finish eddsa

edwards_curve/eddsa25519.go

@@ -4,6 +4,7 @@ package edwards_curve
 // This file is little-endian
 
 import (
+	"fmt"
 	"math/big"
 	"github.com/consensys/gnark/frontend"
 	"github.com/consensys/gnark/std/math/emulated"
@@ -12,8 +13,11 @@ import (
 
 
 func H(api frontend.API, m []frontend.Variable) []frontend.Variable {
-	result := sha512.Sha512Bytes(api, m)
-	return result[:]
+	fmt.Println("sha input", m)
+	rawResult := sha512.Sha512(api, swapByteEndianness(m))
+	sResult := swapByteEndianness(rawResult[:])
+	fmt.Println("sha output", sResult)
+	return sResult
 }
 
 func pow2(n uint) *big.Int {
@@ -32,10 +36,10 @@ func bits_to_scalar(c *EdCurve, s []frontend.Variable) EdCoordinate {
 	elt := emulated.NewElement[Ed25519](0)
 	if len(elt.Limbs) != 4 { panic("bad length") }
 	i := 0
-	elt.Limbs[0] = c.api.FromBinary(s[i:i+64]); i += 64
-	elt.Limbs[1] = c.api.FromBinary(s[i:i+64]); i += 64
-	elt.Limbs[2] = c.api.FromBinary(s[i:i+64]); i += 64
-	elt.Limbs[3] = c.api.FromBinary(s[i:i+64]); i += 64
+	elt.Limbs[0] = c.api.FromBinary(s[i:i+64]...); i += 64
+	elt.Limbs[1] = c.api.FromBinary(s[i:i+64]...); i += 64
+	elt.Limbs[2] = c.api.FromBinary(s[i:i+64]...); i += 64
+	elt.Limbs[3] = c.api.FromBinary(s[i:i+64]...); i += 64
 	if i != len(s) { panic("bad length") }
 	return elt
 }
@@ -54,7 +58,15 @@ func bits_to_scalar(c *EdCurve, s []frontend.Variable) EdCoordinate {
 func bits_to_element(c *EdCurve, input []frontend.Variable) EdPoint {
 	L := emulated.NewElement[Ed25519Scalars](rEd25519)
 	unchecked_point := decodepoint(c, input)
+
+	// TODO: https://github.com/warner/python-pure25519 says this check is not necessary:
+	//
+	// > This library is conservative, and performs full subgroup-membership checks on decoded
+	// > points, which adds considerable overhead. The Curve25519/Ed25519 algorithms were
+	// > designed to not require these checks, so a careful application might be able to
+	// > improve on this slightly (Ed25519 verify down to 6.2ms, DH-finish to 3.2ms).
 	c.AssertIsZero(c.ScalarMul(unchecked_point, L))
+
 	return unchecked_point
 }
 
@@ -64,17 +76,31 @@ func bits_to_element(c *EdCurve, input []frontend.Variable) EdPoint {
 // 	return c.ScalarMul(c.g, a)
 // }
 
-func checkvalid(c *EdCurve, s, m, pk []frontend.Variable) {
+func CheckValid(c *EdCurve, s, m, pk []frontend.Variable) {
 	if len(s) != 512 { panic("bad signature length") }
 	if len(pk) != 256 { panic("bad public key length") }
+	if len(m) % 8 != 0 { panic("bad message length") }
 	R := bits_to_element(c, s[:256])
 	A := bits_to_element(c, pk)
 	h := H(c.api, concat(s[:256], pk, m))
+	fmt.Println("h", h)
+	fmt.Println("g", dbg(c.g.X), dbg(c.g.Y))
+	fmt.Println("s last half", s[256:])
 	v1 := c.ScalarMulBinary(c.g, s[256:])
+	fmt.Println("v1", dbg(v1.X), dbg(v1.Y))
 	v2 := c.Add(R, c.ScalarMulBinary(A, h))
+	fmt.Println("v2", dbg(v2.X), dbg(v2.Y))
 	c.AssertIsEqual(v1, v2)
 }
 
+func reverse[T interface{}](arr []T) []T {
+	result := make([]T, len(arr))
+	for i, v := range arr {
+		result[len(result)-i-1] = v
+	}
+	return result
+}
+
 func concat(args ...[]frontend.Variable) []frontend.Variable {
 	result := []frontend.Variable{}
 	for _, v := range args {
@@ -83,11 +109,11 @@ func concat(args ...[]frontend.Variable) []frontend.Variable {
 	return result
 }
 
-func decodepoint(c *EdCurve, input []frontend.Variable) EdPoint {
-	if len(input) != 256 { panic("bad length") }
+func decodepoint(c *EdCurve, unclamped []frontend.Variable) EdPoint {
+	if len(unclamped) != 256 { panic("bad length") }
 
