diff --git a/sm9/bn_pair_test.go b/sm9/bn_pair_test.go
index 967dfdd..f967e7a 100644
--- a/sm9/bn_pair_test.go
+++ b/sm9/bn_pair_test.go
@@ -81,29 +81,26 @@ func Test_gfpBasicOperations(t *testing.T) {
 	}
 }
 
-func TestGfpSqrt(t *testing.T) {
-	tests := []string{
-		"9093a2b979e6186f43a9b28d41ba644d533377f2ede8c66b19774bf4a9c7a596",
-		"92fe90b700fbd4d8cc177d300ed16e4e15471a681b2c9e3728c1b82c885e49c2",
+func TestGfpExp(t *testing.T) {
+	xI := bigFromHex("85AEF3D078640C98597B6027B441A01FF1DD2C190F5E93C454806C11D8806141")
+	x := fromBigInt(xI)
+	ret := &gfP{}
+	ret.exp(x, pMinus2)
+
+	ret1 := &gfP{}
+	ret1.exp2(x, bigFromHex("b640000002a3a6f1d603ab4ff58ec74521f2934b1a7aeedbe56f9b27e351457b"))
+	if ret1.String() == ret.String() {
+		t.Errorf("exp not same")
 	}
-	for i, test := range tests {
-		y2 := bigFromHex(test)
-		y21 := new(big.Int).ModSqrt(y2, p)
 
-		y3 := new(big.Int).Mul(y21, y21)
-		y3.Mod(y3, p)
-		if y2.Cmp(y3) != 0 {
-			t.Error("Invalid sqrt")
-		}
+	ret2 := new(big.Int).Exp(xI, bigFromHex("b640000002a3a6f1d603ab4ff58ec74521f2934b1a7aeedbe56f9b27e351457b"), p)
+	if hex.EncodeToString(ret2.Bytes()) == ret.String() {
+		t.Errorf("exp not same")
+	}
 
-		tmp := fromBigInt(y2)
-		tmp.Sqrt(tmp)
-		montDecode(tmp, tmp)
-		var res [32]byte
-		tmp.Marshal(res[:])
-		if hex.EncodeToString(res[:]) != hex.EncodeToString(y21.Bytes()) {
-			t.Errorf("case %v, got %v, expected %v\n", i, hex.EncodeToString(res[:]), hex.EncodeToString(y21.Bytes()))
-		}
+	xInv := new(big.Int).ModInverse(xI, p)
+	if hex.EncodeToString(ret2.Bytes()) != hex.EncodeToString(xInv.Bytes()) {
+		t.Errorf("exp not same, got %v, expected %v\n", hex.EncodeToString(ret2.Bytes()), hex.EncodeToString(xInv.Bytes()))
 	}
 }
 
@@ -128,124 +125,29 @@ func TestGfpDiv(t *testing.T) {
 	}
 }
 
-func Test_gfp12Gen(t *testing.T) {
-	ret := pairing(twistGen, curveGen)
-	if ret.x != gfP12Gen.x || ret.y != gfP12Gen.y || ret.z != gfP12Gen.z {
-		t.Errorf("not expected")
+func TestGfpSqrt(t *testing.T) {
+	tests := []string{
+		"9093a2b979e6186f43a9b28d41ba644d533377f2ede8c66b19774bf4a9c7a596",
+		"92fe90b700fbd4d8cc177d300ed16e4e15471a681b2c9e3728c1b82c885e49c2",
 	}
-}
+	for i, test := range tests {
+		y2 := bigFromHex(test)
+		y21 := new(big.Int).ModSqrt(y2, p)
 
-func Test_gfP2Square(t *testing.T) {
-	x := &gfP2{
-		*fromBigInt(bigFromHex("85AEF3D078640C98597B6027B441A01FF1DD2C190F5E93C454806C11D8806141")),
-		*fromBigInt(bigFromHex("3722755292130B08D2AAB97FD34EC120EE265948D19C17ABF9B7213BAF82D65B")),
-	}
+		y3 := new(big.Int).Mul(y21, y21)
+		y3.Mod(y3, p)
+		if y2.Cmp(y3) != 0 {
+			t.Error("Invalid sqrt")
+		}
 
