Contract con_verifier_opt_pairing
| Creator | ae9cfa894495930b8d2f1707ab936325b5c848ace677bb8ba41dfe7dcdb3e3e6 |
| Creation Hash | 9ff10d9c7ee4bfd4e312c22f62f9d8a27abec2f95c0f8703854a6529e8d9fe51 |
| Created On | 828 days ago - 1/11/2022, 10:04:08 PM UTC+0 |
Contract Code
1
# con_verifier_opt_pairing
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pseudo_binary_encoding = [0, 0, 0, 1, 0, 1, 0, -1, 0, 0, 1, -1, 0, 0, 1, 0,
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0, 1, 1, 0, -1, 0, 0, 1, 0, -1, 0, 0, 0, 0, 1, 1,
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1, 0, 0, -1, 0, 0, 1, 0, 0, 0, 0, 0, -1, 0, 0, 1,
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1, 0, 0, -1, 0, 0, 0, 1, 1, 0, -1, 0, 0, 1, 0, 1, 1]
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curve_order = 21888242871839275222246405745257275088548364400416034343698204186575808495617
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p2 = 21888242871839275222246405745257275088696311157297823662689037894645226208583
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u = 4965661367192848881
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xiToPMinus1Over6 = [16469823323077808223889137241176536799009286646108169935659301613961712198316,
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8376118865763821496583973867626364092589906065868298776909617916018768340080]
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xiToPMinus1Over3 = [10307601595873709700152284273816112264069230130616436755625194854815875713954,
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21575463638280843010398324269430826099269044274347216827212613867836435027261]
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xiToPMinus1Over2 = [3505843767911556378687030309984248845540243509899259641013678093033130930403,
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2821565182194536844548159561693502659359617185244120367078079554186484126554]
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xiToPSquaredMinus1Over3 = 21888242871839275220042445260109153167277707414472061641714758635765020556616
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xiTo2PSquaredMinus2Over3 = 2203960485148121921418603742825762020974279258880205651966
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xiToPSquaredMinus1Over6 = 21888242871839275220042445260109153167277707414472061641714758635765020556617
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xiTo2PMinus2Over3 = [19937756971775647987995932169929341994314640652964949448313374472400716661030,
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2581911344467009335267311115468803099551665605076196740867805258568234346338]
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twistB = [266929791119991161246907387137283842545076965332900288569378510910307636690,
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19485874751759354771024239261021720505790618469301721065564631296452457478373]
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curveB = 3
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def FQ(n: int) -> int:
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n = n % p2
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if n < 0:
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n += p2
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return n
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def fq_inv(a: int, n: int = p2) -> int:
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if a == 0:
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return 0
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lm, hm = 1, 0
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low, high = a % n, n
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while low > 1:
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r = high // low
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nm, new = hm - lm * r, high - low * r
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lm, low, hm, high = nm, new, lm, low
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return lm % n
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def fa(self: int, other: int) -> int:
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return FQ(self + other)
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def fm(self: int, other: int) -> int:
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return FQ(self * other)
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def fs(self: int, other: int) -> int:
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return FQ(self - other)
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def fq_eq(self: int, other: int) -> bool:
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return self == other
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def fq_neg(self: int) -> int:
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self = -self
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if self < 0:
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self += p2
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return self
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def bits_of(k):
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return [int(c) for c in "{0:b}".format(k)]
