go/src/crypto/internal/fips/mlkem/field_test.go

// Copyright 2023 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package mlkem

import (
	"math/big"
	"strconv"
	"testing"
)

func TestFieldReduce(t *testing.T) {
	for a := uint32(0); a < 2*q*q; a++ {
		got := fieldReduce(a)
		exp := fieldElement(a % q)
		if got != exp {
			t.Fatalf("reduce(%d) = %d, expected %d", a, got, exp)
		}
	}
}

func TestFieldAdd(t *testing.T) {
	for a := fieldElement(0); a < q; a++ {
		for b := fieldElement(0); b < q; b++ {
			got := fieldAdd(a, b)
			exp := (a + b) % q
			if got != exp {
				t.Fatalf("%d + %d = %d, expected %d", a, b, got, exp)
			}
		}
	}
}

func TestFieldSub(t *testing.T) {
	for a := fieldElement(0); a < q; a++ {
		for b := fieldElement(0); b < q; b++ {
			got := fieldSub(a, b)
			exp := (a - b + q) % q
			if got != exp {
				t.Fatalf("%d - %d = %d, expected %d", a, b, got, exp)
			}
		}
	}
}

func TestFieldMul(t *testing.T) {
	for a := fieldElement(0); a < q; a++ {
		for b := fieldElement(0); b < q; b++ {
			got := fieldMul(a, b)
			exp := fieldElement((uint32(a) * uint32(b)) % q)
			if got != exp {
				t.Fatalf("%d * %d = %d, expected %d", a, b, got, exp)
			}
		}
	}
}

func TestDecompressCompress(t *testing.T) {
	for _, bits := range []uint8{1, 4, 10} {
		for a := uint16(0); a < 1<<bits; a++ {
			f := decompress(a, bits)
			if f >= q {
				t.Fatalf("decompress(%d, %d) = %d >= q", a, bits, f)
			}
			got := compress(f, bits)
			if got != a {
				t.Fatalf("compress(decompress(%d, %d), %d) = %d", a, bits, bits, got)
			}
		}

		for a := fieldElement(0); a < q; a++ {
			c := compress(a, bits)
			if c >= 1<<bits {
				t.Fatalf("compress(%d, %d) = %d >= 2^bits", a, bits, c)
			}
			got := decompress(c, bits)
			diff := min(a-got, got-a, a-got+q, got-a+q)
			ceil := q / (1 << bits)
			if diff > fieldElement(ceil) {
				t.Fatalf("decompress(compress(%d, %d), %d) = %d (diff %d, max diff %d)",
					a, bits, bits, got, diff, ceil)
			}
		}
	}
}

func CompressRat(x fieldElement, d uint8) uint16 {
	if x >= q {
		panic("x out of range")
	}
	if d <= 0 || d >= 12 {
		panic("d out of range")
	}

	precise := big.NewRat((1<<d)*int64(x), q) // (2ᵈ / q) * x == (2ᵈ * x) / q

	// FloatString rounds halves away from 0, and our result should always be positive,
	// so it should work as we expect. (There's no direct way to round a Rat.)
	rounded, err := strconv.ParseInt(precise.FloatString(0), 10, 64)
	if err != nil {
		panic(err)
	}

	// If we rounded up, `rounded` may be equal to 2ᵈ, so we perform a final reduction.
	return uint16(rounded % (1 << d))
}

func TestCompress(t *testing.T) {
	for d := 1; d < 12; d++ {
		for n := 0; n < q; n++ {
			expected := CompressRat(fieldElement(n), uint8(d))
			result := compress(fieldElement(n), uint8(d))
			if result != expected {
				t.Errorf("compress(%d, %d): got %d, expected %d", n, d, result, expected)
			}
		}
	}
}

func DecompressRat(y uint16, d uint8) fieldElement {
	if y >= 1<<d {
		panic("y out of range")
	}
	if d <= 0 || d >= 12 {
		panic("d out of range")
	}

	precise := big.NewRat(q*int64(y), 1<<d) // (q / 2ᵈ) * y  ==  (q * y) / 2ᵈ

	// FloatString rounds halves away from 0, and our result should always be positive,
	// so it should work as we expect. (There's no direct way to round a Rat.)
	rounded, err := strconv.ParseInt(precise.FloatString(0), 10, 64)
	if err != nil {
		panic(err)
	}

	// If we rounded up, `rounded` may be equal to q, so we perform a final reduction.
	return fieldElement(rounded % q)
}

func TestDecompress(t *testing.T) {
	for d := 1; d < 12; d++ {
		for n := 0; n < (1 << d); n++ {
			expected := DecompressRat(uint16(n), uint8(d))
			result := decompress(uint16(n), uint8(d))
			if result != expected {
				t.Errorf("decompress(%d, %d): got %d, expected %d", n, d, result, expected)
			}
		}
	}
}

func BitRev7(n uint8) uint8 {
	if n>>7 != 0 {
		panic("not 7 bits")
	}
	var r uint8
	r |= n >> 6 & 0b0000_0001
	r |= n >> 4 & 0b0000_0010
	r |= n >> 2 & 0b0000_0100
	r |= n /**/ & 0b0000_1000
	r |= n << 2 & 0b0001_0000
	r |= n << 4 & 0b0010_0000
	r |= n << 6 & 0b0100_0000
	return r
}

func TestZetas(t *testing.T) {
	ζ := big.NewInt(17)
	q := big.NewInt(q)
	for k, zeta := range zetas {
		// ζ^BitRev7(k) mod q
		exp := new(big.Int).Exp(ζ, big.NewInt(int64(BitRev7(uint8(k)))), q)
		if big.NewInt(int64(zeta)).Cmp(exp) != 0 {
			t.Errorf("zetas[%d] = %v, expected %v", k, zeta, exp)
		}
	}
}

func TestGammas(t *testing.T) {
	ζ := big.NewInt(17)
	q := big.NewInt(q)
	for k, gamma := range gammas {
		// ζ^2BitRev7(i)+1
		exp := new(big.Int).Exp(ζ, big.NewInt(int64(BitRev7(uint8(k)))*2+1), q)
		if big.NewInt(int64(gamma)).Cmp(exp) != 0 {
			t.Errorf("gammas[%d] = %v, expected %v", k, gamma, exp)
		}
	}
}