicRootOfUnity_modR: "0x30644e72e131a029048b6e193fd84104cc37a73fec2bc5e9b8ca0b2d36636f23"
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# G1 Equation: Y^2 = X^3 + 3
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# G2 Equation: Y^2 = X^3 + 3/(9+𝑖)
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order: "0x30644e72e131a029b85045b68181585d2833e84879b9709143e1f593f0000001"
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orderBitwidth: 254
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cofactor: 1
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eq_form: ShortWeierstrass
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coef_a: 0
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coef_b: 3
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nonresidue_quad_fp: -1 # -1 is not a square in 𝔽p
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nonresidue_cube_fp2: (9, 1) # 9+𝑖 9+𝑖 is not a cube in 𝔽p²
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sexticTwist: D_Twist
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sexticNonResidue_fp2: (9, 1) # 9+𝑖
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curve Curve25519: # Bernstein curve
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bitwidth: 255
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modulus: "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed"
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curve P256: # secp256r1 / NIST P-256
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bitwidth: 256
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modulus: "0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff"
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curve Secp256k1: # Bitcoin curve
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bitwidth: 256
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modulus: "0xFFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F"
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curve BLS12_377:
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# Zexe curve
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# (p41) https://eprint.iacr.org/2018/962.pdf
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# https://github.com/ethereum/EIPs/blob/41dea9615/EIPS/eip-2539.md
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bitwidth: 377
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modulus: "0x01ae3a4617c510eac63b05c06ca1493b1a22d9f300f5138f1ef3622fba094800170b5d44300000008508c00000000001"
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family: BarretoLynnScott
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# u: 3 * 2^46 * (7 * 13 * 499) + 1
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# u: 0x8508c00000000001
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# G1 Equation: y² = x³ + 1
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# G2 Equation: y² = x³ + 1/ with 𝑗 = √-5
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eq_form: ShortWeierstrass
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coef_a: 0
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coef_b: 1
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nonresidue_quad_fp: -5 # -5 is not a square in 𝔽p
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nonresidue_cube_fp2: (0, 1) # √-5 √-5 is not a cube in 𝔽p²
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sexticTwist: D_Twist
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sexticNonResidue_fp2: (0, 1) # √-5
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curve BLS12_381:
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bitwidth: 381
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modulus: "0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaab"
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family: BarretoLynnScott
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# u: -(2^63 + 2^62 + 2^60 + 2^57 + 2^48 + 2^16)
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cubicRootOfUnity_mod_p: "0x1a0111ea397fe699ec02408663d4de85aa0d857d89759ad4897d29650fb85f9b409427eb4f49fffd8bfd00000000aaac"
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# G1 Equation: y² = x³ + 4
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# G2 Equation: y² = x³ + 4 (1+i)
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order: "0x73eda753299d7d483339d80809a1d80553bda402fffe5bfeffffffff00000001"
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orderBitwidth: 255
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cofactor: "0x396c8c005555e1568c00aaab0000aaab"
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eq_form: ShortWeierstrass
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coef_a: 0
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coef_b: 4
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nonresidue_quad_fp: -1 # -1 is not a square in 𝔽p
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nonresidue_cube_fp2: (1, 1) # 1+𝑖 1+𝑖 is not a cube in 𝔽p²
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sexticTwist: M_Twist
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sexticNonResidue_fp2: (1, 1) # 1+𝑖
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curve BN446:
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bitwidth: 446
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modulus: "0x2400000000000000002400000002d00000000d800000021c0000001800000000870000000b0400000057c00000015c000000132000000067"
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family: BarretoNaehrig
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# u = 2^110 + 2^36 + 1
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curve FKM12_447: # Fotiadis-Konstantinou-Martindale
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bitwidth: 447
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modulus: "0x4ce300001338c00001c08180000f20cfffffe5a8bffffd08a000000f228000007e8ffffffaddfffffffdc00000009efffffffca000000007"
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# TNFS Resistant Families of Pairing-Friendly Elliptic Curves
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# Georgios Fotiadis and Elisavet Konstantinou, 2018
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# https://eprint.iacr.org/2018/1017
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#
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# Family 17 choice b of
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# Optimal TNFS-secure pairings on elliptic curves with composite embedding degree
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# Georgios Fotiadis and Chloe Martindale, 2019
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# https://eprint.iacr.org/2019/555
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#
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# A short-list of pairing-friendly curves resistant toSpecial TNFS at the 128-bit security level
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# Aurore Guillevic
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# https://hal.inria.fr/hal-02396352v2/document
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#
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# p(x) = 1728x^6 + 2160x^5 + 1548x^4 + 756x^3 + 240x^2 + 54x + 7
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# t(x) = −6x² + 1, r(x) = 36x^4 + 36x^3 + 18x^2 + 6x + 1.
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# Choice (b):u=−2^72 − 2^71 − 2^36
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#
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# Note the paper mentions 446-bit but it's 447
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curve BLS12_461:
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# Updating Key Size Estimations for Pairings
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# Barbulescu, R. and S. Duquesne, 2018
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# https://hal.archives-ouvertes.fr/hal-01534101/file/main.pdf
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bitwidth: 461
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modulus: "0x15555545554d5a555a55d69414935fbd6f1e32d8bacca47b14848b42a8dffa5c1cc00f26aa91557f00400020000555554aaaaaac0000aaaaaaab"
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# u = −2^77 + 2^50 + 2^33
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# p = (u - 1)^2 (u^4 - u^2 + 1)/3 + u
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# Note there is another BLS12-461 proposed here:
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# https://tools.ietf.org/id/draft-yonezawa-pairing-friendly-curves-00.html#rfc.section.4.2
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curve BN462:
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# Pairing-Friendly Curves
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# IETF Draft
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# https://tools.ietf.org/id/draft-irtf-cfrg-pairing-friendly-curves-02.html
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# Updating Key Size Estimations for Pairings
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# Barbulescu, R. and S. Duquesne, 2018
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# https://hal.archives-ouvertes.fr/hal-01534101/file/main.pdf
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bitwidth: 462
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modulus: "0x240480360120023ffffffffff6ff0cf6b7d9bfca0000000000d812908f41c8020ffffffffff6ff66fc6ff687f640000000002401b00840138013"
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family: BarretoNaehrig
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# u = 2^114 + 2^101 - 2^14 - 1
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