diff --git a/zkp.go b/zkp.go
index a967709..042d682 100644
--- a/zkp.go
+++ b/zkp.go
@@ -74,7 +74,7 @@ func DLogProve(sk *big.Int) (proof *DLogProof, err error) {
 
 	// return
 	proof = &DLogProof{
-		RandomPoint:       fmt.Sprintf("%x,%x", pkr.X, pkr.Y),
+		RandomPoint:       fmt.Sprintf("%064x,%064x", pkr.X, pkr.Y),
 		ChallengeResponse: (*big_Int)(cr),
 	}
 	return proof, nil
@@ -91,12 +91,12 @@ func DLogVerify(pkstr string, proof *DLogProof) bool {
 	// Step 0. get pk & pkr
 	var pk, err1 = HexStringToS256Point(pkstr)
 	if err1 != nil {
-		//errors.New("input pk is invalid")
+		log.Infof("input pk is invalid: %s, pk=[%s]", err1, pkstr)
 		return false
 	}
 	var pkr, err2 = HexStringToS256Point(proof.RandomPoint)
 	if err2 != nil {
-		//errors.New("input pkr is invalid")
+		log.Infof("input pkr is invalid: %s, pkr=[%s]", err2, proof.RandomPoint)
 		return false
 	}
 
@@ -131,11 +131,11 @@ func DLogVerify(pkstr string, proof *DLogProof) bool {
 func HexStringToS256Point(pstr string) (*ecdsa.PublicKey, error) {
 	var pk = ecdsa.PublicKey{Curve: crypto.S256()}
 	if x2y2 := strings.Split(pstr, ","); len(x2y2) != 2 {
-		return nil, errors.New("input pk is invalid")
+		return nil, errors.New("input point is invalid")
 	} else if x, err := hex.DecodeString(x2y2[0]); err != nil {
-		return nil, errors.New("input pk.x is invalid")
+		return nil, fmt.Errorf("input point.x is invalid: [%s]", err)
 	} else if y, err := hex.DecodeString(x2y2[1]); err != nil {
-		return nil, errors.New("input pk.y is invalid")
+		return nil, fmt.Errorf("input point.y is invalid: [%s]", err)
 	} else {
 		pk.X = new(big.Int).SetBytes(x)
 		pk.Y = new(big.Int).SetBytes(y)