core: implement key recover interops

go.mod

@@ -3,6 +3,7 @@ module github.com/nspcc-dev/neo-go
 require (
 	github.com/Workiva/go-datastructures v1.0.50
 	github.com/alicebob/miniredis v2.5.0+incompatible
+	github.com/btcsuite/btcd v0.20.1-beta
 	github.com/dgraph-io/badger/v2 v2.0.3
 	github.com/go-redis/redis v6.10.2+incompatible
 	github.com/go-yaml/yaml v2.1.0+incompatible

go.sum

@@ -13,6 +13,8 @@ github.com/abiosoft/ishell v2.0.0+incompatible h1:zpwIuEHc37EzrsIYah3cpevrIc8Oma
 github.com/abiosoft/ishell v2.0.0+incompatible/go.mod h1:HQR9AqF2R3P4XXpMpI0NAzgHf/aS6+zVXRj14cVk9qg=
 github.com/abiosoft/readline v0.0.0-20180607040430-155bce2042db h1:CjPUSXOiYptLbTdr1RceuZgSFDQ7U15ITERUGrUORx8=
 github.com/abiosoft/readline v0.0.0-20180607040430-155bce2042db/go.mod h1:rB3B4rKii8V21ydCbIzH5hZiCQE7f5E9SzUb/ZZx530=
+github.com/aead/siphash v1.0.1 h1:FwHfE/T45KPKYuuSAKyyvE+oPWcaQ+CUmFW0bPlM+kg=
+github.com/aead/siphash v1.0.1/go.mod h1:Nywa3cDsYNNK3gaciGTWPwHt0wlpNV15vwmswBAUSII=
 github.com/alecthomas/template v0.0.0-20160405071501-a0175ee3bccc/go.mod h1:LOuyumcjzFXgccqObfd/Ljyb9UuFJ6TxHnclSeseNhc=
 github.com/alecthomas/template v0.0.0-20190718012654-fb15b899a751 h1:JYp7IbQjafoB+tBA3gMyHYHrpOtNuDiK/uB5uXxq5wM=
 github.com/alecthomas/template v0.0.0-20190718012654-fb15b899a751/go.mod h1:LOuyumcjzFXgccqObfd/Ljyb9UuFJ6TxHnclSeseNhc=
@@ -28,6 +30,22 @@ github.com/beorn7/perks v0.0.0-20180321164747-3a771d992973/go.mod h1:Dwedo/Wpr24
 github.com/beorn7/perks v1.0.0/go.mod h1:KWe93zE9D1o94FZ5RNwFwVgaQK1VOXiVxmqh+CedLV8=
 github.com/beorn7/perks v1.0.1 h1:VlbKKnNfV8bJzeqoa4cOKqO6bYr3WgKZxO8Z16+hsOM=
 github.com/beorn7/perks v1.0.1/go.mod h1:G2ZrVWU2WbWT9wwq4/hrbKbnv/1ERSJQ0ibhJ6rlkpw=
+github.com/btcsuite/btcd v0.20.1-beta h1:Ik4hyJqN8Jfyv3S4AGBOmyouMsYE3EdYODkMbQjwPGw=
+github.com/btcsuite/btcd v0.20.1-beta/go.mod h1:wVuoA8VJLEcwgqHBwHmzLRazpKxTv13Px/pDuV7OomQ=
+github.com/btcsuite/btclog v0.0.0-20170628155309-84c8d2346e9f h1:bAs4lUbRJpnnkd9VhRV3jjAVU7DJVjMaK+IsvSeZvFo=
+github.com/btcsuite/btclog v0.0.0-20170628155309-84c8d2346e9f/go.mod h1:TdznJufoqS23FtqVCzL0ZqgP5MqXbb4fg/WgDys70nA=
+github.com/btcsuite/btcutil v0.0.0-20190425235716-9e5f4b9a998d h1:yJzD/yFppdVCf6ApMkVy8cUxV0XrxdP9rVf6D87/Mng=
+github.com/btcsuite/btcutil v0.0.0-20190425235716-9e5f4b9a998d/go.mod h1:+5NJ2+qvTyV9exUAL/rxXi3DcLg2Ts+ymUAY5y4NvMg=
+github.com/btcsuite/go-socks v0.0.0-20170105172521-4720035b7bfd h1:R/opQEbFEy9JGkIguV40SvRY1uliPX8ifOvi6ICsFCw=
+github.com/btcsuite/go-socks v0.0.0-20170105172521-4720035b7bfd/go.mod h1:HHNXQzUsZCxOoE+CPiyCTO6x34Zs86zZUiwtpXoGdtg=
+github.com/btcsuite/goleveldb v0.0.0-20160330041536-7834afc9e8cd h1:qdGvebPBDuYDPGi1WCPjy1tGyMpmDK8IEapSsszn7HE=
