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102 lines
3.3 KiB
Python
102 lines
3.3 KiB
Python
# flake8: noqa
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from fields import Fq, Fq2
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# BLS parameter used to generate the other parameters
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# Spec is found here: https://github.com/zkcrypto/pairing/tree/master/src/bls12_381
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x = -0xD201000000010000
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# 381 bit prime
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# Also see fields:bls12381_q
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q = 0x1A0111EA397FE69A4B1BA7B6434BACD764774B84F38512BF6730D2A0F6B0F6241EABFFFEB153FFFFB9FEFFFFFFFFAAAB
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# a,b and a2, b2, define the elliptic curve and twisted curve.
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# y^2 = x^3 + 4
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# y^2 = x^3 + 4(u + 1)
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a = Fq(q, 0)
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b = Fq(q, 4)
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a_twist = Fq2(q, 0, 0)
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b_twist = Fq2(q, 4, 4)
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# The generators for g1 and g2
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gx = Fq(
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q,
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0x17F1D3A73197D7942695638C4FA9AC0FC3688C4F9774B905A14E3A3F171BAC586C55E83FF97A1AEFFB3AF00ADB22C6BB,
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)
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gy = Fq(
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q,
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0x08B3F481E3AAA0F1A09E30ED741D8AE4FCF5E095D5D00AF600DB18CB2C04B3EDD03CC744A2888AE40CAA232946C5E7E1,
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)
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g2x = Fq2(
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q,
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352701069587466618187139116011060144890029952792775240219908644239793785735715026873347600343865175952761926303160,
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3059144344244213709971259814753781636986470325476647558659373206291635324768958432433509563104347017837885763365758,
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)
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g2y = Fq2(
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q,
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1985150602287291935568054521177171638300868978215655730859378665066344726373823718423869104263333984641494340347905,
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927553665492332455747201965776037880757740193453592970025027978793976877002675564980949289727957565575433344219582,
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)
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# The order of all three groups (g1, g2, and gt). Note, the elliptic curve E_twist
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# actually has more valid points than this. This is relevant when hashing onto the
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# curve, where we use a point that is not in g2, and map it into g2.
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n = 0x73EDA753299D7D483339D80809A1D80553BDA402FFFE5BFEFFFFFFFF00000001
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# Cofactor used to generate r torsion points
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h = 0x396C8C005555E1568C00AAAB0000AAAB
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# https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-07#section-8.8.2
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h_eff = 0xBC69F08F2EE75B3584C6A0EA91B352888E2A8E9145AD7689986FF031508FFE1329C2F178731DB956D82BF015D1212B02EC0EC69D7477C1AE954CBC06689F6A359894C0ADEBBF6B4E8020005AAA95551
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# Embedding degree
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k = 12
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# sqrt(-3) mod q
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sqrt_n3 = 1586958781458431025242759403266842894121773480562120986020912974854563298150952611241517463240701
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# (sqrt(-3) - 1) / 2 mod q
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sqrt_n3m1o2 = 793479390729215512621379701633421447060886740281060493010456487427281649075476305620758731620350
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# This is the normal elliptic curve. G1 points are on here.
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def parameters():
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return (q, a, b, gx, gy, g2x, g2y, n, h, x, k, sqrt_n3, sqrt_n3m1o2)
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# This is the sextic twist used to send elements of G2 from
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# coordinates in Fq12 to coordinates in Fq2. It's isomorphic
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# to the above elliptic curve. See Page 63 of Costello.
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def parameters_twist():
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return (
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q,
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a_twist,
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b_twist,
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gx,
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gy,
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g2x,
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g2y,
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n,
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h_eff,
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x,
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k,
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sqrt_n3,
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sqrt_n3m1o2,
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)
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"""
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Copyright 2020 Chia Network Inc
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Licensed under the Apache License, Version 2.0 (the "License");
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you may not use this file except in compliance with the License.
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You may obtain a copy of the License at
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http://www.apache.org/licenses/LICENSE-2.0
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Unless required by applicable law or agreed to in writing, software
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distributed under the License is distributed on an "AS IS" BASIS,
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WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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See the License for the specific language governing permissions and
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limitations under the License.
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"""
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