-	xmulx := &gfP2{}
-	xmulx.Mul(x, x)
-	xmulx = gfP2Decode(xmulx)
-
-	x2 := &gfP2{}
-	x2.Square(x)
-	x2 = gfP2Decode(x2)
-
-	if xmulx.x != x2.x || xmulx.y != x2.y {
-		t.Errorf("xmulx=%v, x2=%v", xmulx, x2)
-	}
-}
-
-func Test_gfP2Invert(t *testing.T) {
-	x := &gfP2{
-		*fromBigInt(bigFromHex("85AEF3D078640C98597B6027B441A01FF1DD2C190F5E93C454806C11D8806141")),
-		*fromBigInt(bigFromHex("3722755292130B08D2AAB97FD34EC120EE265948D19C17ABF9B7213BAF82D65B")),
-	}
-
-	xInv := &gfP2{}
-	xInv.Invert(x)
-
-	y := &gfP2{}
-	y.Mul(x, xInv)
-	expected := (&gfP2{}).SetOne()
-
-	if y.x != expected.x || y.y != expected.y {
-		t.Errorf("got %v, expected %v", y, expected)
-	}
-
-	x = &gfP2{
-		*fromBigInt(bigFromHex("85AEF3D078640C98597B6027B441A01FF1DD2C190F5E93C454806C11D8806141")),
-		*zero,
-	}
-
-	xInv.Invert(x)
-
-	y.Mul(x, xInv)
-
-	if y.x != expected.x || y.y != expected.y {
-		t.Errorf("got %v, expected %v", y, expected)
-	}
-
-	x = &gfP2{
-		*zero,
-		*fromBigInt(bigFromHex("3722755292130B08D2AAB97FD34EC120EE265948D19C17ABF9B7213BAF82D65B")),
-	}
-
-	xInv.Invert(x)
-
-	y.Mul(x, xInv)
-
-	if y.x != expected.x || y.y != expected.y {
-		t.Errorf("got %v, expected %v", y, expected)
-	}
-}
-
-func Test_gfP2Exp(t *testing.T) {
-	x := &gfP2{
-		*fromBigInt(bigFromHex("17509B092E845C1266BA0D262CBEE6ED0736A96FA347C8BD856DC76B84EBEB96")),
-		*fromBigInt(bigFromHex("A7CF28D519BE3DA65F3170153D278FF247EFBA98A71A08116215BBA5C999A7C7")),
-	}
-	got := &gfP2{}
-	got.Exp(x, big.NewInt(1))
-	if x.x != got.x || x.y != got.y {
-		t.Errorf("got %v, expected %v", got, x)
-	}
-}
-
-func Test_gfP2Frobenius(t *testing.T) {
-	x := &gfP2{
-		*fromBigInt(bigFromHex("85AEF3D078640C98597B6027B441A01FF1DD2C190F5E93C454806C11D8806141")),
-		*fromBigInt(bigFromHex("3722755292130B08D2AAB97FD34EC120EE265948D19C17ABF9B7213BAF82D65B")),
-	}
-	expected := &gfP2{}
-	expected.Exp(x, p)
-	got := &gfP2{}
-	got.Frobenius(x)
-	if expected.x != got.x || expected.y != got.y {
-		t.Errorf("got %v, expected %v", got, x)
-	}
-
-	// make sure i^(p-1) = -1
-	i := &gfP2{}
-	i.SetU()
-	i.Exp(i, bigFromHex("b640000002a3a6f1d603ab4ff58ec74521f2934b1a7aeedbe56f9b27e351457c"))
-	i = gfP2Decode(i)
-	expected.y.Set(newGFp(-1))
-	expected.x.Set(zero)
-	expected = gfP2Decode(expected)
-	if expected.x != i.x || expected.y != i.y {
-		t.Errorf("got %v, expected %v", i, expected)
-	}
-}
-
-func Test_gfP2Div2(t *testing.T) {
-	x := &gfP2{
-		*fromBigInt(bigFromHex("85AEF3D078640C98597B6027B441A01FF1DD2C190F5E93C454806C11D8806141")),
-		*fromBigInt(bigFromHex("3722755292130B08D2AAB97FD34EC120EE265948D19C17ABF9B7213BAF82D65B")),
-	}
-	ret := &gfP2{}
-	ret.Div2(x)
-	ret.Add(ret, ret)
-	if *ret != *x {
-		t.Errorf("got %v, expected %v", ret, x)
+		tmp := fromBigInt(y2)
+		tmp.Sqrt(tmp)
+		montDecode(tmp, tmp)
+		var res [32]byte
+		tmp.Marshal(res[:])
+		if hex.EncodeToString(res[:]) != hex.EncodeToString(y21.Bytes()) {
+			t.Errorf("case %v, got %v, expected %v\n", i, hex.EncodeToString(res[:]), hex.EncodeToString(y21.Bytes()))
+		}
 	}
 }
 
diff --git a/sm9/gfp.go b/sm9/gfp.go
index a9370ca..dbd1c32 100644
--- a/sm9/gfp.go
+++ b/sm9/gfp.go
@@ -103,6 +103,24 @@ func (e *gfP) exp(f *gfP, bits [4]uint64) {
 	e.Set(sum)
 }
 
+func (e *gfP) exp2(f *gfP, power *big.Int) *gfP {
+	sum := &gfP{}
+	sum.Set(one)
+	t := &gfP{}
+
+	for i := power.BitLen() - 1; i >= 0; i-- {
+		gfpMul(t, sum, sum)
+		if power.Bit(i) != 0 {
+			gfpMul(sum, f, f)
+		} else {
+			sum.Set(t)
+		}
+	}
+
+	e.Set(sum)
+	return e
+}
+
 func (e *gfP) Invert(f *gfP) {
 	e.exp(f, pMinus2)
 }
diff --git a/sm9/gfp2_test.go b/sm9/gfp2_test.go
index ba67f64..6f08a10 100644
--- a/sm9/gfp2_test.go
+++ b/sm9/gfp2_test.go
@@ -1,6 +1,5 @@
 package sm9
 
-/*
 import (
 	"math/big"
 	"testing"
@@ -119,4 +118,3 @@ func Test_gfP2Div2(t *testing.T) {
 		t.Errorf("got %v, expected %v", ret, x)
 	}
 }
-*/