-	s := make([]frontend.Variable, len(input))
-	copy(s, input)
+	s := make([]frontend.Variable, len(unclamped))
+	copy(s, unclamped)
 	s[255] = 0
 	y := bits_to_scalar(c, s)
 //     unclamped = int(binascii.hexlify(s[:32][::-1]), 16)
@@ -99,7 +125,7 @@ func decodepoint(c *EdCurve, input []frontend.Variable) EdPoint {
 
 	xbits := c.baseApi.ToBinary(x)
 	if len(xbits) != 256 { panic("bad length") }
-	mismatch := c.api.Xor(xbits[0], xbits[255])
+	mismatch := c.api.Xor(xbits[0], unclamped[255])
 	x = c.baseApi.Select(mismatch, c.baseApi.Neg(x), x).(EdCoordinate)
 //     if bool(x & 1) != bool(unclamped & (1<<255)): x = Q-x
 
@@ -115,6 +141,21 @@ func decodepoint(c *EdCurve, input []frontend.Variable) EdPoint {
 	return P
 }
 
+func toValue(s EdCoordinate) *big.Int {
+	result := big.NewInt(0)
+	placeValue := big.NewInt(1)
+	for _, v := range s.Limbs {
+		q := new(big.Int).Mul(placeValue, v.(*big.Int))
+		result.Add(result, q)
+		placeValue.Lsh(placeValue, Ed25519{}.BitsPerLimb())
+	}
+	return result
+}
+
+func dbg(s EdCoordinate) string {
+	return toValue(s).Text(16)
+}
+
 func _const(x int64) EdCoordinate {
 	return emulated.NewElement[Ed25519](big.NewInt(x))
 }
@@ -149,8 +190,8 @@ func xrecover(c *EdCurve, y EdCoordinate) EdCoordinate {
 	x = c.baseApi.Select(matches, x, c.baseApi.Mul(x, emulated.NewElement[Ed25519](I))).(EdCoordinate)
 	// if (x*x - xx) % Q != 0: x = (x*I) % Q
 
-	even := c.baseApi.ToBinary(x)[0]
-	x = c.baseApi.Select(even, x, c.baseApi.Neg(x)).(EdCoordinate)
+	odd := c.baseApi.ToBinary(x)[0]
+	x = c.baseApi.Select(odd, c.baseApi.Neg(x), x).(EdCoordinate)
 	// if x % 2 != 0: x = Q-x
 
 	return x
@@ -169,6 +210,17 @@ func pow(c *EdCurve, base EdCoordinate, exponent *big.Int) EdCoordinate {
 	return result
 }
 
+func swapByteEndianness(in []frontend.Variable) []frontend.Variable {
+	if len(in) % 8 != 0 { panic("must be a multiple of 8 bits") }
+	result := make([]frontend.Variable, len(in))
+	for i := 0; i < len(in); i += 8 {
+		for j := 0; j < 8; j++ {
+			result[i+j] = in[i+7-j]
+		}
+	}
+	return result
+}
+
 // def checkvalid(s, m, pk):
 //     if len(s) != 64: raise Exception("signature length is wrong")
 //     if len(pk) != 32: raise Exception("public-key length is wrong")

edwards_curve/eddsa25519_test.go

@@ -0,0 +1,65 @@
+package edwards_curve
+
+import (
+	"testing"
+	"encoding/hex"
+
+	"github.com/consensys/gnark/frontend"
+	"github.com/consensys/gnark/test"
+)
+
+type Eddsa25519Circuit struct {
+	m []frontend.Variable
+	pk []frontend.Variable
+	sig []frontend.Variable
+}
+
+func (circuit *Eddsa25519Circuit) Define(api frontend.API) error {
+	c, err := New[Ed25519, Ed25519Scalars](api)
+	if err != nil {
+		return err
+	}
+	CheckValid(c, circuit.sig, circuit.m, circuit.pk)
+	return nil
+}
+
+func TestEddsa25519(t *testing.T) {
+	assert := test.NewAssert(t)
+
+	m := "53756363696e6374204c616273"
+	pk := "f7ec1c43f4de9d49556de87b86b26a98942cb078486fdb44de38b80864c39731"
+	sig := "35c323757c20640a294345c89c0bfcebe3d554fdb0c7b7a0bdb72222c531b1ec849fed99a053e0f5b02dd9a25bb6eb018885526d9f583cdbde0b1e9f6329da09"
+
+	circuit := Eddsa25519Circuit {
+		m: hexToBits(m),
+		pk: hexToBits(pk),
+		sig: hexToBits(sig),
+	}
+	witness := Eddsa25519Circuit {
+		m: hexToBits(m),
+		pk: hexToBits(pk),
+		sig: hexToBits(sig),
+	}
+
+	err := test.IsSolved(&circuit, &witness, testCurve.ScalarField())
+	assert.NoError(err)
+}
+
+func hexToBits(h string) []frontend.Variable {
+	b, err := hex.DecodeString(h)
+	if err != nil {
+		panic(err)
+	}
+	result := make([]frontend.Variable, len(b) * 8)
+	for i, v := range b {
+		for j := 0; j < 8; j++ {
+			if (v & (1 << j)) != 0 {
+				result[i*8+j] = 1
+			} else {
+				result[i*8+j] = 0
+			}
+		}
+	}
+	return result
+}
+

