mldsa: supplement test cases and comments

mldsa/compress.go

@@ -97,3 +97,18 @@ func useHint(h, r fieldElement, gamma2 uint32) fieldElement {
 		return fieldElement(r1 - 1)
 	}
 }
+
+func vectorMakeHint(ct0, cs2, w, hint []ringElement, gamma2 uint32) {
+	for i := range ct0 {
+		for j := range ct0[i] {
+			hint[i][j] = makeHint(ct0[i][j], cs2[i][j], w[i][j], gamma2)
+		}
+	}
+}
+
+func makeHint(ct0, cs2, w fieldElement, gamma2 uint32) fieldElement {
+	rPlusZ := fieldSub(w, cs2)
+	r := fieldAdd(rPlusZ, ct0)
+
+	return fieldElement(1 ^ uint32(subtle.ConstantTimeEq(int32(compressHighBits(r, gamma2)), int32(compressHighBits(rPlusZ, gamma2)))))
+}

mldsa/field.go

@@ -40,9 +40,9 @@ func fieldSub(a, b fieldElement) fieldElement {
 }
 
 const (
-	qInv    = 58728449
-	qNegInv = 4236238847
-	r       = 4193792 // 2^32 mod q
+	qInv    = 58728449   // q^-1 satisfies: q^-1 * q = 1 mod 2^32
+	qNegInv = 4236238847 // inverse of -q modulo 2^32
+	r       = 4193792    // 2^32 mod q
 )
 
 func fieldReduce(a uint64) fieldElement {
@@ -90,7 +90,7 @@ type nttElement [n]fieldElement
 // As this implementation uses montgomery form with a multiplier of 2^32.
 // The values need to be transformed i.e.
 //
-// zetasMontgomery[k] = fieldReduce(zeta[k] * (2^32 * 2^32 mod(q)))
+// zetasMontgomery[k] = fieldReduce(zeta[k] * (2^32 * 2^32 mod(q))) = (zeta[k] * r^2) mod q
 var zetasMontgomery = [n]fieldElement{
 	4193792, 25847, 5771523, 7861508, 237124, 7602457, 7504169, 466468,
 	1826347, 2353451, 8021166, 6288512, 3119733, 5495562, 3111497, 2680103,
@@ -134,7 +134,7 @@ func ntt(f ringElement) nttElement {
 	// len: 128, 64, 32, ..., 1
 	for len := 128; len >= 1; len /= 2 {
 		// start
-		for start := 0; start < 256; start += 2 * len {
+		for start := 0; start < n; start += 2 * len {
 			zeta := zetasMontgomery[k]
 			k++
 			// Bounds check elimination hint.
@@ -154,8 +154,8 @@ func ntt(f ringElement) nttElement {
 // It implements NTT⁻¹, according to FIPS 204, Algorithm 42.
 func inverseNTT(f nttElement) ringElement {
 	k := 255
-	for len := 1; len < 256; len *= 2 {
-		for start := 0; start < 256; start += 2 * len {
+	for len := 1; len < n; len *= 2 {
+		for start := 0; start < n; start += 2 * len {
 			zeta := q - zetasMontgomery[k]
 			k--
 			// Bounds check elimination hint.
@@ -240,17 +240,3 @@ func vectorCountOnes(a []ringElement) int {
 	return oneCount
 }
 
-func vectorMakeHint(ct0, cs2, w, hint []ringElement, gamma2 uint32) {
-	for i := range ct0 {
-		for j := range ct0[i] {
-			hint[i][j] = makeHint(ct0[i][j], cs2[i][j], w[i][j], gamma2)
-		}
-	}
-}
-
-func makeHint(ct0, cs2, w fieldElement, gamma2 uint32) fieldElement {
-	rPulusZ := fieldSub(w, cs2)
-	r := fieldAdd(rPulusZ, ct0)
-
-	return fieldElement(1 ^ uint32(subtle.ConstantTimeEq(int32(compressHighBits(r, gamma2)), int32(compressHighBits(rPulusZ, gamma2)))))
-}

mldsa/field_barrett.go

@@ -105,10 +105,10 @@ func inverseBarrettNTT(f nttElement) ringElement {
 	return ringElement(f)
 }
 
-//func nttBarrettMul(f, g nttElement) nttElement {
-//	var ret nttElement
-//	for i, v := range f {
-//		ret[i] = fieldBarrettMul(v, g[i])
-//	}
-//	return ret
-//}
+func nttBarrettMul(f, g nttElement) nttElement {
+	var ret nttElement
+	for i, v := range f {
+		ret[i] = fieldBarrettMul(v, g[i])
+	}
+	return ret
+}

mldsa/field_test.go

@@ -8,10 +8,74 @@ package mldsa
 
 import (
 	"fmt"
+	"math/big"
 	mathrand "math/rand/v2"
 	"testing"
 )
 
