core: implement key recover interops

closes #1003

pkg/core/interop_neo.go

@@ -1,9 +1,11 @@
 package core
 
 import (
+	"crypto/elliptic"
 	"errors"
 	"fmt"
 	"math"
+	"math/big"
 
 	"github.com/nspcc-dev/neo-go/pkg/core/state"
 	"github.com/nspcc-dev/neo-go/pkg/core/storage"
@@ -600,6 +602,33 @@ func (ic *interopContext) contractMigrate(v *vm.VM) error {
 	return ic.contractDestroy(v)
 }
 
+// secp256k1Recover recovers speck256k1 public key.
+func (ic *interopContext) secp256k1Recover(v *vm.VM) error {
+	return ic.eccRecover(keys.Secp256k1(), v)
+}
+
+// secp256r1Recover recovers speck256r1 public key.
+func (ic *interopContext) secp256r1Recover(v *vm.VM) error {
+	return ic.eccRecover(elliptic.P256(), v)
+}
+
+// eccRecover recovers public key using ECCurve set
+func (ic *interopContext) eccRecover(curve elliptic.Curve, v *vm.VM) error {
+	rBytes := append(util.ArrayReverse(v.Estack().Pop().Bytes()), 1)
+	sBytes := append(util.ArrayReverse(v.Estack().Pop().Bytes()), 1)
+	r := new(big.Int).SetBytes(rBytes)
+	s := new(big.Int).SetBytes(sBytes)
+	isEven := v.Estack().Pop().Bool()
+	messageHash := v.Estack().Pop().Bytes()
+	pKey, err := keys.KeyRecover(curve, r, s, messageHash, isEven)
+	if err != nil {
+		v.Estack().PushVal(vm.NewByteArrayItem([]byte{}))
+		return nil
+	}
+	v.Estack().PushVal(vm.NewByteArrayItem(pKey.Bytes()[1:]))
+	return nil
+}
+
 // assetCreate creates an asset.
 func (ic *interopContext) assetCreate(v *vm.VM) error {
 	if ic.trigger != trigger.Application {

pkg/core/interops.go

@@ -166,6 +166,8 @@ var neoInterops = []interopedFunction{
 	{Name: "Neo.Contract.GetStorageContext", Func: (*interopContext).contractGetStorageContext, Price: 1},
 	{Name: "Neo.Contract.IsPayable", Func: (*interopContext).contractIsPayable, Price: 1},
 	{Name: "Neo.Contract.Migrate", Func: (*interopContext).contractMigrate, Price: 0},
+	{Name: "Neo.Cryptography.Secp256k1Recover", Func: (*interopContext).secp256k1Recover, Price: 100},
+	{Name: "Neo.Cryptography.Secp256r1Recover", Func: (*interopContext).secp256r1Recover, Price: 100},
 	{Name: "Neo.Enumerator.Concat", Func: (*interopContext).enumeratorConcat, Price: 1},
 	{Name: "Neo.Enumerator.Create", Func: (*interopContext).enumeratorCreate, Price: 1},
 	{Name: "Neo.Enumerator.Next", Func: (*interopContext).enumeratorNext, Price: 1},

pkg/crypto/keys/publickey.go

@@ -134,15 +134,30 @@ func NewPublicKeyFromASN1(data []byte) (*PublicKey, error) {
 }
 
 // decodeCompressedY performs decompression of Y coordinate for given X and Y's least significant bit.
-func decodeCompressedY(x *big.Int, ylsb uint) (*big.Int, error) {
-	c := elliptic.P256()
-	cp := c.Params()
-	three := big.NewInt(3)
+// We use here a short-form Weierstrass curve (https://www.hyperelliptic.org/EFD/g1p/auto-shortw.html)
+// y² = x³ + ax + b. Two types of elliptic curves are supported:
+// 1. Secp256k1 (Koblitz curve): y² = x³ + b,
+// 2. Secp256r1 (Random curve): y² = x³ - 3x + b.
+// To decode compressed curve point we perform the following operation: y = sqrt(x³ + ax + b mod p)
+// where `p` denotes the order of the underlying curve field
+func decodeCompressedY(x *big.Int, ylsb uint, curve elliptic.Curve) (*big.Int, error) {
+	var a *big.Int
+	switch curve.Params().Name {
+	case Secp256k1Curve:
+		a = big.NewInt(0)
+	case elliptic.P256().Params().Name:
+		a = big.NewInt(3)
+	default:
+		// actually, we do support all curves from standard elliptic package as far as
+		// these curves have a=-3 which is hard-coded in the package
+		return nil, errors.New("Secp256k1 and Secp256r1 are only supported")
+	}
+	cp := curve.Params()
 	/* y**2 = x**3 + a*x + b  % p */
-	xCubed := new(big.Int).Exp(x, three, cp.P)
-	threeX := new(big.Int).Mul(x, three)
-	threeX.Mod(threeX, cp.P)
-	ySquared := new(big.Int).Sub(xCubed, threeX)
+	xCubed := new(big.Int).Exp(x, big.NewInt(3), cp.P)
+	aX := new(big.Int).Mul(x, a)
+	aX.Mod(aX, cp.P)
+	ySquared := new(big.Int).Sub(xCubed, aX)
 	ySquared.Add(ySquared, cp.B)
 	ySquared.Mod(ySquared, cp.P)
 	y := new(big.Int).ModSqrt(ySquared, cp.P)
@@ -196,7 +211,7 @@ func (p *PublicKey) DecodeBinary(r *io.BinReader) {
 		}
 		x = new(big.Int).SetBytes(xbytes)
 		ylsb := uint(prefix & 0x1)
-		y, err = decodeCompressedY(x, ylsb)
+		y, err = decodeCompressedY(x, ylsb, p256)
 		if err != nil {
 			r.Err = err
 			return
@@ -306,3 +321,87 @@ func (p *PublicKey) UnmarshalJSON(data []byte) error {
 