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def FQ2(coeffs: list) -> list:
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assert len(coeffs) == 2, f'FQ2 must have 2 coefficients but had {len(coeffs)}'
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return coeffs
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def FQ6(coeffs: list) -> list:
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assert len(coeffs) == 3 and len(coeffs[0]) == 2, 'FQ6 must have 3 FQ2s'
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return coeffs
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def FQ12(coeffs: list) -> list:
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assert len(coeffs) == 2 and len(coeffs[0]) == 3, 'FQ12 must have 2 FQ6s'
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return coeffs
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def fq2_one(n: int = 0) -> list:
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return [0, 1]
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def fq2_zero(n: int = 0) -> list:
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return [0, 0]
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def fq2_is_one(self: list) -> bool:
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return self[0] == 0 and self[1] == 1
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def fq2_is_zero(self: list) -> bool:
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return self[0] == 0 and self[1] == 0
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def fq2_conjugate(self: list) -> list:
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return [fq_neg(self[0]), self[1]]
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def fq2_neg(self: list) -> list:
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return [fq_neg(self[0]), fq_neg(self[1])]
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def f2a(self: list, other: list) -> list:
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return [fa(self[0], other[0]), fa(self[1], other[1])]
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def f2s(self: list, other: list) -> list:
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return [fs(self[0], other[0]), fs(self[1], other[1])]
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def f2m(self: list, other: list) -> list:
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tx = fm(self[0], other[1])
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t = fm(other[0], self[1])
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tx = fa(tx, t)
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ty = fm(self[1], other[1])
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t = fm(self[0], other[0])
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ty = fs(ty, t)
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return [tx, ty]
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def f2m_scalar(self: list, other: int) -> list:
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x = fm(self[0], other)
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y = fm(self[1], other)
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return [x, y]
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def f2m_xi(self: list) -> list:
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tx = fa(self[0], self[0])
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tx = fa(tx, tx)
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tx = fa(tx, tx)
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tx = fa(tx, self[0])
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tx = fa(tx, self[1])
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ty = fa(self[1], self[1])
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ty = fa(ty, ty)
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ty = fa(ty, ty)
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ty = fa(ty, self[1])
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ty = fs(ty, self[0])
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return [tx, ty]
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def fq2_eq(self: list, other: list) -> bool:
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return self[0] == other[0] and self[1] == other[1]
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def fq2_square(self: list) -> list:
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tx = fs(self[1], self[0])
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ty = fa(self[0], self[1])
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ty = fm(tx, ty)
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tx = fm(self[0], self[1])
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tx = fa(tx, tx)
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return [tx, ty]
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def fq2_invert(self: list) -> list:
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t1 = fm(self[0], self[0])
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t2 = fm(self[1], self[1])
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t1 = fa(t1, t2)
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inv = fq_inv(t1)
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t1 = fq_neg(self[0])