+github.com/btcsuite/goleveldb v0.0.0-20160330041536-7834afc9e8cd/go.mod h1:F+uVaaLLH7j4eDXPRvw78tMflu7Ie2bzYOH4Y8rRKBY=
+github.com/btcsuite/snappy-go v0.0.0-20151229074030-0bdef8d06723 h1:ZA/jbKoGcVAnER6pCHPEkGdZOV7U1oLUedErBHCUMs0=
+github.com/btcsuite/snappy-go v0.0.0-20151229074030-0bdef8d06723/go.mod h1:8woku9dyThutzjeg+3xrA5iCpBRH8XEEg3lh6TiUghc=
+github.com/btcsuite/websocket v0.0.0-20150119174127-31079b680792 h1:R8vQdOQdZ9Y3SkEwmHoWBmX1DNXhXZqlTpq6s4tyJGc=
+github.com/btcsuite/websocket v0.0.0-20150119174127-31079b680792/go.mod h1:ghJtEyQwv5/p4Mg4C0fgbePVuGr935/5ddU9Z3TmDRY=
+github.com/btcsuite/winsvc v1.0.0 h1:J9B4L7e3oqhXOcm+2IuNApwzQec85lE+QaikUcCs+dk=
+github.com/btcsuite/winsvc v1.0.0/go.mod h1:jsenWakMcC0zFBFurPLEAyrnc/teJEM1O46fmI40EZs=
 github.com/cespare/xxhash v1.1.0 h1:a6HrQnmkObjyL+Gs60czilIUGqrzKutQD6XZog3p+ko=
 github.com/cespare/xxhash v1.1.0/go.mod h1:XrSqR1VqqWfGrhpAt58auRo0WTKS1nRRg3ghfAqPWnc=
 github.com/cespare/xxhash/v2 v2.1.0 h1:yTUvW7Vhb89inJ+8irsUqiWjh8iT6sQPZiQzI6ReGkA=
@@ -41,6 +59,7 @@ github.com/coreos/etcd v3.3.10+incompatible/go.mod h1:uF7uidLiAD3TWHmW31ZFd/JWoc
 github.com/coreos/go-etcd v2.0.0+incompatible/go.mod h1:Jez6KQU2B/sWsbdaef3ED8NzMklzPG4d5KIOhIy30Tk=
 github.com/coreos/go-semver v0.2.0/go.mod h1:nnelYz7RCh+5ahJtPPxZlU+153eP4D4r3EedlOD2RNk=
 github.com/cpuguy83/go-md2man v1.0.10/go.mod h1:SmD6nW6nTyfqj6ABTjUi3V3JVMnlJmwcJI5acqYI6dE=
+github.com/davecgh/go-spew v0.0.0-20171005155431-ecdeabc65495/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
 github.com/davecgh/go-spew v1.1.0 h1:ZDRjVQ15GmhC3fiQ8ni8+OwkZQO4DARzQgrnXU1Liz8=
 github.com/davecgh/go-spew v1.1.0/go.mod h1:J7Y8YcW2NihsgmVo/mv3lAwl/skON4iLHjSsI+c5H38=
 github.com/davecgh/go-spew v1.1.1 h1:vj9j/u1bqnvCEfJOwUhtlOARqs3+rkHYY13jYWTU97c=
@@ -91,9 +110,15 @@ github.com/hashicorp/hcl v1.0.0/go.mod h1:E5yfLk+7swimpb2L/Alb/PJmXilQ/rhwaUYs4T
 github.com/hpcloud/tail v1.0.0 h1:nfCOvKYfkgYP8hkirhJocXT2+zOD8yUNjXaWfTlyFKI=
 github.com/hpcloud/tail v1.0.0/go.mod h1:ab1qPbhIpdTxEkNHXyeSf5vhxWSCs/tWer42PpOxQnU=
 github.com/inconshreveable/mousetrap v1.0.0/go.mod h1:PxqpIevigyE2G7u3NXJIT2ANytuPF1OarO4DADm73n8=
+github.com/jessevdk/go-flags v0.0.0-20141203071132-1679536dcc89 h1:12K8AlpT0/6QUXSfV0yi4Q0jkbq8NDtIKFtF61AoqV0=
+github.com/jessevdk/go-flags v0.0.0-20141203071132-1679536dcc89/go.mod h1:4FA24M0QyGHXBuZZK/XkWh8h0e1EYbRYJSGM75WSRxI=
+github.com/jrick/logrotate v1.0.0 h1:lQ1bL/n9mBNeIXoTUoYRlK4dHuNJVofX9oWqBtPnSzI=
+github.com/jrick/logrotate v1.0.0/go.mod h1:LNinyqDIJnpAur+b8yyulnQw/wDuN1+BYKlTRt3OuAQ=
 github.com/json-iterator/go v1.1.6/go.mod h1:+SdeFBvtyEkXs7REEP0seUULqWtbJapLOCVDaaPEHmU=
