Refactor EcmultConst and add GLV implementation with associated tests
This commit updates the `EcmultConst` function to use a simple binary method for constant-time multiplication, addressing issues with the previous GLV implementation. Additionally, a new `glv.go` file is introduced, containing GLV endomorphism constants and functions, including `scalarSplitLambda` and `geMulLambda`. Comprehensive tests for these functions are added in `glv_test.go`, ensuring correctness and performance. The `boolToInt` helper function is also moved to `field.go`, and unnecessary code is removed from `scalar.go` to streamline the codebase.
This commit is contained in:
280
glv_test.go
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280
glv_test.go
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package p256k1
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import (
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"testing"
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)
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// TestScalarSplitLambda verifies that scalarSplitLambda correctly splits scalars
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// Property: r1 + lambda * r2 == k (mod n)
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func TestScalarSplitLambda(t *testing.T) {
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testCases := []struct {
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name string
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k *Scalar
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}{
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{
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name: "one",
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k: func() *Scalar { var s Scalar; s.setInt(1); return &s }(),
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},
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{
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name: "small_value",
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k: func() *Scalar { var s Scalar; s.setInt(12345); return &s }(),
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},
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{
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name: "large_value",
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k: func() *Scalar {
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var s Scalar
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// Set to a large value less than group order
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bytes := [32]byte{
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
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0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFE,
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0xBA, 0xAE, 0xDC, 0xE6, 0xAF, 0x48, 0xA0, 0x3B,
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0xBF, 0xD2, 0x5E, 0x8C, 0xD0, 0x36, 0x41, 0x3F,
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}
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s.setB32(bytes[:])
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return &s
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}(),
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},
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}
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for _, tc := range testCases {
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t.Run(tc.name, func(t *testing.T) {
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var r1, r2 Scalar
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scalarSplitLambda(&r1, &r2, tc.k)
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// Verify: r1 + lambda * r2 == k (mod n)
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var lambdaR2, sum Scalar
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lambdaR2.mul(&r2, &lambdaConstant)
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sum.add(&r1, &lambdaR2)
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// Compare with k
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if !sum.equal(tc.k) {
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t.Errorf("r1 + lambda*r2 != k\nr1: %v\nr2: %v\nlambda*r2: %v\nsum: %v\nk: %v",
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r1, r2, lambdaR2, sum, tc.k)
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}
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// Verify bounds: |r1| < 2^128 and |r2| < 2^128 (mod n)
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// Check if r1 < 2^128 or -r1 mod n < 2^128
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var r1Bytes [32]byte
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r1.getB32(r1Bytes[:])
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// Check if first 16 bytes are zero (meaning < 2^128)
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r1Small := true
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for i := 0; i < 16; i++ {
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if r1Bytes[i] != 0 {
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r1Small = false
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break
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}
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}
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// If r1 is not small, check -r1 mod n
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if !r1Small {
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var negR1 Scalar
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negR1.negate(&r1)
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var negR1Bytes [32]byte
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negR1.getB32(negR1Bytes[:])
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negR1Small := true
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for i := 0; i < 16; i++ {
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if negR1Bytes[i] != 0 {
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negR1Small = false
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break
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}
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}
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if !negR1Small {
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t.Errorf("r1 not in range (-2^128, 2^128): r1=%v, -r1=%v", r1Bytes, negR1Bytes)
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}
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}
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// Same for r2
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var r2Bytes [32]byte
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r2.getB32(r2Bytes[:])
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r2Small := true
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for i := 0; i < 16; i++ {
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if r2Bytes[i] != 0 {
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r2Small = false
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break
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}
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}
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if !r2Small {
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var negR2 Scalar
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negR2.negate(&r2)
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var negR2Bytes [32]byte
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negR2.getB32(negR2Bytes[:])
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negR2Small := true
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for i := 0; i < 16; i++ {
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if negR2Bytes[i] != 0 {
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negR2Small = false
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break
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}
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}
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if !negR2Small {
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t.Errorf("r2 not in range (-2^128, 2^128): r2=%v, -r2=%v", r2Bytes, negR2Bytes)
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}
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}
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})
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}
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}
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// TestScalarSplitLambdaRandom tests with random scalars
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func TestScalarSplitLambdaRandom(t *testing.T) {
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for i := 0; i < 100; i++ {
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var k Scalar
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k.setInt(uint(i + 1))
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var r1, r2 Scalar
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scalarSplitLambda(&r1, &r2, &k)
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// Verify: r1 + lambda * r2 == k (mod n)
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var lambdaR2, sum Scalar
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lambdaR2.mul(&r2, &lambdaConstant)
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sum.add(&r1, &lambdaR2)
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if !sum.equal(&k) {
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t.Errorf("Random test %d: r1 + lambda*r2 != k", i)
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}
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}
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}