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x = fm(t1, inv)
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y = fm(self[1], inv)
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return [x, y]
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def fq6_one(n: int = 0) -> list:
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return [fq2_zero(), fq2_zero(), fq2_one()]
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def fq6_zero(n: int = 0) -> list:
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return [fq2_zero(), fq2_zero(), fq2_zero()]
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def fq6_is_zero(self: list) -> bool:
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return fq2_is_zero(self[0]) and fq2_is_zero(self[1]) and fq2_is_zero(self[2])
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def fq6_is_one(self: list) -> bool:
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return fq2_is_zero(self[0]) and fq2_is_zero(self[1]) and fq2_is_one(self[2])
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def fq6_neg(self: list) -> list:
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return [fq2_neg(self[0]), fq2_neg(self[1]), fq2_neg(self[2])]
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def fq6_frobenius(self: list) -> list:
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x = fq2_conjugate(self[0])
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y = fq2_conjugate(self[1])
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z = fq2_conjugate(self[2])
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x = f2m(x, xiTo2PMinus2Over3)
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y = f2m(y, xiToPMinus1Over3)
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return [x, y, z]
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def fq6_frobenius_p2(self: list) -> list:
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x = f2m_scalar(self[0], xiTo2PSquaredMinus2Over3)
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y = f2m_scalar(self[1], xiToPSquaredMinus1Over3)
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return [x, y, self[2]]
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def f6a(self: list, other: list) -> list:
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return [f2a(self[0], other[0]), f2a(self[1], other[1]), f2a(self[2], other[2])]
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def f6s(self: list, other: list) -> list:
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return [f2s(self[0], other[0]), f2s(self[1], other[1]), f2s(self[2], other[2])]
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def f6m(self: list, other: list) -> list:
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v0 = f2m(self[2], other[2])
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v1 = f2m(self[1], other[1])
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v2 = f2m(self[0], other[0])
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t0 = f2a(self[0], self[1])
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t1 = f2a(other[0], other[1])
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tz = f2m(t0, t1)
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tz = f2s(tz, v1)
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tz = f2s(tz, v2)
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tz = f2m_xi(tz)
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tz = f2a(tz, v0)
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t0 = f2a(self[1], self[2])
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t1 = f2a(other[1], other[2])
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ty = f2m(t0, t1)
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t0 = f2m_xi(v2)
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ty = f2s(ty, v0)
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ty = f2s(ty, v1)
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ty = f2a(ty, t0)
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t0 = f2a(self[0], self[2])
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t1 = f2a(other[0], other[2])
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tx = f2m(t0, t1)
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tx = f2s(tx, v0)
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tx = f2a(tx, v1)
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tx = f2s(tx, v2)
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return [tx, ty, tz]
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def f6m_scalar(self: list, other: list) -> list:
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return [f2m(self[0], other), f2m(self[1], other), f2m(self[2], other)]
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def f6m_gfp(self: list, other: int) -> list:
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return [f2m_scalar(self[0], other), f2m_scalar(self[1], other), f2m_scalar(self[2], other)]
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def f6m_tau(self: list) -> list:
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tz = f2m_xi(self[0])
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ty = self[1]
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return [ty, self[2], tz]