+func bitreverse(x byte) byte {
+	var y byte
+	for i := range 8 {
+		y |= (x & 1) << (7 - i)
+		x >>= 1
+	}
+	return y
+}
+
+func TestConstants(t *testing.T) {
+	q1 := big.NewInt(q)
+	a := big.NewInt(1 << 32)
+
+	q1Inv := new(big.Int)
+	q1Inv.ModInverse(q1, a)
+	if q1Inv.Cmp(big.NewInt(int64(qInv))) != 0 {
+		t.Fatalf("q^-1 mod 2^32 = %d, expected %d", q1, qInv)
+	}
+
+	q1Neg := new(big.Int)
+	q1Neg.Sub(a, q1)
+	q1NegInv := new(big.Int)
+	q1NegInv.ModInverse(q1Neg, a)
+	if q1NegInv.Cmp(big.NewInt(int64(qNegInv))) != 0 {
+		t.Fatalf("-q^-1 mod 2^32 = %d, expected %d", q1Neg, qNegInv)
+	}
+
+	r1 := new(big.Int)
+	r1.Mod(a, q1)
+	if r1.Cmp(big.NewInt(int64(r))) != 0 {
+		t.Fatalf("r = 2^32 mod q = %d, expected %d", r1, r)
+	}
+
+	dgreeInv := new(big.Int)
+	dgreeInv.ModInverse(big.NewInt(int64(256)), q1)
+	dgreeInv.Mul(dgreeInv, r1)
+	dgreeInv.Mul(dgreeInv, r1)
+	dgreeInv.Mod(dgreeInv, q1)
+	if dgreeInv.Int64() != 41978 {
+		t.Fatalf("dgreeInv = ((256^(-1) mod q) * r^2) mod q  = %d, expected 41978", dgreeInv)
+	}
+
+	// test zetas
+	zeta := big.NewInt(1753)
+	for i := 1; i < 256; i++ {
+		bitRev := bitreverse(byte(i))
+		zetaV := new(big.Int).Exp(zeta, big.NewInt(int64(bitRev)), q1)
+		if uint32(zetaV.Int64()) != uint32(zetas[i]) {
+			t.Fatalf("zetas[%d] = %d, expected %d", i, uint32(zetaV.Int64()), zetas[i])
+		}
+	}
+
+	// test zetasMontgomery
+	for i, z := range zetas {
+		zMont := big.NewInt(int64(z))
+		zMont.Mul(zMont, r1)
+		zMont.Mod(zMont, q1)
+		if zMont.Cmp(big.NewInt(int64(zetasMontgomery[i]))) != 0 {
+			t.Fatalf("zetasMontgomery[%d] = %d, expected %d", i, zMont, zetasMontgomery[i])
+		}
+	}
+}
+
 func TestFieldAdd(t *testing.T) {
 	for a := fieldElement(q - 1000); a < q; a++ {
 		for b := fieldElement(q - 1000); b < q; b++ {
@@ -108,6 +172,37 @@ func TestInverseBarrettNTT(t *testing.T) {
 	}
 }
 
+// this is the real use case for NTT:
+//
+//  - convert to NTT
+//  - multiply in NTT
+//  - inverse NTT
+func TestInverseNTTWithMultiply(t *testing.T) {
+	r1 := randomRingElement()
+	r2 := randomRingElement()
+
+	// Montgomery Method
+	r11 := r1
+	r111 := ntt(r11)
+	r22 := r2
+	r222 := ntt(r22)
+	r31 := nttMul(r111, r222)
+	r32 := inverseNTT(r31)
+
+	// Barrett Method
+	b11 := barrettNTT(r1)
+	b22 := barrettNTT(r2)
+	r33 := nttBarrettMul(b11, b22)
+	r34 := inverseBarrettNTT(r33)
+
+	// Check if the results are equal
+	for i := range r32 {
+		if r32[i] != r34[i] {
+			t.Errorf("expected %v, got %v", r34[i], r32[i])
+		}
+	}
+}
+
 func TestInfinityNorm(t *testing.T) {
 	cases := []struct {
 		input    fieldElement

mldsa/mldsa44.go

@@ -25,7 +25,7 @@ import (
 
 const (
 	// ML-DSA global constants.
-	n           = 256
+	n           = 256     // # of coefficients in the polynomials
 	q           = 8380417 // 2^23 - 2^13 + 1
 	qMinus1Div2 = (q - 1) / 2
 	d           = 13 // # of dropped bits from t