285 lines
7.0 KiB
Nim
285 lines
7.0 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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# Standard library
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unittest, times, random,
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# Internals
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../constantine/tower_field_extensions/[abelian_groups, fp2_complex],
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../constantine/config/[common, curves],
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../constantine/arithmetic,
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# Test utilities
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../helpers/prng
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const Iters = 128
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var rng: RngState
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let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32
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rng.seed(seed)
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echo "test_fp2 xoshiro512** seed: ", seed
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# Import: wrap in field element tests in small procedures
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# otherwise they will become globals,
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# and will create binary size issues.
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# Also due to Nim stack scanning,
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# having too many elements on the stack (a couple kB)
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# will significantly slow down testing (100x is possible)
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suite "𝔽p2 = 𝔽p[𝑖] (irreducible polynomial x²+1)":
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test "Fp2 '1' coordinates in canonical domain":
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template test(C: static Curve) =
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block:
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proc testInstance() =
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let oneFp2 = block:
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var O{.noInit.}: Fp2[C]
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O.setOne()
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O
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let oneBig = block:
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var O{.noInit.}: typeof(C.Mod.mres)
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O.setOne()
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O
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var r: typeof(C.Mod.mres)
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r.redc(oneFp2.c0.mres, C.Mod.mres, C.getNegInvModWord(), canUseNoCarryMontyMul = false)
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check:
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bool(r == oneBig)
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bool(oneFp2.c1.mres.isZero())
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test(BN254)
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test(BLS12_381)
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test(P256)
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test(Secp256k1)
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test "Squaring 1 returns 1":
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template test(C: static Curve) =
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block:
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proc testInstance() =
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let One = block:
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var O{.noInit.}: Fp2[C]
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O.setOne()
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O
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block:
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var r{.noinit.}: Fp2[C]
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r.square(One)
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check: bool(r == One)
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block:
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var r{.noinit.}: Fp2[C]
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r.prod(One, One)
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check: bool(r == One)
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testInstance()
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test(BN254)
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test(P256)
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test(Secp256k1)
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test(BLS12_377)
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test(BLS12_381)
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test(BN446)
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test(FKM12_447)
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test(BLS12_461)
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test(BN462)
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test "Multiplication by 0 and 1":
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template test(C: static Curve, body: untyped) =
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block:
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proc testInstance() =
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let Zero {.inject.} = block:
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var Z{.noInit.}: Fp2[C]
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Z.setZero()
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Z
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let One {.inject.} = block:
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var O{.noInit.}: Fp2[C]
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O.setOne()
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O
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for _ in 0 ..< Iters:
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let x {.inject.} = rng.random(Fp2[C])
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var r{.noinit, inject.}: Fp2[C]
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body
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testInstance()
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test(BN254):
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r.prod(x, Zero)
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check: bool(r == Zero)
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test(BN254):
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r.prod(Zero, x)
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check: bool(r == Zero)
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test(BN254):
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r.prod(x, One)
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check: bool(r == x)
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test(BN254):
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r.prod(One, x)
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check: bool(r == x)
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test(BLS12_381):
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r.prod(x, Zero)
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check: bool(r == Zero)
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test(BLS12_381):
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r.prod(Zero, x)
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check: bool(r == Zero)
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test(BLS12_381):
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r.prod(x, One)
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check: bool(r == x)
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test(BLS12_381):
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r.prod(One, x)
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check: bool(r == x)
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test(P256):
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r.prod(x, Zero)
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check: bool(r == Zero)
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test(P256):
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r.prod(Zero, x)
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check: bool(r == Zero)
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test(P256):
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r.prod(x, One)
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check: bool(r == x)
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test(P256):
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r.prod(One, x)
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check: bool(r == x)
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test(Secp256k1):
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r.prod(x, Zero)
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check: bool(r == Zero)
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test(Secp256k1):
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r.prod(Zero, x)
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check: bool(r == Zero)
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test(Secp256k1):
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r.prod(x, One)
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check: bool(r == x)
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test(Secp256k1):
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r.prod(One, x)
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check: bool(r == x)
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test "𝔽p2 = 𝔽p[𝑖] addition is associative and commutative":
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proc abelianGroup(curve: static Curve) =
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for _ in 0 ..< Iters:
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let a = rng.random(Fp2[curve])
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let b = rng.random(Fp2[curve])
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let c = rng.random(Fp2[curve])
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var tmp1{.noInit.}, tmp2{.noInit.}: Fp2[curve]
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# r0 = (a + b) + c
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tmp1.sum(a, b)
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tmp2.sum(tmp1, c)
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let r0 = tmp2
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# r1 = a + (b + c)
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tmp1.sum(b, c)
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tmp2.sum(a, tmp1)
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let r1 = tmp2
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# r2 = (a + c) + b
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tmp1.sum(a, c)
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tmp2.sum(tmp1, b)
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let r2 = tmp2
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# r3 = a + (c + b)
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tmp1.sum(c, b)
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tmp2.sum(a, tmp1)
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let r3 = tmp2
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# r4 = (c + a) + b
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tmp1.sum(c, a)
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tmp2.sum(tmp1, b)
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let r4 = tmp2
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# ...