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def fq6_square(self: list) -> list:
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v0 = fq2_square(self[2])
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v1 = fq2_square(self[1])
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v2 = fq2_square(self[0])
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c0 = f2a(self[0], self[1])
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c0 = fq2_square(c0)
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c0 = f2s(c0, v1)
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c0 = f2s(c0, v2)
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c0 = f2m_xi(c0)
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c0 = f2a(c0, v0)
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c1 = f2a(self[1], self[2])
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c1 = fq2_square(c1)
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c1 = f2s(c1, v0)
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c1 = f2s(c1, v1)
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xiV2 = f2m_xi(v2)
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c1 = f2a(c1, xiV2)
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c2 = f2a(self[0], self[2])
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c2 = fq2_square(c2)
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c2 = f2s(c2, v0)
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c2 = f2a(c2, v1)
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c2 = f2s(c2, v2)
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return [c2, c1, c0]
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def fq6_invert(self: list) -> list:
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XX = fq2_square(self[0])
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YY = fq2_square(self[1])
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ZZ = fq2_square(self[2])
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XY = f2m(self[0], self[1])
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XZ = f2m(self[0], self[2])
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YZ = f2m(self[1], self[2])
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A = f2s(ZZ, f2m_xi(XY))
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B = f2s(f2m_xi(XX), YZ)
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C = f2s(YY, XZ)
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F = f2m_xi(f2m(C, self[1]))
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F = f2a(F, f2m(A, self[2]))
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F = f2a(F, f2m_xi(f2m(B, self[0])))
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F = fq2_invert(F)
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return [f2m(C, F), f2m(B, F), f2m(A, F)]
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def fq12_one(n: int = 0) -> list:
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return [fq6_zero(), fq6_one()]
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def fq12_is_one(self: list) -> bool:
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return fq6_is_zero(self[0]) and fq6_is_one(self[1])
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def fq12_conjugate(self: list) -> list:
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return [fq6_neg(self[0]), self[1]]
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def fq12_frobenius(self: list) -> list:
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x = fq6_frobenius(self[0])
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x = f6m_scalar(x, xiToPMinus1Over6)
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return [x, fq6_frobenius(self[1])]
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def fq12_frobenius_p2(self: list) -> list:
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x = fq6_frobenius_p2(self[0])
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x = f6m_gfp(x, xiToPSquaredMinus1Over6)
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return [x, fq6_frobenius_p2(self[1])]
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def f12a(self: list, other: list) -> list:
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return [f6a(self[0], other[0]), f6a(self[1], other[1])]
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def f12s(self: list, other: list) -> list:
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return [f6s(self[0], other[0]), f6s(self[1], other[1])]
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def f12m(self: list, other: list) -> list:
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tx = f6m(self[0], other[1])
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t = f6m(self[1], other[0])
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tx = f6a(tx, t)
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ty = f6m(self[1], other[1])
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t = f6m(self[0], other[0])
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t = f6m_tau(t)
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return [tx, f6a(ty, t)]
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def f12m_scalar(self: list, other: list) -> list:
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return [f6m(self[0], other), f6m(self[1], other)]
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def fq12_exp(self: list, other: int) -> list:
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sum = fq12_one()
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for i in range(other.bit_length() - 1, -1, -1):
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t = fq12_square(sum)
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if other >> i & 1 != 0:
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sum = f12m(t, self)
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else:
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sum = t
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return sum
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def fq12_square(self: list) -> list:
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v0 = f6m(self[0], self[1])
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t = f6m_tau(self[0])
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t = f6a(self[1], t)
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ty = f6a(self[0], self[1])
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ty = f6m(ty, t)
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ty = f6s(ty, v0)
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t = f6m_tau(v0)
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ty = f6s(ty, t)
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return [f6a(v0, v0), ty]
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def fq12_invert(self: list) -> list:
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t1 = fq6_square(self[0])
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t2 = fq6_square(self[1])
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t1 = f6m_tau(t1)
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t1 = f6s(t2, t1)
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t2 = fq6_invert(t1)
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return f12m_scalar([fq6_neg(self[0]), self[1]], t2)
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def line_function_add(r: list, p: list, q: list, r2: list) -> tuple:
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B = f2m(p[0], r[3])
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D = f2a(p[1], r[2])
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D = fq2_square(D)
392
D = f2s(D, r2)
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D = f2s(D, r[3])
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D = f2m(D, r[3])
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H = f2s(B, r[0])
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I = fq2_square(H)
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E = f2a(I, I)
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E = f2a(E, E)
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J = f2m(H, E)
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L1 = f2s(D, r[1])
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L1 = f2s(L1, r[1])
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V = f2m(r[0], E)
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rOutX = fq2_square(L1)
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rOutX = f2s(rOutX, J)
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rOutX = f2s(rOutX, f2a(V, V))
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rOutZ = f2a(r[2], H)
414
rOutZ = fq2_square(rOutZ)
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rOutZ = f2s(rOutZ, r[3])
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rOutZ = f2s(rOutZ, I)
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t = f2s(V, rOutX)
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t = f2m(t, L1)
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t2 = f2m(r[1], J)
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t2 = f2a(t2, t2)
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rOutY = f2s(t, t2)
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rOutT = fq2_square(rOutZ)
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t = f2a(p[1], rOutZ)
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t = fq2_square(t)
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t = f2s(t, r2)
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t = f2s(t, rOutT)
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t2 = f2m(L1, p[0])
431
t2 = f2a(t2, t2)
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a = f2s(t2, t)
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c = f2m_scalar(rOutZ, q[1])
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c = f2a(c, c)
436
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b = fq2_neg(L1)
438
b = f2m_scalar(b, q[0])
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b = f2a(b, b)
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return a, b, c, [rOutX, rOutY, rOutZ, rOutT]
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def line_function_double(r: list, q: list) -> tuple:
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A = fq2_square(r[0])
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B = fq2_square(r[1])
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C = fq2_square(B)
448
449
D = f2a(r[0], B)