edwards_curve/edpoint.go

@@ -185,16 +185,17 @@ func (c *Curve[T, S]) ScalarMul(p AffinePoint[T], s emulated.Element[S]) AffineP
 }
 
 func (c *Curve[T, S]) ScalarMulBinary(p AffinePoint[T], sBits []frontend.Variable) AffinePoint[T] {
-	res := p
-	acc := c.Double(p)
+	res := AffinePoint[T]{
+		X: emulated.NewElement[T](0),
+		Y: emulated.NewElement[T](1),
+	}
+	acc := p
 
-	for i := 1; i < len(sBits); i++ {
+	for i := 0; i < len(sBits); i++ {
 		tmp := c.Add(res, acc)
 		res = c.Select(sBits[i], tmp, res)
 		acc = c.Double(acc)
 	}
 
-	tmp := c.Add(res, c.Neg(p))
-	res = c.Select(sBits[0], res, tmp)
 	return res
 }

sha512/sha512.go

@@ -15,18 +15,7 @@ func _right_rotate(n [64]frontend.Variable, bits int) [64]frontend.Variable {
 	return result
 }
 
-func Sha512Bytes(api frontend.API, in []frontend.Variable) ([512]frontend.Variable) {
-	bits := []frontend.Variable{}
-	for _, v := range in {
-		b := api.ToBinary(v, 8)
-		for i := 0; i < 8; i++ {
-			bits = append(bits, b[7-i])
-		}
-	}
-	return Sha512Bits(api, bits)
-}
-
-func Sha512Bits(api frontend.API, in []frontend.Variable) ([512]frontend.Variable) {
+func Sha512(api frontend.API, in []frontend.Variable) ([512]frontend.Variable) {
 	_not := func(x [64]frontend.Variable) [64]frontend.Variable {
 		return not(api, x)
 	}

sha512/sha_test.go

@@ -15,7 +15,7 @@ type Sha512Circuit struct {
 }
 
 func (circuit *Sha512Circuit) Define(api frontend.API) error {
-	res := Sha512Bits(api, circuit.in)
+	res := Sha512(api, circuit.in)
 	if len(res) != 512 { panic("bad length") }
 	for i := 0; i < 512; i++ {
 		api.AssertIsEqual(res[i], circuit.out[i])
@@ -28,8 +28,7 @@ var testCurve = ecc.BN254
 func TestSha512(t *testing.T) {
 	assert := test.NewAssert(t)
 
-	testCase := func(input, output string) {
-		in := toBytes(input)
+	testCase := func(in []byte, output string) {
 		out, err := hex.DecodeString(output)
 		if err != nil { panic(err) }
 		if len(out) != 512 / 8 { panic("bad output length") }
@@ -46,8 +45,9 @@ func TestSha512(t *testing.T) {
 		assert.NoError(err)
 	}
 
-	testCase("", "cf83e1357eefb8bdf1542850d66d8007d620e4050b5715dc83f4a921d36ce9ce47d0d13c5d85f2b0ff8318d2877eec2f63b931bd47417a81a538327af927da3e")
-	testCase("Succinct Labs", "503ace098aa03f6feec1b5df0a38aee923f744a775508bc81f2b94ad139be297c2e8cd8c44af527b5d3f017a7fc929892c896604047e52e3f518924f52bff0dc")
+	testCase([]byte(""), "cf83e1357eefb8bdf1542850d66d8007d620e4050b5715dc83f4a921d36ce9ce47d0d13c5d85f2b0ff8318d2877eec2f63b931bd47417a81a538327af927da3e")
+	testCase([]byte("Succinct Labs"), "503ace098aa03f6feec1b5df0a38aee923f744a775508bc81f2b94ad139be297c2e8cd8c44af527b5d3f017a7fc929892c896604047e52e3f518924f52bff0dc")
+	testCase(decode("35c323757c20640a294345c89c0bfcebe3d554fdb0c7b7a0bdb72222c531b1ecf7ec1c43f4de9d49556de87b86b26a98942cb078486fdb44de38b80864c3973153756363696e6374204c616273"), "4388243c4452274402673de881b2f942ff5730fd2c7d8ddb94c3e3d789fb3754380cba8faa40554d9506a0730a681e88ab348a04bc5c41d18926f140b59aed39")
 }
 
 func toBits(arr []byte) []frontend.Variable {
@@ -64,6 +64,10 @@ func toBits(arr []byte) []frontend.Variable {
 	return result
 }
 
-func toBytes(s string) []byte {
-	return []byte(s)
+func decode(s string) []byte {
+	result, err := hex.DecodeString(s)
+	if err != nil {
+		panic(err)
+	}
+	return result
 }