 	return nil
 }
+
+// KeyRecover recovers public key from the given signature (r, s) on the given message hash using given elliptic curve.
+// Algorithm source: SEC 1 Ver 2.0, section 4.1.6, pages 47-48.
+// Flag isEven denotes Y's least significant bit in decompression algorithm.
+func KeyRecover(curve elliptic.Curve, r, s *big.Int, messageHash []byte, isEven bool) (PublicKey, error) {
+	var (
+		res PublicKey
+		err error
+	)
+	if r.Cmp(big.NewInt(1)) == -1 || s.Cmp(big.NewInt(1)) == -1 {
+		return res, errors.New("invalid signature")
+	}
+	params := curve.Params()
+	// calculate h = (Q + 1 + 2 * Sqrt(Q)) / N
+	num := new(big.Int).Add(new(big.Int).Add(params.P, big.NewInt(1)), new(big.Int).Mul(big.NewInt(2), new(big.Int).Sqrt(params.P)))
+	h := new(big.Int).Div(num, params.N)
+	for i := 0; i <= int(h.Int64()); i++ {
+		// step 1.1: x = (n * i) + r
+		Rx := new(big.Int).Mul(params.N, big.NewInt(int64(i)))
+		Rx.Add(Rx, r)
+		if Rx.Cmp(params.P) == 1 {
+			break
+		}
+
+		// steps 1.2 and 1.3: get point R (Ry)
+		var R *big.Int
+		if isEven {
+			R, err = decodeCompressedY(Rx, 0, curve)
+		} else {
+			R, err = decodeCompressedY(Rx, 1, curve)
+		}
+		if err != nil {
+			return res, err
+		}
+
+		// step 1.4: check n*R is point at infinity
+		// TODO: curve.ScalarMult suppose we're dealing with a=-3 in the elliptic curve equation.
+		// This line will give wrong results for secp256k1 unless we define our own implementation
+		// of ScalarMult for secp256k1 curve with a=0.
+		nRx, nR := curve.ScalarMult(Rx, R, curve.Params().N.Bytes())
+		if nRx.Sign() != 0 || nR.Sign() != 0 {
+			continue
+		}
+
+		// step 1.5: compute e
+		e := hashToInt(messageHash, curve)
+
+		// step 1.6: Q = r^-1 (sR-eG)
+		invr := new(big.Int).ModInverse(r, params.N)
+		// first term.
+		invrS := new(big.Int).Mul(invr, s)
+		invrS.Mod(invrS, params.N)
+		// TODO: implement ScalarMult for secp256k1
+		sRx, sR := curve.ScalarMult(Rx, R, invrS.Bytes())
+		// second term.
+		e.Neg(e)
+		e.Mod(e, params.N)
+		e.Mul(e, invr)
+		e.Mod(e, params.N)
+		// TODO: it won't be difficult to implement ScalarBaseMult having ScalarMult for secp256k1.
+		minuseGx, minuseGy := curve.ScalarBaseMult(e.Bytes())
+		// TODO: the same thing for secp256k1.
+		Qx, Qy := curve.Add(sRx, sR, minuseGx, minuseGy)
+		res.X = Qx
+		res.Y = Qy
+	}
+	return res, nil
+}
+
+// copied from crypto/ecdsa
+func hashToInt(hash []byte, c elliptic.Curve) *big.Int {
+	orderBits := c.Params().N.BitLen()
+	orderBytes := (orderBits + 7) / 8
+	if len(hash) > orderBytes {
+		hash = hash[:orderBytes]
+	}
+
+	ret := new(big.Int).SetBytes(hash)
+	excess := len(hash)*8 - orderBits
+	if excess > 0 {
+		ret.Rsh(ret, uint(excess))
+	}
+	return ret
+}

pkg/crypto/keys/secp256k1.go

@@ -0,0 +1,36 @@
+package keys
+
+import (
+	"crypto/elliptic"
+	"math/big"
+	"sync"
+)
+
+// Secp256k1Curve represents the name of Secp256k1 elliptic curve, which is set to be "Secp256k1".
+const Secp256k1Curve string = "Secp256k1"
+
+type secp256k1Curve struct {
+	*elliptic.CurveParams
+}
+
+var (
+	initonce  sync.Once
+	secp256k1 secp256k1Curve
+)
+
+func initSecp256k1() {
+	secp256k1.CurveParams = &elliptic.CurveParams{Name: Secp256k1Curve}
+	secp256k1.P, _ = new(big.Int).SetString("fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f", 16)
+	secp256k1.N, _ = new(big.Int).SetString("fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141", 16)
+	secp256k1.B, _ = new(big.Int).SetString("0000000000000000000000000000000000000000000000000000000000000007", 16)
+	secp256k1.Gx, _ = new(big.Int).SetString("79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798", 16)
+	secp256k1.Gy, _ = new(big.Int).SetString("483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8", 16)
+	secp256k1.BitSize = 256
+}
+
+// Secp256k1 returns a Curve which implements secp256k1 elliptic curve.
+// The CurveParams.Name of this Curve is "Secp256k1".
+func Secp256k1() elliptic.Curve {
+	initonce.Do(initSecp256k1)
+	return secp256k1
+}