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D = fq2_square(D)
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D = f2s(D, A)
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D = f2s(D, C)
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D = f2a(D, D)
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E = f2a(f2a(A, A), A)
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F = fq2_square(E)
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C8 = f2a(C, C)
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C8 = f2a(C8, C8)
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C8 = f2a(C8, C8)
461
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rX = f2s(F, f2a(D, D))
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rY = f2m(E, f2s(D, rX))
464
rY = f2s(rY, C8)
465
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rZ = f2a(r[1], r[2])
467
rZ = fq2_square(rZ)
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rZ = f2s(rZ, B)
469
rZ = f2s(rZ, r[3])
470
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a = f2a(r[0], E)
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a = fq2_square(a)
473
B4 = f2a(B, B)
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B4 = f2a(B4, B4)
475
a = f2s(a, f2a(A, f2a(F, B4)))
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477
t = f2m(E, r[3])
478
t = f2a(t, t)
479
b = fq2_neg(t)
480
b = f2m_scalar(b, q[0])
481
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c = f2m(rZ, r[3])
483
c = f2a(c, c)
484
c = f2m_scalar(c, q[1])
485
486
rT = fq2_square(rZ)
487
return a, b, c, [rX, rY, rZ, rT]
488
489
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def line_function_mul(ret: list, a: list, b: list, c: list) -> list:
491
a2 = [fq2_zero(), a, b]
492
a2 = f6m(a2, ret[0])
493
t3 = f6m_scalar(ret[1], c)
494
495
t = f2a(b, c)
496
t2 = [fq2_zero(), a, t]
497
rX = f6a(ret[0], ret[1])
498
rY = t3
499
500
rX = f6m(rX, t2)
501
rX = f6s(rX, a2)
502
rX = f6s(rX, rY)
503
a2 = f6m_tau(a2)
504
rY = f6a(rY, a2)
505
return [rX, rY]
506
507
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def miller(q: list, p: list) -> list:
509
ret = fq12_one()
510
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aAffine = twist_make_affine(q)
512
bAffine = curve_make_affine(p)
513
514
minusA = twist_neg(aAffine)
515
516
r = aAffine
517
r2 = fq2_square(aAffine[1])
518
519
for i in range(len(pseudo_binary_encoding) - 1, 0, -1):
520
a, b, c, r = line_function_double(r, bAffine)
521
if i != len(pseudo_binary_encoding) - 1:
522
ret = fq12_square(ret)
523
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ret = line_function_mul(ret, a, b, c)
525
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s = pseudo_binary_encoding[i - 1]
527
if s == 1:
528
a, b, c, r = line_function_add(r, aAffine, bAffine, r2)
529
elif s == -1:
530
a, b, c, r = line_function_add(r, minusA, bAffine, r2)
531
else:
532
continue
533
534
ret = line_function_mul(ret, a, b, c)
535
536
q1 = [
537
f2m(fq2_conjugate(aAffine[0]), xiToPMinus1Over3),
538
f2m(fq2_conjugate(aAffine[1]), xiToPMinus1Over2),
539
fq2_one(),
540
fq2_one(),
541
]
542
543
minusQ2 = [
544
f2m_scalar(aAffine[0], xiToPSquaredMinus1Over3),
545
aAffine[1],
546
fq2_one(),
547
fq2_one(),
548
]
549
550
r2 = fq2_square(q1[1])
551
a, b, c, r = line_function_add(r, q1, bAffine, r2)
552
553
ret = line_function_mul(ret, a, b, c)
554
555
r2 = fq2_square(minusQ2[1])
556
a, b, c, r = line_function_add(r, minusQ2, bAffine, r2)
557
ret = line_function_mul(ret, a, b, c)
558
return ret
559
560
561
def final_exponentiation(p: list) -> list:
562
t1 = fq12_conjugate(p)
563
inv = fq12_invert(p)
564
565
t1 = f12m(t1, inv)
566
567
t2 = fq12_frobenius_p2(t1)
568
t1 = f12m(t1, t2)
569
570
fp = fq12_frobenius(t1)
571
fp2 = fq12_frobenius_p2(t1)
572
fp3 = fq12_frobenius(fp2)
573
574
fu = fq12_exp(t1, u)
575
fu2 = fq12_exp(fu, u)
576
fu3 = fq12_exp(fu2, u)
577
578
y3 = fq12_frobenius(fu)
579
fu2p = fq12_frobenius(fu2)
580
fu3p = fq12_frobenius(fu3)
581
y2 = fq12_frobenius_p2(fu2)
582
583
y0 = f12m(fp, fp2)
584
y0 = f12m(y0, fp3)
585
586
y1 = fq12_conjugate(t1)
587
y5 = fq12_conjugate(fu2)
588
y3 = fq12_conjugate(y3)
589
y4 = f12m(fu, fu2p)
590
y4 = fq12_conjugate(y4)
591
592
y6 = f12m(fu3, fu3p)
593
y6 = fq12_conjugate(y6)
594
595
t0 = fq12_square(y6)
596
t0 = f12m(t0, y4)
597
t0 = f12m(t0, y5)
598
599
t1 = f12m(y3, y5)
600
t1 = f12m(t1, t0)
601
t0 = f12m(t0, y2)
602
t1 = fq12_square(t1)
603
t1 = f12m(t1, t0)
604
t1 = fq12_square(t1)
605
t0 = f12m(t1, y1)
606
t1 = f12m(t1, y0)
607
t0 = fq12_square(t0)
608
t0 = f12m(t0, t1)
609
return t0
610
611
612
def twist_make_affine(c: list) -> list:
613
if fq2_is_one(c[2]):
614
return c
615
elif fq2_is_zero(c[2]):
616
return [
617
fq2_zero(),
618
fq2_one(),
619
fq2_zero(),
620
fq2_zero()
621
]
622
else:
623
zInv = fq2_invert(c[2])
624
zInv2 = fq2_square(zInv)
625
zInv3 = f2m(zInv2, zInv)
626
return [
627
f2m(c[0], zInv2),
628
f2m(c[1], zInv3),
629
fq2_one(),
630
fq2_one(),
631
]
632
633
634
def twist_add(a: list, b: list) -> list:
635
if twist_is_infinity(a):
636
return b
637
if twist_is_infinity(b):
638
return a
639
640
z12 = fq2_square(a[2])
641
z22 = fq2_square(b[2])
642
643
u1 = f2m(a[0], z22)
644
u2 = f2m(b[0], z12)
645
646
t = f2m(b[2], z22)
647
s1 = f2m(a[1], t)
648
649
t = f2m(a[2], z12)
650
