diff --git a/bigint.go b/bigint.go
new file mode 100644
index 0000000..0656327
--- /dev/null
+++ b/bigint.go
@@ -0,0 +1,26 @@
+package zkp
+
+import (
+	"fmt"
+	"math/big"
+)
+
+type big_Int big.Int
+
+func (b big_Int) MarshalJSON() ([]byte, error) {
+	i := big.Int(b)
+	v := fmt.Sprintf("\"%x\"", i.Bytes())
+	return []byte(v), nil
+}
+
+func (b *big_Int) UnmarshalJSON(p []byte) error {
+	if string(p) == "null" {
+		return nil
+	}
+	var v = []byte{}
+	if _, err := fmt.Sscanf(string(p), "\"%x\"", &v); err != nil {
+		return fmt.Errorf("not a valid big integer: %s", p)
+	}
+	*b = big_Int(*new(big.Int).SetBytes(v))
+	return nil
+}
diff --git a/zkp.go b/zkp.go
index 920d56c..a3df908 100644
--- a/zkp.go
+++ b/zkp.go
@@ -4,6 +4,7 @@ import (
 	"crypto/ecdsa"
 	"crypto/sha256"
 	"encoding/hex"
+	"encoding/json"
 	"errors"
 	"fmt"
 	"math/big"
@@ -14,8 +15,9 @@ import (
 )
 
 type DLogProof struct {
-	ChallengeResponse *big.Int `json:"cr"`
-	RandomPoint       string   `json:"pkr"`
+	ChallengeResponse     *big_Int `json:"cr"`
+	ChallengeResponseXXXX *big.Int `json:"cr___TODO______debug"`
+	RandomPoint           string   `json:"pkr"`
 }
 
 /*
@@ -38,7 +40,7 @@ func DLogProve(sk *big.Int) (proof *DLogProof, err error) {
 	randomkey, err := crypto.GenerateKey()
 	if err != nil {
 		log.Warningf("Gernerate random Q1 failed: '%s'", err.Error())
-		return errors.New("generate random key/number failed")
+		return nil, errors.New("generate random key/number failed")
 	}
 	var skr = randomkey.D
 	var pkr = randomkey.PublicKey
@@ -47,16 +49,21 @@ func DLogProve(sk *big.Int) (proof *DLogProof, err error) {
 	// Step 2. caculate challenge: c = SHA256(pkr || G || pk)
 	challenge := fmt.Sprintf(
 		"%x,%x@%x,%x@%x,%x", pkr.X, pkr.Y, Gx, Gy, pk.X, pk.Y)
-	var c = new(big.Int).SetBytes(sha256.Sum256([]byte(challenge))[:])
+	chash256 := sha256.Sum256([]byte(challenge))
+	var c = new(big.Int).SetBytes(chash256[:])
+	log.Debugf("challenge='%s',c='%x'", challenge, c)
 
 	// Step 3. caculate challenge response: cr = skr - c * sk
+	cvN := cv.Params().N
 	tmp := new(big.Int).Mul(c, sk)
-	var cr = new(big.Int).Mul(skr)
+	var cr = new(big.Int).Sub(skr, tmp)
+	cr = new(big.Int).Mod(cr, cvN)
 
 	// return
 	proof = &DLogProof{
-		RandomPoint:       fmt.Sprintf("%x,%x", pkr.X, pkr.Y),
-		ChallengeResponse: cr,
+		RandomPoint:           fmt.Sprintf("%x,%x", pkr.X, pkr.Y),
+		ChallengeResponse:     (*big_Int)(cr),
+		ChallengeResponseXXXX: cr,
 	}
 	return proof, nil
 }
@@ -70,13 +77,13 @@ func DLogProve(sk *big.Int) (proof *DLogProof, err error) {
  */
 func DLogVerify(pkstr string, proof *DLogProof) bool {
 	// Step 0. get pk & pkr
-	var pk, err = HexStringToS256Point(pkstr)
-	if err != nil {
+	var pk, err1 = HexStringToS256Point(pkstr)
+	if err1 != nil {
 		//errors.New("input pk is invalid")
 		return false
 	}
-	var pkr, err = HexStringToS256Point(proof.RandomPoint)
-	if err != nil {
+	var pkr, err2 = HexStringToS256Point(proof.RandomPoint)
+	if err2 != nil {
 		//errors.New("input pkr is invalid")
 		return false
 	}
@@ -87,25 +94,30 @@ func DLogVerify(pkstr string, proof *DLogProof) bool {
 	Gy := cv.Params().Gy
 	challenge := fmt.Sprintf(
 		"%x,%x@%x,%x@%x,%x", pkr.X, pkr.Y, Gx, Gy, pk.X, pk.Y)
-	var c = new(big.Int).SetBytes(sha256.Sum256([]byte(challenge))[:])
-	var cr = proof.ChallengeResponse
+	chash256 := sha256.Sum256([]byte(challenge))
+	var c = new(big.Int).SetBytes(chash256[:])
+	var cr = (*big.Int)(proof.ChallengeResponse)
+	log.Debugf("challenge='%s',c='%x',cr='%x'", challenge, c, cr)
 
 	// Step 2. caculate proof verify: pkv = cr * G + c * pk
 	var pkv = ecdsa.PublicKey{Curve: crypto.S256()}
 	pkv.X, pkv.Y = cv.ScalarBaseMult(cr.Bytes())
 	tempX, tempY := cv.ScalarMult(pk.X, pk.Y, c.Bytes())
 	tempX, tempY = cv.Add(pkv.X, pkv.Y, tempX, tempY)
+	log.Debugf("pkv='%x,%x'", tempX, tempY)
 
 	// return
-	if pkr.X == tempX && pkr.Y == Y {
-		return true
+	if pkr.X.Cmp(tempX) != 0 || pkr.Y.Cmp(tempY) != 0 {
+		log.Debugf("pkr='%x,%x'", pkr.X, pkr.Y)
+		log.Debugf("pkv='%x,%x'", tempX, tempY)
+		return false
 	}
-	return false
+	return true
 }
 
-func HexStringToS256Point(p string) (*ecdsa.PublicKey, error) {
+func HexStringToS256Point(pstr string) (*ecdsa.PublicKey, error) {
 	var pk = ecdsa.PublicKey{Curve: crypto.S256()}
-	if x2y2 := strings.Split(pkstr, ","); len(x2y2) != 2 {
+	if x2y2 := strings.Split(pstr, ","); len(x2y2) != 2 {
 		return nil, errors.New("input pk is invalid")
 	} else if x, err := hex.DecodeString(x2y2[0]); err != nil {
 		return nil, errors.New("input pk.x is invalid")
@@ -115,5 +127,18 @@ func HexStringToS256Point(p string) (*ecdsa.PublicKey, error) {
 		pk.X = new(big.Int).SetBytes(x)
 		pk.Y = new(big.Int).SetBytes(y)
 	}
-	return pk, nil
+	return &pk, nil
+}
+
+func (dlogproof *DLogProof) ToString() string {
+	var b, _ = json.Marshal(dlogproof)
+	return string(b)
+}
+
+func DLogProofFromString(jsonstr string) (*DLogProof, error) {
+	var proof = DLogProof{}
+	if err := json.Unmarshal([]byte(jsonstr), &proof); err != nil {
+		return nil, err
+	}
+	return &proof, nil
 }