constantine/tests/test_finite_fields_powinv.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.

import  ../constantine/arithmetic,
        ../constantine/io/[io_bigints, io_fields],
        ../constantine/config/curves,
        # Test utilities
        ../helpers/prng,
        # Standard library
        std/unittest, std/times

static: doAssert defined(testingCurves), "This modules requires the -d:testingCurves compile option"

const Iters = 512

var rng: RngState
let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32
rng.seed(seed)
echo "test_finite_fields_powinv xoshiro512** seed: ", seed

proc main() =
  suite "Modular exponentiation over finite fields":
    test "n² mod 101":
      let exponent = BigInt[64].fromUint(2'u64)

      block: # 1*1 mod 101
        var n, expected: Fp[Fake101]

        n.fromUint(1'u32)
        expected = n

        var r: Fp[Fake101]
        r.prod(n, n)

        var r_bytes: array[8, byte]
        r_bytes.exportRawUint(r, cpuEndian)
        let rU64 = cast[uint64](r_bytes)

        check:
          # Check equality in the Montgomery domain
          bool(r == expected)
          # Check equality when converting back to natural domain
          1'u64 == rU64

      block: # 1^2 mod 101
        var n, expected: Fp[Fake101]

        n.fromUint(1'u32)
        expected = n

        n.pow(exponent)

        var n_bytes: array[8, byte]
        n_bytes.exportRawUint(n, cpuEndian)
        let r = cast[uint64](n_bytes)

        check:
          # Check equality in the Montgomery domain
          bool(n == expected)
          # Check equality when converting back to natural domain
          1'u64 == r

      block: # 2^2 mod 101
        var n, expected: Fp[Fake101]

        n.fromUint(2'u32)
        expected.fromUint(4'u32)

        n.pow(exponent)

        var n_bytes: array[8, byte]
        n_bytes.exportRawUint(n, cpuEndian)
        let r = cast[uint64](n_bytes)

        check:
          # Check equality in the Montgomery domain
          bool(n == expected)
          # Check equality when converting back to natural domain
          4'u64 == r

      block: # 10^2 mod 101
        var n, expected: Fp[Fake101]

        n.fromUint(10'u32)
        expected.fromUint(100'u32)

        n.pow(exponent)

        var n_bytes: array[8, byte]
        n_bytes.exportRawUint(n, cpuEndian)
        let r = cast[uint64](n_bytes)

        check:
          # Check equality in the Montgomery domain
          bool(n == expected)
          # Check equality when converting back to natural domain
          100'u64 == r

      block: # 11^2 mod 101
        var n, expected: Fp[Fake101]

        n.fromUint(11'u32)
        expected.fromUint(20'u32)

        n.pow(exponent)

        var n_bytes: array[8, byte]
        n_bytes.exportRawUint(n, cpuEndian)
        let r = cast[uint64](n_bytes)

        check:
          # Check equality in the Montgomery domain
          bool(n == expected)
          # Check equality when converting back to natural domain
          20'u64 == r

    test "x^(p-2) mod p (modular inversion if p prime)":
      block:
        var x: Fp[BLS12_381]

        # BN254 field modulus
        x.fromHex("0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47")
        # BLS12-381 prime - 2
        let exponent = BigInt[381].fromHex("0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaa9")

        let expected = "0x0636759a0f3034fa47174b2c0334902f11e9915b7bd89c6a2b3082b109abbc9837da17201f6d8286fe6203caa1b9d4c8"

        x.pow(exponent)
        let computed = x.toHex()

        check:
          computed == expected

      block:
        var x: Fp[BLS12_381]

        # BN254 field modulus
        x.fromHex("0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47")
        # BLS12-381 prime - 2
        let exponent = BigInt[381].fromHex("0x1a0111ea397fe69a4b1ba7b6434bacd764774b84f38512bf6730d2a0f6b0f6241eabfffeb153ffffb9feffffffffaaa9")

        let expected = "0x0636759a0f3034fa47174b2c0334902f11e9915b7bd89c6a2b3082b109abbc9837da17201f6d8286fe6203caa1b9d4c8"

        x.powUnsafeExponent(exponent)
        let computed = x.toHex()

        check:
          computed == expected

  suite "Modular inversion over prime fields":
    test "Specific test on Fp[BLS12_381]":
      var r, x: Fp[BLS12_381]

      # BN254 field modulus
      x.fromHex("0x30644e72e131a029b85045b68181585d97816a916871ca8d3c208c16d87cfd47")

      let expected = "0x0636759a0f3034fa47174b2c0334902f11e9915b7bd89c6a2b3082b109abbc9837da17201f6d8286fe6203caa1b9d4c8"
      r.inv(x)
      let computed = r.toHex()

      check:
        computed == expected

    test "Specific tests on Fp[BN254_Snarks]":
      block:
        var r, x: Fp[BN254_Snarks]
        x.setOne()
        r.inv(x)
        check: bool r.isOne()

      block:
        var r, x, expected: Fp[BN254_Snarks]
        x.fromHex"0x076ef96647587df443d86a7ac8aa12f3f52d5d775287a6f5e47764a59d378309"
        expected.fromHex"2d2ef0cd23dd8ec9e9b47c130942ecd7d7fda5e2dd5af19114bc34565ee355b8"

        r.inv(x)
        check: bool(r == expected)

      block:
        var r, x, expected: Fp[BN254_Snarks]
        x.fromHex"0x0d2007d8aaface1b8501bfbe792974166e8f9ad6106e5b563604f0aea9ab06f6"
        expected.fromHex"1b632d8aa572c4356debe80f772228dee49c203f34066a998fba5194b98e56c3"

        r.inv(x)
        check: bool(r == expected)

    proc testRandomInv(curve: static Curve) =
      test "Random inversion testing on " & $Curve(curve):
        var aInv, r: Fp[curve]

        for _ in 0 ..< Iters:
          let a = rng.random(Fp[curve])
          aInv.inv(a)
          r.prod(a, aInv)
          check: bool r.isOne()
          r.prod(aInv, a)
          check: bool r.isOne()

    testRandomInv P224
    testRandomInv BN254_Nogami
    testRandomInv BN254_Snarks
    testRandomInv Curve25519
    testRandomInv P256
    testRandomInv Secp256k1
    testRandomInv BLS12_377
    testRandomInv BLS12_381
    testRandomInv BN446
    testRandomInv FKM12_447
    testRandomInv BLS12_461
    testRandomInv BN462

main()