259 lines
7.0 KiB
Nim
259 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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std/[unittest, times],
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# Internal
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../constantine/arithmetic,
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../constantine/io/[io_bigints, io_fields],
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../constantine/config/[curves, common, type_bigint],
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# Test utilities
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../helpers/prng_unsafe
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const Iters = 24
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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 "\n------------------------------------------------------\n"
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echo "test_finite_fields_mulsquare xoshiro512** seed: ", seed
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static: doAssert defined(testingCurves), "This modules requires the -d:testingCurves compile option"
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proc sanity(C: static Curve) =
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test "Squaring 0,1,2 with "& $Curve(C) & " [FastSquaring = " & $C.canUseNoCarryMontySquare & "]":
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block: # 0² mod
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var n: Fp[C]
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n.fromUint(0'u32)
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let expected = n
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# Out-of-place
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var r: Fp[C]
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r.square(n)
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# In-place
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n.square()
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check:
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bool(r == expected)
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bool(n == expected)
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block: # 1² mod
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var n: Fp[C]
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n.fromUint(1'u32)
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let expected = n
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# Out-of-place
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var r: Fp[C]
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r.square(n)
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# In-place
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n.square()
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check:
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bool(r == expected)
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bool(n == expected)
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block: # 2² mod
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var n, expected: Fp[C]
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n.fromUint(2'u32)
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expected.fromUint(4'u32)
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# Out-of-place
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var r: Fp[C]
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r.square(n)
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# In-place
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n.square()
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check:
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bool(r == expected)
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bool(n == expected)
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proc mainSanity() =
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suite "Modular squaring is consistent with multiplication on special elements" & " [" & $WordBitwidth & "-bit mode]":
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sanity Fake101
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sanity Mersenne61
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sanity Mersenne127
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sanity P224 # P224 uses the fast-path with 64-bit words and the slow path with 32-bit words
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sanity P256
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sanity BLS12_381
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mainSanity()
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proc mainSelectCases() =
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suite "Modular Squaring: selected tricky cases" & " [" & $WordBitwidth & "-bit mode]":
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test "P-256 [FastSquaring = " & $P256.canUseNoCarryMontySquare & "]":
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block:
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# Triggered an issue in the (t[N+1], t[N]) = t[N] + (A1, A0)
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# between the squaring and reduction step, with t[N+1] and A1 being carry bits.
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var a: Fp[P256]
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a.fromHex"0xa0da36b4885df98997ee89a22a7ceb64fa431b2ecc87342fc083587da3d6ebc7"
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var r_mul, r_sqr: Fp[P256]
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r_mul.prod(a, a)
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r_sqr.square(a)
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doAssert bool(r_mul == r_sqr)
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mainSelectCases()
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proc randomCurve(C: static Curve) =
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let a = rng.random_unsafe(Fp[C])
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var r_mul, r_sqr: Fp[C]
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r_mul.prod(a, a)
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r_sqr.square(a)
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doAssert bool(r_mul == r_sqr)
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proc randomHighHammingWeight(C: static Curve) =
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let a = rng.random_highHammingWeight(Fp[C])
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var r_mul, r_sqr: Fp[C]
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r_mul.prod(a, a)
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r_sqr.square(a)
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doAssert bool(r_mul == r_sqr)
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proc random_long01Seq(C: static Curve) =
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let a = rng.random_long01Seq(Fp[C])
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var r_mul, r_sqr: Fp[C]
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r_mul.prod(a, a)
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r_sqr.square(a)
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doAssert bool(r_mul == r_sqr)
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suite "Random Modular Squaring is consistent with Modular Multiplication" & " [" & $WordBitwidth & "-bit mode]":
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test "Random squaring mod P-224 [FastSquaring = " & $P224.canUseNoCarryMontySquare & "]":
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for _ in 0 ..< Iters:
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randomCurve(P224)
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for _ in 0 ..< Iters:
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randomHighHammingWeight(P224)
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for _ in 0 ..< Iters:
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random_long01Seq(P224)
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test "Random squaring mod P-256 [FastSquaring = " & $P256.canUseNoCarryMontySquare & "]":
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for _ in 0 ..< Iters:
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randomCurve(P256)
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for _ in 0 ..< Iters:
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randomHighHammingWeight(P256)
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for _ in 0 ..< Iters:
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random_long01Seq(P256)
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test "Random squaring mod BLS12_381 [FastSquaring = " & $BLS12_381.canUseNoCarryMontySquare & "]":
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for _ in 0 ..< Iters:
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randomCurve(BLS12_381)
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for _ in 0 ..< Iters:
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randomHighHammingWeight(BLS12_381)
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for _ in 0 ..< Iters:
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random_long01Seq(BLS12_381)
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suite "Modular squaring - bugs highlighted by property-based testing":
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test "a² == (-a)² on for Fp[2^127 - 1] - #61":
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var a{.noInit.}: Fp[Mersenne127]
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a.fromHex"0x75bfffefbfffffff7fd9dfd800000000"
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var na{.noInit.}: Fp[Mersenne127]
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na.neg(a)
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a.square()
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na.square()
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check:
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bool(a == na)
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var a2{.noInit.}, na2{.noInit.}: Fp[Mersenne127]
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a2.fromHex"0x75bfffefbfffffff7fd9dfd800000000"
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na2.neg(a2)
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a2 *= a2
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na2 *= na2
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check:
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bool(a2 == na2)
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bool(a2 == a)
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bool(a2 == na)
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test "a² == (-a)² on for Fp[2^127 - 1] - #62":
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var a{.noInit.}: Fp[Mersenne127]
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a.fromHex"0x7ff7ffffffffffff1dfb7fafc0000000"
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var na{.noInit.}: Fp[Mersenne127]
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na.neg(a)
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a.square()
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na.square()
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check:
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bool(a == na)
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var a2{.noInit.}, na2{.noInit.}: Fp[Mersenne127]
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a2.fromHex"0x7ff7ffffffffffff1dfb7fafc0000000"
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na2.neg(a2)
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a2 *= a2
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na2 *= na2
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check:
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bool(a2 == na2)
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bool(a2 == a)
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bool(a2 == na)
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test "32-bit fast squaring on BLS12-381 - #42":
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# x = -(2^63 + 2^62 + 2^60 + 2^57 + 2^48 + 2^16)
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# p = (x - 1)^2 * (x^4 - x^2 + 1)//3 + x
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# Fp = GF(p)
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# a = Fp(Integer('0x091F02EFA1C9B99C004329E94CD3C6B308164CBE02037333D78B6C10415286F7C51B5CD7F917F77B25667AB083314B1B'))
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# a2 = a*a
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# print('a²: ' + Integer(a2).hex())
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var a{.noInit.}, expected{.noInit.}: Fp[BLS12_381]
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a.fromHex"0x091F02EFA1C9B99C004329E94CD3C6B308164CBE02037333D78B6C10415286F7C51B5CD7F917F77B25667AB083314B1B"
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expected.fromHex"0x129e84715b197f76766c8604002cfc287fbe3d16774e18c599853ce48d03dc26bf882e159323ee3d25e52e4809ff4ccc"
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var a2mul = a
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var a2sqr = a
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a2mul.prod(a, a)
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a2sqr.square(a)
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check:
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bool(a2mul == expected)
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bool(a2sqr == expected)
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test "32-bit fast squaring on BLS12-381 - #43":
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# x = -(2^63 + 2^62 + 2^60 + 2^57 + 2^48 + 2^16)
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# p = (x - 1)^2 * (x^4 - x^2 + 1)//3 + x
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# Fp = GF(p)
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# a = Fp(Integer('0x0B7C8AFE5D43E9A973AF8649AD8C733B97D06A78CFACD214CBE9946663C3F682362E0605BC8318714305B249B505AFD9'))
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# a2 = a*a
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# print('a²: ' + Integer(a2).hex())
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var a{.noInit.}, expected{.noInit.}: Fp[BLS12_381]
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a.fromHex"0x0B7C8AFE5D43E9A973AF8649AD8C733B97D06A78CFACD214CBE9946663C3F682362E0605BC8318714305B249B505AFD9"
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expected.fromHex"0x94b12b599042198a4ad5ad05ed4da1a3332fe50518b6eb718d258d7e3c60a48a89f7417a0b413b92537c24c9e94e038"
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var a2mul = a
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var a2sqr = a
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a2mul.prod(a, a)
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a2sqr.square(a)
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check:
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bool(a2mul == expected)
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bool(a2sqr == expected)
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