constantine/tests/t_fp_tower_template.nim

461 lines
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Nim

# 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.
# ############################################################
#
# Template tests for towered extension fields
#
# ############################################################
import
# Standard library
std/[unittest, times],
# Internals
../constantine/towers,
../constantine/config/[common, curves],
../constantine/arithmetic,
# Test utilities
../helpers/[prng_unsafe, static_for]
echo "\n------------------------------------------------------\n"
template ExtField(degree: static int, curve: static Curve): untyped =
when degree == 2:
Fp2[curve]
elif degree == 6:
Fp6[curve]
elif degree == 12:
Fp12[curve]
else:
{.error: "Unconfigured extension degree".}
type
RandomGen = enum
Uniform
HighHammingWeight
Long01Sequence
func random_elem(rng: var RngState, F: typedesc, gen: static RandomGen): F {.inline, noInit.} =
when gen == Uniform:
result = rng.random_unsafe(F)
elif gen == HighHammingWeight:
result = rng.random_highHammingWeight(F)
else:
result = rng.random_long01Seq(F)
proc runTowerTests*[N](
ExtDegree: static int,
Iters: static int,
TestCurves: static array[N, Curve],
moduleName: string,
testSuiteDesc: string
) =
# Random seed for reproducibility
var rng: RngState
let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32
rng.seed(seed)
echo moduleName, " xoshiro512** seed: ", seed
suite testSuiteDesc & " [" & $WordBitwidth & "-bit mode]":
test "Comparison sanity checks":
proc test(Field: typedesc) =
var z, o {.noInit.}: Field
z.setZero()
o.setOne()
check: not bool(z == o)
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve))
test "Addition, substraction negation are consistent":
proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
# Try to exercise all code paths for in-place/out-of-place add/sum/sub/diff/double/neg
# (1 - (-a) - b + (-a) - 2a) + (2a + 2b + (-b)) == 1
var accum {.noInit.}, One {.noInit.}, a{.noInit.}, na{.noInit.}, b{.noInit.}, nb{.noInit.}, a2 {.noInit.}, b2 {.noInit.}: Field
for _ in 0 ..< Iters:
One.setOne()
a = rng.random_elem(Field, gen)
a2 = a
a2.double()
na.neg(a)
b = rng.random_elem(Field, gen)
b2.double(b)
nb.neg(b)
accum.diff(One, na)
accum -= b
accum += na
accum -= a2
var t{.noInit.}: Field
t.sum(a2, b2)
t += nb
accum += t
check: bool accum.isOne()
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
test "Division by 2":
proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
for _ in 0 ..< Iters:
let a = rng.random_elem(Field, gen)
var a2 = a
a2.double()
a2.div2()
check: bool(a == a2)
a2.div2()
a2.double()
check: bool(a == a2)
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
test "Squaring 1 returns 1":
proc test(Field: typedesc) =
let One = block:
var O{.noInit.}: Field
O.setOne()
O
block:
var r{.noinit.}: Field
r.square(One)
check: bool(r == One)
block:
var r{.noinit.}: Field
r.prod(One, One)
check: bool(r == One)
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve))
test "Squaring 2 returns 4":
proc test(Field: typedesc) =
let One = block:
var O{.noInit.}: Field
O.setOne()
O
var Two: Field
Two.double(One)
var Four: Field
Four.double(Two)
block:
var r: Field
r.square(Two)
check: bool(r == Four)
block:
var r: Field
r.prod(Two, Two)
check: bool(r == Four)
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve))
test "Squaring 3 returns 9":
proc test(Field: typedesc) =
let One = block:
var O{.noInit.}: Field
O.setOne()
O
var Three: Field
for _ in 0 ..< 3:
Three += One
var Nine: Field
for _ in 0 ..< 9:
Nine += One
block:
var u: Field
u.square(Three)
check: bool(u == Nine)
block:
var u: Field
u.prod(Three, Three)
check: bool(u == Nine)
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve))
test "Squaring -3 returns 9":
proc test(Field: typedesc) =
let One = block:
var O{.noInit.}: Field
O.setOne()
O
var MinusThree: Field
for _ in 0 ..< 3:
MinusThree -= One
var Nine: Field
for _ in 0 ..< 9:
Nine += One
block:
var u: Field
u.square(MinusThree)
check: bool(u == Nine)
block:
var u: Field
u.prod(MinusThree, MinusThree)
check: bool(u == Nine)
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve))
