constantine/tests/t_finite_fields_sqrt.nim

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# Constantine
# Copyright (c) 2018-2019 Status Research & Development GmbH
# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
# Licensed and distributed under either of
# * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
# * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
# at your option. This file may not be copied, modified, or distributed except according to those terms.
import
# Standard library
std/[tables, unittest, times],
# Internal
../constantine/[arithmetic, primitives],
../constantine/io/[io_fields],
../constantine/config/[curves, common],
# Test utilities
../helpers/prng_unsafe
const Iters = 8
var rng: RngState
let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32
rng.seed(seed)
echo "\n------------------------------------------------------\n"
echo "test_finite_fields_sqrt xoshiro512** seed: ", seed
static: doAssert defined(testingCurves), "This modules requires the -d:testingCurves compile option"
proc exhaustiveCheck(C: static Curve, modulus: static int) =
test "Exhaustive square root check for " & $Curve(C):
var squares_to_roots: Table[uint16, set[uint16]]
# Create all squares
# -------------------------
for i in 0'u16 ..< modulus:
var a{.noInit.}: Fp[C]
a.fromUint(i)
a.square()
var r_bytes: array[8, byte]
r_bytes.exportRawUint(a, cpuEndian)
let r = uint16(cast[uint64](r_bytes))
squares_to_roots.mgetOrPut(r, default(set[uint16])).incl(i)
# From Euler's criterion
# there is exactly (p-1)/2 squares in 𝔽p* (without 0)
# and so (p-1)/2 + 1 in 𝔽p (with 0)
check: squares_to_roots.len == (modulus-1) div 2 + 1
# Check squares
# -------------------------
for i in 0'u16 ..< modulus:
var a{.noInit.}: Fp[C]
a.fromUint(i)
if i in squares_to_roots:
var a2 = a
check:
bool a.isSquare()
bool a.sqrt_if_square()
# 2 different code paths have the same result
# (despite 2 square roots existing per square)
a2.sqrt()
check: bool(a == a2)
var r_bytes: array[8, byte]
r_bytes.exportRawUint(a, cpuEndian)
let r = uint16(cast[uint64](r_bytes))
# r is one of the 2 square roots of `i`
check: r in squares_to_roots[i]
else:
let a2 = a
check:
bool not a.isSquare()
bool not a.sqrt_if_square()
bool (a == a2) # a shouldn't be modified
template testImpl(a: untyped): untyped {.dirty.} =
var na{.noInit.}: typeof(a)
na.neg(a)
var a2 = a
var na2 = na
a2.square()
na2.square()
check:
bool a2 == na2
bool a2.isSquare()
var r, s = a2
r.sqrt()
let ok = s.sqrt_if_square()
check:
bool ok
bool(r == s)
bool(r == a or r == na)
proc randomSqrtCheck(C: static Curve) =
test "Random square root check for " & $Curve(C):
for _ in 0 ..< 1: # Iters:
let a = rng.random_unsafe(Fp[C])
testImpl(a)
for _ in 0 ..< Iters:
let a = rng.randomHighHammingWeight(Fp[C])
testImpl(a)
for _ in 0 ..< Iters:
let a = rng.random_long01Seq(Fp[C])
testImpl(a)
proc main() =
suite "Modular square root" & " [" & $WordBitwidth & "-bit mode]":
exhaustiveCheck Fake103, 103
# exhaustiveCheck Fake10007, 10007
# exhaustiveCheck Fake65519, 65519
randomSqrtCheck BN254_Nogami
randomSqrtCheck BN254_Snarks
randomSqrtCheck BLS12_377 # p ≢ 3 (mod 4)
randomSqrtCheck BLS12_381
randomSqrtCheck BW6_761
suite "Modular square root - 32-bit bugs highlighted by property-based testing " & " [" & $WordBitwidth & "-bit mode]":
2020-09-27 11:13:45 +00:00
# test "FKM12_447 - #30": - Deactivated, we don't support the curve as no one uses it.
# var a: Fp[FKM12_447]
# a.fromHex"0x406e5e74ee09c84fa0c59f2db3ac814a4937e2f57ecd3c0af4265e04598d643c5b772a6549a2d9b825445c34b8ba100fe8d912e61cfda43d"
# a.square()
# check: bool a.isSquare()
test "Fused modular square root on 32-bit - inconsistent with isSquare - #42":
var a: Fp[BLS12_381]
a.fromHex"0x184d02ce4f24d5e59b4150a57a31b202fd40a4b41d7518c22b84bee475fbcb7763100448ef6b17a6ea603cf062e5db51"
check:
bool(not a.isSquare())
bool(not a.sqrt_if_square())
test "Fused modular square root on 32-bit - inconsistent with isSquare - #43":
var a: Fp[BLS12_381]
a.fromHex"0x0f16d7854229d8804bcadd889f70411d6a482bde840d238033bf868e89558d39d52f9df60b2d745e02584375f16c34a3"
check:
bool(not a.isSquare())
bool(not a.sqrt_if_square())
test "Fp[2^127 - 1] - #61":
var a: Fp[Mersenne127]
a.fromHex"0x75bfffefbfffffff7fd9dfd800000000"
testImpl(a)
test "Fp[2^127 - 1] - #62":
var a: Fp[Mersenne127]
a.fromHex"0x7ff7ffffffffffff1dfb7fafc0000000"
testImpl(a)
main()