 github.com/json-iterator/go v1.1.7/go.mod h1:KdQUCv79m/52Kvf8AW2vK1V8akMuk1QjK/uOdHXbAo4=
 github.com/julienschmidt/httprouter v1.2.0/go.mod h1:SYymIcj16QtmaHHD7aYtjjsJG7VTCxuUUipMqKk8s4w=
+github.com/kkdai/bstream v0.0.0-20161212061736-f391b8402d23 h1:FOOIBWrEkLgmlgGfMuZT83xIwfPDxEI2OHu6xUmJMFE=
+github.com/kkdai/bstream v0.0.0-20161212061736-f391b8402d23/go.mod h1:J+Gs4SYgM6CZQHDETBtE9HaSEkGmuNXF86RwHhHUvq4=
 github.com/konsorten/go-windows-terminal-sequences v1.0.1 h1:mweAR1A6xJ3oS2pRaGiHgQ4OO8tzTaLawm8vnODuwDk=
 github.com/konsorten/go-windows-terminal-sequences v1.0.1/go.mod h1:T0+1ngSBFLxvqU3pZ+m/2kptfBszLMUkC4ZK/EgS/cQ=
 github.com/kr/logfmt v0.0.0-20140226030751-b84e30acd515/go.mod h1:+0opPa2QZZtGFBFZlji/RkVcI2GknAs/DXo4wKdlNEc=
@@ -144,10 +169,12 @@ github.com/nspcc-dev/rfc6979 v0.2.0 h1:3e1WNxrN60/6N0DW7+UYisLeZJyfqZTNOjeV/toYv
 github.com/nspcc-dev/rfc6979 v0.2.0/go.mod h1:exhIh1PdpDC5vQmyEsGvc4YDM/lyQp/452QxGq/UEso=
 github.com/onsi/ginkgo v1.6.0 h1:Ix8l273rp3QzYgXSR+c8d1fTG7UPgYkOSELPhiY/YGw=
 github.com/onsi/ginkgo v1.6.0/go.mod h1:lLunBs/Ym6LB5Z9jYTR76FiuTmxDTDusOGeTQH+WWjE=
+github.com/onsi/ginkgo v1.7.0/go.mod h1:lLunBs/Ym6LB5Z9jYTR76FiuTmxDTDusOGeTQH+WWjE=
 github.com/onsi/ginkgo v1.10.3 h1:OoxbjfXVZyod1fmWYhI7SEyaD8B00ynP3T+D5GiyHOY=
 github.com/onsi/ginkgo v1.10.3/go.mod h1:lLunBs/Ym6LB5Z9jYTR76FiuTmxDTDusOGeTQH+WWjE=
 github.com/onsi/gomega v1.4.2 h1:3mYCb7aPxS/RU7TI1y4rkEn1oKmPRjNJLNEXgw7MH2I=
 github.com/onsi/gomega v1.4.2/go.mod h1:ex+gbHU/CVuBBDIJjb2X0qEXbFg53c61hWP/1CpauHY=
+github.com/onsi/gomega v1.4.3/go.mod h1:ex+gbHU/CVuBBDIJjb2X0qEXbFg53c61hWP/1CpauHY=
 github.com/onsi/gomega v1.7.1 h1:K0jcRCwNQM3vFGh1ppMtDh/+7ApJrjldlX8fA0jDTLQ=
 github.com/onsi/gomega v1.7.1/go.mod h1:XdKZgCCFLUoM/7CFJVPcG8C1xQ1AJ0vpAezJrB7JYyY=
 github.com/pelletier/go-toml v1.2.0/go.mod h1:5z9KED0ma1S8pY6P1sdut58dfprrGBbd/94hg7ilaic=
@@ -212,6 +239,7 @@ go.uber.org/multierr v1.1.0 h1:HoEmRHQPVSqub6w2z2d2EOVs2fjyFRGyofhKuyDq0QI=
 go.uber.org/multierr v1.1.0/go.mod h1:wR5kodmAFQ0UK8QlbwjlSNy0Z68gJhDJUG5sjR94q/0=
 go.uber.org/zap v1.10.0 h1:ORx85nbTijNz8ljznvCMR1ZBIPKFn3jQrag10X2AsuM=
 go.uber.org/zap v1.10.0/go.mod h1:vwi/ZaCAaUcBkycHslxD9B2zi4UTXhF60s6SWpuDF0Q=
+golang.org/x/crypto v0.0.0-20170930174604-9419663f5a44/go.mod h1:6SG95UA2DQfeDnfUPMdvaQW0Q7yPrPDi9nlGo2tz2b4=
 golang.org/x/crypto v0.0.0-20180904163835-0709b304e793/go.mod h1:6SG95UA2DQfeDnfUPMdvaQW0Q7yPrPDi9nlGo2tz2b4=
 golang.org/x/crypto v0.0.0-20181203042331-505ab145d0a9/go.mod h1:6SG95UA2DQfeDnfUPMdvaQW0Q7yPrPDi9nlGo2tz2b4=
 golang.org/x/crypto v0.0.0-20190308221718-c2843e01d9a2 h1:VklqNMn3ovrHsnt90PveolxSbWFaJdECFbxSq0Mqo2M=