test "Multiplication by 0 and 1":
template test(Field: typedesc, body: untyped) =
block:
proc testInstance() =
let Z {.inject.} = block:
var Z{.noInit.}: Field
Z.setZero()
Z
let O {.inject.} = block:
var O{.noInit.}: Field
O.setOne()
O
for _ in 0 ..< Iters:
let x {.inject.} = rng.random_unsafe(Field)
var r{.noinit, inject.}: Field
body
testInstance()
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve)):
r.prod(x, Z)
check: bool(r == Z)
test(ExtField(ExtDegree, curve)):
r.prod(Z, x)
check: bool(r == Z)
test(ExtField(ExtDegree, curve)):
r.prod(x, O)
check: bool(r == x)
test(ExtField(ExtDegree, curve)):
r.prod(O, x)
check: bool(r == x)
test "Multiplication and Squaring are consistent":
proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
for _ in 0 ..< Iters:
let a = rng.random_elem(Field, gen)
var rMul{.noInit.}, rSqr{.noInit.}: Field
rMul.prod(a, a)
rSqr.square(a)
check: bool(rMul == rSqr)
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
test "Squaring the opposite gives the same result":
proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
for _ in 0 ..< Iters:
let a = rng.random_elem(Field, gen)
var na{.noInit.}: Field
na.neg(a)
var rSqr{.noInit.}, rNegSqr{.noInit.}: Field
rSqr.square(a)
rNegSqr.square(na)
check: bool(rSqr == rNegSqr)
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
test "Multiplication and Addition/Substraction are consistent":
proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
for _ in 0 ..< Iters:
let factor = rng.random_unsafe(-30..30)
let a = rng.random_elem(Field, gen)
if factor == 0: continue
var sum{.noInit.}, one{.noInit.}, f{.noInit.}: Field
one.setOne()
if factor < 0:
sum.neg(a)
f.neg(one)
for i in 1 ..< -factor:
sum -= a
f -= one
else:
sum = a
f = one
for i in 1 ..< factor:
sum += a
f += one
var r{.noInit.}: Field
r.prod(a, f)
check: bool(r == sum)
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
test "Addition is associative and commutative":
proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
for _ in 0 ..< Iters:
let a = rng.random_elem(Field, gen)
let b = rng.random_elem(Field, gen)
let c = rng.random_elem(Field, gen)
var tmp1{.noInit.}, tmp2{.noInit.}: Field
# r0 = (a + b) + c
tmp1.sum(a, b)
tmp2.sum(tmp1, c)
let r0 = tmp2
# r1 = a + (b + c)
tmp1.sum(b, c)
tmp2.sum(a, tmp1)
let r1 = tmp2
# r2 = (a + c) + b
tmp1.sum(a, c)
tmp2.sum(tmp1, b)
let r2 = tmp2
# r3 = a + (c + b)
tmp1.sum(c, b)
tmp2.sum(a, tmp1)
let r3 = tmp2
# r4 = (c + a) + b
tmp1.sum(c, a)
tmp2.sum(tmp1, b)
let r4 = tmp2
# ...
check:
bool(r0 == r1)
bool(r0 == r2)
bool(r0 == r3)
bool(r0 == r4)
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
test "Multiplication is associative and commutative":
proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
for _ in 0 ..< Iters:
let a = rng.random_elem(Field, gen)
let b = rng.random_elem(Field, gen)
let c = rng.random_elem(Field, gen)
var tmp1{.noInit.}, tmp2{.noInit.}: Field
# r0 = (a * b) * c
tmp1.prod(a, b)
tmp2.prod(tmp1, c)
let r0 = tmp2
# r1 = a * (b * c)
tmp1.prod(b, c)
tmp2.prod(a, tmp1)
let r1 = tmp2
# r2 = (a * c) * b
tmp1.prod(a, c)
tmp2.prod(tmp1, b)
let r2 = tmp2
# r3 = a * (c * b)
tmp1.prod(c, b)
tmp2.prod(a, tmp1)
let r3 = tmp2
# r4 = (c * a) * b
tmp1.prod(c, a)
tmp2.prod(tmp1, b)
let r4 = tmp2
# ...
check:
bool(r0 == r1)
bool(r0 == r2)
bool(r0 == r3)
bool(r0 == r4)
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
test "Extension field multiplicative inverse":
proc test(Field: typedesc, Iters: static int, gen: static RandomGen) =
var aInv, r{.noInit.}: Field
for _ in 0 ..< Iters:
let a = rng.random_elem(Field, gen)
aInv.inv(a)
r.prod(a, aInv)
check: bool(r.isOne())
r.prod(aInv, a)
check: bool(r.isOne())
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve), Iters, gen = Uniform)
test(ExtField(ExtDegree, curve), Iters, gen = HighHammingWeight)
test(ExtField(ExtDegree, curve), Iters, gen = Long01Sequence)
test "0 does not have a multiplicative inverse and should return 0 for projective/jacobian => affine coordinates conversion":
proc test(Field: typedesc) =
var z: Field
z.setZero()
var zInv{.noInit.}: Field
zInv.inv(z)
check: bool zInv.isZero()
staticFor(curve, TestCurves):
test(ExtField(ExtDegree, curve))