diff --git a/keytools/secp256k1.go b/keytools/secp256k1.go
index d8c5c4f..a379a2d 100644
--- a/keytools/secp256k1.go
+++ b/keytools/secp256k1.go
@@ -18,7 +18,6 @@ package keytools
 
 import (
 	"crypto/rand"
-	"io"
 	"math/big"
 
 	"github.com/Zilliqa/gozilliqa-sdk/util"
@@ -32,19 +31,18 @@ var (
 type PrivateKey [32]byte
 
 func GeneratePrivateKey() (PrivateKey, error) {
-	pvk := [32]byte{}
-
+	var bytes [32]byte
 	for {
-		_, err := io.ReadFull(rand.Reader, pvk[:])
+		privk, err := btcec.NewPrivateKey(Secp256k1)
 		if err == nil {
-			pvkInt := new(big.Int).SetBytes(pvk[:])
+			pvkInt := privk.D
 			if pvkInt.Cmp(big.NewInt(0)) == 1 && pvkInt.Cmp(Secp256k1.N) == -1 {
+				privk.D.FillBytes(bytes[:])
 				break
 			}
 		}
 	}
-
-	return PrivateKey(pvk), nil
+	return bytes,nil
 }
 
 func GetPublicKeyFromPrivateKey(privateKey []byte, compress bool) []byte {
diff --git a/schnorr/schnorr.go b/schnorr/schnorr.go
index c56bc3d..4dddd18 100644
--- a/schnorr/schnorr.go
+++ b/schnorr/schnorr.go
@@ -17,6 +17,7 @@
 package go_schnorr
 
 import (
+	"bytes"
 	"encoding/hex"
 	"errors"
 	"fmt"
@@ -58,7 +59,7 @@ func TrySign(privateKey []byte, publicKey []byte, message []byte, k []byte) ([]b
 
 	// 3. Compute the challenge r = H(Q || pubKey || msg)
 	// mod reduce r by the order of secp256k1, n
-	r := new(big.Int).SetBytes(util.Hash(Q, publicKey, message[:]))
+	r := new(big.Int).SetBytes(hash(Q, publicKey, message[:]))
 	r = r.Mod(r, keytools.Secp256k1.N)
 
 	if r.Cmp(bintZero) == 0 {
@@ -68,7 +69,8 @@ func TrySign(privateKey []byte, publicKey []byte, message []byte, k []byte) ([]b
 	//4. Compute s = k - r * prv
 	// 4a. Compute r * prv
 	_r := *r
-	s := new(big.Int).Mod(_r.Sub(bintK, _r.Mul(&_r, priKey)), keytools.Secp256k1.N)
+	s := new(big.Int).Mod(_r.Mul(&_r, priKey),keytools.Secp256k1.N)
+	s = new(big.Int).Mod(new(big.Int).Sub(bintK, s), keytools.Secp256k1.N)
 
 	if s.Cmp(big.NewInt(0)) == 0 {
 		return nil, nil, errors.New("invalid s")
@@ -112,10 +114,18 @@ func Verify(publicKey []byte, msg []byte, r []byte, s []byte) bool {
 	Qx, Qy := keytools.Secp256k1.Add(rx, ry, lx, ly)
 	Q := util.Compress(keytools.Secp256k1, Qx, Qy, true)
 
-	_r := util.Hash(Q, publicKey, msg)
+	_r := hash(Q, publicKey, msg)
 
 	rn := new(big.Int).SetBytes(r)
-	_rn := new(big.Int).SetBytes(_r)
+	_rn := new(big.Int).Mod(new(big.Int).SetBytes(_r),keytools.Secp256k1.N)
 	fmt.Printf("r = %s, _r = %s\n", hex.EncodeToString(r), hex.EncodeToString(_r))
 	return rn.Cmp(_rn) == 0
 }
+
+func hash(Q []byte, pubKey []byte, msg []byte) []byte {
+	var buffer bytes.Buffer
+	buffer.Write(Q)
+	buffer.Write(pubKey[:33])
+	buffer.Write(msg)
+	return util.Sha256(buffer.Bytes())
+}
diff --git a/schnorr/schnorr_test.go b/schnorr/schnorr_test.go
index 815b8ce..11e5cae 100644
--- a/schnorr/schnorr_test.go
+++ b/schnorr/schnorr_test.go
@@ -78,7 +78,7 @@ func run_verify_test(t *testing.T) {
 		panic("unmarshal failed")
 	}
 
-	fmt.Printf("test data number = %d", len(data))
+	fmt.Printf("test data number = %d\n", len(data))
 
 	n := 0
 
diff --git a/util/util.go b/util/util.go
index 8ad334d..ff2112f 100644
--- a/util/util.go
+++ b/util/util.go
@@ -88,14 +88,6 @@ func bigIntToBytes(bi *big.Int) []byte {
 	return b1[:]
 }
 
-func Hash(Q []byte, pubKey []byte, msg []byte) []byte {
-	var buffer bytes.Buffer
-	buffer.Write(Q)
-	buffer.Write(pubKey[:33])
-	buffer.Write(msg)
-	return Sha256(buffer.Bytes())
-}
-
 func GenerateMac(derivedKey, cipherText, iv []byte) []byte {
 	buffer := bytes.NewBuffer(nil)
 	buffer.Write(derivedKey[16:32])