pkg/core/interop_neo.go

@@ -1,10 +1,13 @@
 package core
 
 import (
+	"crypto/elliptic"
 	"errors"
 	"fmt"
 	"math"
+	"math/big"
 
+	"github.com/btcsuite/btcd/btcec"
 	"github.com/nspcc-dev/neo-go/pkg/core/state"
 	"github.com/nspcc-dev/neo-go/pkg/core/storage"
 	"github.com/nspcc-dev/neo-go/pkg/core/transaction"
@@ -600,6 +603,33 @@ 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(btcec.S256(), 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 := v.Estack().Pop().Bytes()
+	sBytes := v.Estack().Pop().Bytes()
+	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([]byte{})
+		return nil
+	}
+	v.Estack().PushVal(pKey.Bytes()[1:])
+	return nil
+}
+
 // assetCreate creates an asset.
 func (ic *interopContext) assetCreate(v *vm.VM) error {
 	if ic.trigger != trigger.Application {

pkg/core/interop_neo_test.go

@@ -1,14 +1,17 @@
 package core
 
 import (
+	"bytes"
 	"math/big"
 	"testing"
 
+	"github.com/btcsuite/btcd/btcec"
 	"github.com/nspcc-dev/neo-go/pkg/core/block"
 	"github.com/nspcc-dev/neo-go/pkg/core/dao"
 	"github.com/nspcc-dev/neo-go/pkg/core/state"
 	"github.com/nspcc-dev/neo-go/pkg/core/storage"
 	"github.com/nspcc-dev/neo-go/pkg/core/transaction"
+	"github.com/nspcc-dev/neo-go/pkg/crypto/hash"
 	"github.com/nspcc-dev/neo-go/pkg/crypto/keys"
 	"github.com/nspcc-dev/neo-go/pkg/internal/random"
 	"github.com/nspcc-dev/neo-go/pkg/smartcontract"
@@ -457,8 +460,81 @@ func TestAssetGetPrecision(t *testing.T) {
 	require.Equal(t, big.NewInt(int64(assetState.Precision)), precision)
 }
 