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check:
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bool(r0 == r1)
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bool(r0 == r2)
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bool(r0 == r3)
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bool(r0 == r4)
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abelianGroup(BN254)
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abelianGroup(P256)
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abelianGroup(Secp256k1)
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abelianGroup(BLS12_377)
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abelianGroup(BLS12_381)
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abelianGroup(BN446)
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abelianGroup(FKM12_447)
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abelianGroup(BLS12_461)
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abelianGroup(BN462)
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test "𝔽p2 = 𝔽p[𝑖] multiplication is associative and commutative":
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proc commutativeRing(curve: static Curve) =
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for _ in 0 ..< Iters:
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let a = rng.random(Fp2[curve])
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let b = rng.random(Fp2[curve])
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let c = rng.random(Fp2[curve])
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var tmp1{.noInit.}, tmp2{.noInit.}: Fp2[curve]
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# r0 = (a * b) * c
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tmp1.prod(a, b)
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tmp2.prod(tmp1, c)
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let r0 = tmp2
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# r1 = a * (b * c)
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tmp1.prod(b, c)
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tmp2.prod(a, tmp1)
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let r1 = tmp2
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# r2 = (a * c) * b
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tmp1.prod(a, c)
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tmp2.prod(tmp1, b)
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let r2 = tmp2
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# r3 = a * (c * b)
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tmp1.prod(c, b)
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tmp2.prod(a, tmp1)
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let r3 = tmp2
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# r4 = (c * a) * b
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tmp1.prod(c, a)
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tmp2.prod(tmp1, b)
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let r4 = tmp2
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# ...
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check:
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bool(r0 == r1)
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bool(r0 == r2)
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bool(r0 == r3)
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bool(r0 == r4)
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commutativeRing(BN254)
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commutativeRing(P256)
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commutativeRing(Secp256k1)
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commutativeRing(BLS12_377)
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commutativeRing(BLS12_381)
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commutativeRing(BN446)
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commutativeRing(FKM12_447)
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commutativeRing(BLS12_461)
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commutativeRing(BN462)
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test "𝔽p2 = 𝔽p[𝑖] extension field multiplicative inverse":
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proc mulInvOne(curve: static Curve) =
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var one: Fp2[curve]
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one.setOne()
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var aInv, r{.noInit.}: Fp2[curve]
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for _ in 0 ..< Iters:
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let a = rng.random(Fp2[curve])
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aInv.inv(a)
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r.prod(a, aInv)
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check: bool(r == one)
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r.prod(aInv, a)
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check: bool(r == one)
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mulInvOne(BN254)
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mulInvOne(P256)
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mulInvOne(Secp256k1)
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mulInvOne(BLS12_377)
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mulInvOne(BLS12_381)
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mulInvOne(BN446)
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mulInvOne(FKM12_447)
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mulInvOne(BLS12_461)
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mulInvOne(BN462)
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