122 lines
3.6 KiB
Nim
122 lines
3.6 KiB
Nim
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# 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 std/unittest, std/times,
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../constantine/[arithmetic, primitives],
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../constantine/io/[io_fields],
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../constantine/config/[curves, common],
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# Test utilities
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../helpers/prng,
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# Standard library
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std/tables
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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_finite_fields_sqrt xoshiro512** seed: ", seed
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static: doAssert defined(testingCurves), "This modules requires the -d:testingCurves compile option"
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proc exhaustiveCheck_p3mod4(C: static Curve, modulus: static int) =
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test "Exhaustive square root check for p ≡ 3 (mod 4) on " & $Curve(C):
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var squares_to_roots: Table[uint16, set[uint16]]
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# Create all squares
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# -------------------------
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for i in 0'u16 ..< modulus:
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var a{.noInit.}: Fp[C]
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a.fromUint(i)
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a.square()
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var r_bytes: array[8, byte]
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r_bytes.exportRawUint(a, cpuEndian)
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let r = uint16(cast[uint64](r_bytes))
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squares_to_roots.mgetOrPut(r, default(set[uint16])).incl(i)
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# From Euler's criterion
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# there is exactly (p-1)/2 squares in 𝔽p* (without 0)
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# and so (p-1)/2 + 1 in 𝔽p (with 0)
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check: squares_to_roots.len == (modulus-1) div 2 + 1
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# Check squares
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# -------------------------
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for i in 0'u16 ..< modulus:
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var a{.noInit.}: Fp[C]
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a.fromUint(i)
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if i in squares_to_roots:
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var a2 = a
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check:
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bool a.isSquare()
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bool a.sqrt_if_square_p3mod4()
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# 2 different code paths have the same result
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# (despite 2 square roots existing per square)
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a2.sqrt_p3mod4()
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check: bool(a == a2)
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var r_bytes: array[8, byte]
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r_bytes.exportRawUint(a, cpuEndian)
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let r = uint16(cast[uint64](r_bytes))
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# r is one of the 2 square roots of `i`
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check: r in squares_to_roots[i]
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else:
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let a2 = a
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check:
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bool not a.isSquare()
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bool not a.sqrt_if_square_p3mod4()
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bool (a == a2) # a shouldn't be modified
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proc randomSqrtCheck_p3mod4(C: static Curve) =
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test "Random square root check for p ≡ 3 (mod 4) on " & $Curve(C):
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for _ in 0 ..< Iters:
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let a = rng.random(Fp[C])
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var na{.noInit.}: Fp[C]
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na.neg(a)
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var a2 = a
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var na2 = na
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a2.square()
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na2.square()
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check:
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bool a2 == na2
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bool a2.isSquare()
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var r, s = a2
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r.sqrt_p3mod4()
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let ok = s.sqrt_if_square_p3mod4()
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check:
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bool ok
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bool(r == s)
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bool(r == a or r == na)
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proc main() =
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suite "Modular square root":
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exhaustiveCheck_p3mod4 Fake103, 103
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exhaustiveCheck_p3mod4 Fake10007, 10007
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exhaustiveCheck_p3mod4 Fake65519, 65519
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randomSqrtCheck_p3mod4 Mersenne61
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randomSqrtCheck_p3mod4 Mersenne127
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randomSqrtCheck_p3mod4 BN254
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randomSqrtCheck_p3mod4 P256
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randomSqrtCheck_p3mod4 Secp256k1
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randomSqrtCheck_p3mod4 BLS12_381
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randomSqrtCheck_p3mod4 BN446
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randomSqrtCheck_p3mod4 FKM12_447
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randomSqrtCheck_p3mod4 BLS12_461
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randomSqrtCheck_p3mod4 BN462
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main()
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