+func TestSecp256k1Recover(t *testing.T) {
+	v, context, chain := createVM(t)
+	defer chain.Close()
+
+	privateKey, err := btcec.NewPrivateKey(btcec.S256())
+	require.NoError(t, err)
+	message := []byte("The quick brown fox jumps over the lazy dog")
+	signature, err := privateKey.Sign(message)
+	require.NoError(t, err)
+	require.True(t, signature.Verify(message, privateKey.PubKey()))
+	pubKey := keys.PublicKey{
+		X: privateKey.PubKey().X,
+		Y: privateKey.PubKey().Y,
+	}
+	expected := pubKey.Bytes()[1:]
+
+	// We don't know which of two recovered keys suites, so let's try both.
+	putOnStackGetResult := func(isEven bool) []byte {
+		v.Estack().PushVal(message)
+		v.Estack().PushVal(isEven)
+		v.Estack().PushVal(signature.S.Bytes())
+		v.Estack().PushVal(signature.R.Bytes())
+		err = context.secp256k1Recover(v)
+		require.NoError(t, err)
+		return v.Estack().Pop().Value().([]byte)
+	}
+
+	// First one:
+	actualFalse := putOnStackGetResult(false)
+	// Second one:
+	actualTrue := putOnStackGetResult(true)
+
+	require.True(t, bytes.Compare(expected, actualFalse) != bytes.Compare(expected, actualTrue))
+}
+
+func TestSecp256r1Recover(t *testing.T) {
+	v, context, chain := createVM(t)
+	defer chain.Close()
+
+	privateKey, err := keys.NewPrivateKey()
+	require.NoError(t, err)
+	message := []byte("The quick brown fox jumps over the lazy dog")
+	messageHash := hash.Sha256(message).BytesBE()
+	signature := privateKey.Sign(message)
+	require.True(t, privateKey.PublicKey().Verify(signature, messageHash))
+	expected := privateKey.PublicKey().Bytes()[1:]
+
+	// We don't know which of two recovered keys suites, so let's try both.
+	putOnStackGetResult := func(isEven bool) []byte {
+		v.Estack().PushVal(messageHash)
+		v.Estack().PushVal(isEven)
+		v.Estack().PushVal(signature[32:64])
+		v.Estack().PushVal(signature[0:32])
+		err = context.secp256r1Recover(v)
+		require.NoError(t, err)
+		return v.Estack().Pop().Value().([]byte)
+	}
+
+	// First one:
+	actualFalse := putOnStackGetResult(false)
+	// Second one:
+	actualTrue := putOnStackGetResult(true)
+
+	require.True(t, bytes.Compare(expected, actualFalse) != bytes.Compare(expected, actualTrue))
+}
+
 // Helper functions to create VM, InteropContext, TX, Account, Contract, Asset.
 
+func createVM(t *testing.T) (*vm.VM, *interopContext, *Blockchain) {
+	v := vm.New()
+	chain := newTestChain(t)
+	context := chain.newInteropContext(trigger.Application, dao.NewSimple(storage.NewMemoryStore()), nil, nil)
+	return v, context, chain
+}
+
 func createVMAndPushBlock(t *testing.T) (*vm.VM, *block.Block, *interopContext, *Blockchain) {
 	v := vm.New()
 	block := newDumbBlock()

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

@@ -10,6 +10,7 @@ import (
 	"fmt"
 	"math/big"
 
+	"github.com/btcsuite/btcd/btcec"
 	"github.com/nspcc-dev/neo-go/pkg/crypto/hash"
 	"github.com/nspcc-dev/neo-go/pkg/encoding/address"
 	"github.com/nspcc-dev/neo-go/pkg/io"
@@ -134,15 +135,25 @@ 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)
-	/* 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)
+// 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.(type) {
+	case *btcec.KoblitzCurve:
+		a = big.NewInt(0)
+	default:
+		a = big.NewInt(3)
+	}
+	cp := curve.Params()
+	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 +207,7 @@ 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 +317,84 @@ 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 (https://www.secg.org/sec1-v2.pdf).
+// 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)
+	// We are skipping this step for secp256k1 and secp256r1 because we know cofactor of these curves (h=1)
+	// (see section 2.4 of http://www.secg.org/sec2-v2.pdf)
+	h := 1
+	for i := 0; i <= h; 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
+		nRx, nR := curve.ScalarMult(Rx, R, 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)
+		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)
+		minuseGx, minuseGy := curve.ScalarBaseMult(e.Bytes())
+		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
+}