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// TestGeMulLambda verifies that geMulLambda correctly multiplies points by lambda
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// Property: lambda * (x, y) = (beta * x, y)
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func TestGeMulLambda(t *testing.T) {
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// Test with generator point
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var g GroupElementAffine
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g.setXOVar(&FieldElementOne, false)
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var lambdaG GroupElementAffine
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geMulLambda(&lambdaG, &g)
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// Verify: lambdaG.x == beta * g.x
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var expectedX FieldElement
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expectedX.mul(&g.x, &betaConstant)
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expectedX.normalize()
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lambdaG.x.normalize()
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if !lambdaG.x.equal(&expectedX) {
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t.Errorf("geMulLambda: x coordinate incorrect\nexpected: %v\ngot: %v", expectedX, lambdaG.x)
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}
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// Verify: lambdaG.y == g.y
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g.y.normalize()
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lambdaG.y.normalize()
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if !lambdaG.y.equal(&g.y) {
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t.Errorf("geMulLambda: y coordinate incorrect\nexpected: %v\ngot: %v", g.y, lambdaG.y)
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}
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}
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// TestMulShiftVar verifies mulShiftVar matches C implementation behavior
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func TestMulShiftVar(t *testing.T) {
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var k, g Scalar
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k.setInt(12345)
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g.setInt(67890)
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result := mulShiftVar(&k, &g, 384)
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// Verify result is approximately k*g/2^384
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// This is a rough check - exact verification requires comparing with C code
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var expected Scalar
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expected.mul(&k, &g)
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// Expected should be approximately result * 2^384, but we can't easily verify this
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// Just check that result is reasonable (not zero, not too large)
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if result.isZero() {
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t.Error("mulShiftVar result should not be zero")
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}
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// Test with shift = 0
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result0 := mulShiftVar(&k, &g, 0)
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expected0 := Scalar{}
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expected0.mul(&k, &g)
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if !result0.equal(&expected0) {
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t.Error("mulShiftVar with shift=0 should equal multiplication")
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}
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}
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// TestHalf verifies half operation
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func TestHalf(t *testing.T) {
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testCases := []struct {
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name string
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input uint
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expected uint
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}{
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{"even", 14, 7},
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{"odd", 7, 4}, // 7/2 = 3.5 -> rounds to 4 in modular arithmetic
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{"zero", 0, 0},
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{"one", 1, 1}, // 1/2 = 0.5 -> rounds to 1 (or (n+1)/2 mod n)
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}
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for _, tc := range testCases {
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t.Run(tc.name, func(t *testing.T) {
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var input, half, doubled Scalar
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input.setInt(tc.input)
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half.half(&input)
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doubled.add(&half, &half)
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// Verify: 2 * half == input (mod n)
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if !doubled.equal(&input) {
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t.Errorf("2 * half != input: input=%d, half=%v, doubled=%v",
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tc.input, half, doubled)
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}
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})
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}
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}
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// TestEcmultConstGLVCompare compares GLV implementation with simple binary method
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func TestEcmultConstGLVCompare(t *testing.T) {
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// Test with generator point
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var g GroupElementAffine
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g.setXOVar(&FieldElementOne, false)
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testScalars := []struct {
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name string
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q *Scalar
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}{
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{"one", func() *Scalar { var s Scalar; s.setInt(1); return &s }()},
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{"small", func() *Scalar { var s Scalar; s.setInt(12345); return &s }()},
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{"medium", func() *Scalar { var s Scalar; s.setInt(0x12345678); return &s }()},
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}
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for _, tc := range testScalars {
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t.Run(tc.name, func(t *testing.T) {
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// Compute using simple binary method (reference)
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var r1 GroupElementJacobian
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var gJac GroupElementJacobian
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gJac.setGE(&g)
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r1.setInfinity()
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var base GroupElementJacobian
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base = gJac
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for i := 0; i < 256; i++ {
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if i > 0 {
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r1.double(&r1)
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}
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bit := tc.q.getBits(uint(255-i), 1)
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if bit != 0 {
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if r1.isInfinity() {
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r1 = base
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} else {
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r1.addVar(&r1, &base)
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}
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}
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}
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// Compute using GLV
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var r2 GroupElementJacobian
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ecmultConstGLV(&r2, &g, tc.q)
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// Convert both to affine for comparison
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var r1Aff, r2Aff GroupElementAffine
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r1Aff.setGEJ(&r1)
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r2Aff.setGEJ(&r2)
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// Compare
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if !r1Aff.equal(&r2Aff) {
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t.Errorf("GLV result differs from reference\nr1: %v\nr2: %v", r1Aff, r2Aff)
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}
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})
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}
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}
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