s2 = f2m(b[1], t)
651
652
h = f2s(u2, u1)
653
xEqual = fq2_eq(h, fq2_zero())
654
655
t = f2a(h, h)
656
i = fq2_square(t)
657
j = f2m(h, i)
658
t = f2s(s2, s1)
659
660
yEqual = fq2_eq(t, fq2_zero())
661
662
if (xEqual and yEqual):
663
return twist_double(a)
664
665
r = f2a(t, t)
666
v = f2m(u1, i)
667
668
t4 = fq2_square(r)
669
t = f2a(v, v)
670
t6 = f2s(t4, j)
671
672
cX = f2s(t6, t)
673
674
t = f2s(v, cX)
675
t4 = f2m(s1, j)
676
t6 = f2a(t4, t4)
677
t4 = f2m(r, t)
678
cY = f2s(t4, t6)
679
680
t = f2a(a[2], b[2])
681
t4 = fq2_square(t)
682
t = f2s(t4, z12)
683
t4 = f2s(t, z22)
684
cZ = f2m(t4, h)
685
return [cX, cY, cZ]
686
687
688
def twist_double(a: list) -> list:
689
A = f2m(a[0], a[0])
690
B = f2m(a[1], a[1])
691
C = f2m(B, B)
692
693
t = f2a(a[0], B)
694
t2 = f2m(t, t)
695
t = f2s(t2, A)
696
t2 = f2s(t, C)
697
698
d = f2a(t2, t2)
699
t = f2a(A, A)
700
e = f2a(t, A)
701
f = f2m(e, e)
702
703
t = f2a(d, d)
704
cX = f2s(f, t)
705
706
cZ = f2m(a[1], a[2])
707
cZ = f2a(cZ, cZ)
708
709
t = f2a(C, C)
710
t2 = f2a(t, t)
711
t = f2a(t2, t2)
712
cY = f2s(d, cX)
713
t2 = f2m(e, cY)
714
cY = f2s(t2, t)
715
return [cX, cY, cZ]
716
717
718
def twist_mul(pt: list, k: int) -> list:
719
if int(k) == 0:
720
return [fq2_one(), fq2_one(), fq2_zero()]
721
722
R = [[fq2_zero(), fq2_zero(), fq2_zero()],
723
pt]
724
725
for kb in bits_of(k):
726
R[kb ^ 1] = twist_add(R[kb], R[kb ^ 1])
727
R[kb] = twist_double(R[kb])
728
return R[0]
729
730
731
def twist_neg(c: list) -> list:
732
return [
733
c[0],
734
fq2_neg(c[1]),
735
c[2],
736
fq2_zero(),
737
]
738
739
740
def twist_is_infinity(c: list) -> bool:
741
return fq2_is_zero(c[2])
742
743
744
def twist_is_on_curve(c: list) -> bool:
745
c = twist_make_affine(c)
746
if twist_is_infinity(c):
747
return True
748
749
y2 = fq2_square(c[1])
750
x3 = fq2_square(c[0])
751
x3 = f2m(x3, c[0])
752
753
y2 = f2s(y2, x3)
754
y2 = f2s(y2, twistB)
755
return fq2_is_zero(y2)
756
757
758
def curve_add(a: list, b: list) -> list:
759
if curve_is_infinity(a):
760
return b
761
if curve_is_infinity(b):
762
return a
763
764
z12 = fm(a[2], a[2])
765
z22 = fm(b[2], b[2])
766
767
u1 = fm(a[0], z22)
768
u2 = fm(b[0], z12)
769
770
t = fm(b[2], z22)
771
s1 = fm(a[1], t)
772
773
t = fm(a[2], z12)
774
s2 = fm(b[1], t)
775
776
h = fs(u2, u1)
777
xEqual = fq_eq(h, 0)
778
779
t = fa(h, h)
780
781
i = fm(t, t)
782
783
j = fm(h, i)
784
785
t = fs(s2, s1)
786
787
yEqual = fq_eq(t, 0)
788
789
if (xEqual and yEqual):
790
return curve_double(a)
791
792
r = fa(t, t)
793
794
v = fm(u1, i)
795
796
t4 = fm(r, r)
797
t = fa(v, v)
798
t6 = fs(t4, j)
799
800
cX = fs(t6, t)
801
802
t = fs(v, cX)
803
t4 = fm(s1, j)
804
t6 = fa(t4, t4)
805
t4 = fm(r, t)
806
cY = fs(t4, t6)
807
808
t = fa(a[2], b[2])
809
t4 = fm(t, t)
810
t = fs(t4, z12)
811
t4 = fs(t, z22)
812
cZ = fm(t4, h)
813
return [cX, cY, cZ]
814
815
816
def curve_double(a: list) -> list:
817
A = fm(a[0], a[0])
818
B = fm(a[1], a[1])
819
C = fm(B, B)
820
821
t = fa(a[0], B)
822
t2 = fm(t, t)
823
t = fs(t2, A)
824
t2 = fs(t, C)
825
826
d = fa(t2, t2)
827
t = fa(A, A)
828
e = fa(t, A)
829
f = fm(e, e)
830
831
t = fa(d, d)
832
cX = fs(f, t)
833
834
cZ = fm(a[1], a[2])
835
cZ = fa(cZ, cZ)
836
837
t = fa(C, C)
838
t2 = fa(t, t)
839
t = fa(t2, t2)
840
cY = fs(d, cX)
841
t2 = fm(e, cY)
842
cY = fs(t2, t)
843
return [cX, cY, cZ]
844
845
846
def curve_mul(pt: list, k: int) -> list:
847
if int(k) == 0:
848
return [1, 1, 0]
849
850
R = [[0, 0, 0],
851
pt]
852
853
for kb in bits_of(k):
854
R[kb ^ 1] = curve_add(R[kb], R[kb ^ 1])
855
R[kb] = curve_double(R[kb])
856
return R[0]
857
858
859
def curve_is_infinity(c: list) -> bool:
860
return c[2] == 0
861
862
863
def curve_neg(c: list) -> list:
864
return [
865
c[0],
866
fq_neg(c[1]),
867
c[2],
868
0,
869
]
870
871
872
def curve_make_affine(c: list) -> list:
873
if fq_eq(c[2], 1):
874
return c
875
elif fq_eq(c[2], 0):
876
return [
877
0,
878
1,
879
0,
880
0
881
]
882
else:
883
zInv = fq_inv(c[2])
884
t = fm(c[1], zInv)
885
zInv2 = fm(zInv, zInv)
886
cX = fm(c[0], zInv2)
887
cY = fm(t, zInv2)
888
return [
889
cX,
890
cY,
891
1,
892
1,
893
]
894
895
896
def curve_is_on_curve(c: list) -> bool:
897
c = curve_make_affine(c)
898
if curve_is_infinity(c):
899
return True
900
901
y2 = fm(c[1], c[1])
902
x3 = fm(c[0], c[0])
903
x3 = fm(x3, c[0])
904
x3 = fa(x3, curveB)
905
return fq_eq(y2, x3)
906
907
908
def pairing(Q: list, P: list) -> list:
909
assert curve_is_on_curve(P), f'P is not on the curve.'
910
assert twist_is_on_curve(Q), f'Q is not on the curve.'
911
if curve_is_infinity(P) or twist_is_infinity(Q):
912
return fq12_one()
913
r = miller(Q, P)
914
return r
915
916
@export
917
def compute_vk(IC: list, inputs: list) -> list:
918
vk_x = IC[0]
919
for i in range(len(inputs)):
920
assert inputs[i] < curve_order, "verifier-gte-snark-scalar-field"
921
vk_x = curve_add(vk_x, curve_mul(IC[i + 1], inputs[i]))
922
return vk_x
923
924
@export
925
def final_result(p: list, q: list) -> int:
926
p[0] = curve_neg(p[0])
927
928
x = fq12_one()
929
for i in range(4):
930
if twist_is_infinity(q[i]) or curve_is_infinity(p[i]):
931
continue
932
x = f12m(x, pairing(q[i], p[i]))
933
934
x = final_exponentiation(x)
935
if not fq12_is_one(x):
936
return 1
937
return 0
938
Byte Code
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