diff --git a/README.md b/README.md
index 266fe2f..47dc757 100644
--- a/README.md
+++ b/README.md
@@ -1,7 +1,8 @@
 # KGC_TEST（狠狠感谢ljn）
 
-#### 1.调用Miracl库，基本实现了密钥生成
+### 1.调用Miracl库，基本实现了密钥生成
 
-#### 2.实现了Go语言调用C静态库，完成了大数、点和Go语言字节切片的相互转换
+### 2.实现了Go语言调用C静态库，完成了大数、点和Go语言字节切片的相互转换
+
+### 3.实现了基本的无证书的签名验签功能（Go语言实现和C语言实现）
 
-#### 3.实现了基本的无证书的签名验签功能
\ No newline at end of file
diff --git a/go_test/.idea/.gitignore b/go_test/.idea/.gitignore
new file mode 100644
index 0000000..13566b8
--- /dev/null
+++ b/go_test/.idea/.gitignore
@@ -0,0 +1,8 @@
+# Default ignored files
+/shelf/
+/workspace.xml
+# Editor-based HTTP Client requests
+/httpRequests/
+# Datasource local storage ignored files
+/dataSources/
+/dataSources.local.xml
diff --git a/go_test/.idea/.name b/go_test/.idea/.name
new file mode 100644
index 0000000..30de634
--- /dev/null
+++ b/go_test/.idea/.name
@@ -0,0 +1 @@
+main.go
\ No newline at end of file
diff --git a/go_test/.idea/go_test.iml b/go_test/.idea/go_test.iml
new file mode 100644
index 0000000..5e764c4
--- /dev/null
+++ b/go_test/.idea/go_test.iml
@@ -0,0 +1,9 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<module type="WEB_MODULE" version="4">
+  <component name="Go" enabled="true" />
+  <component name="NewModuleRootManager">
+    <content url="file://$MODULE_DIR$" />
+    <orderEntry type="inheritedJdk" />
+    <orderEntry type="sourceFolder" forTests="false" />
+  </component>
+</module>
\ No newline at end of file
diff --git a/go_test/.idea/modules.xml b/go_test/.idea/modules.xml
new file mode 100644
index 0000000..3b69742
--- /dev/null
+++ b/go_test/.idea/modules.xml
@@ -0,0 +1,8 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<project version="4">
+  <component name="ProjectModuleManager">
+    <modules>
+      <module fileurl="file://$PROJECT_DIR$/.idea/go_test.iml" filepath="$PROJECT_DIR$/.idea/go_test.iml" />
+    </modules>
+  </component>
+</project>
\ No newline at end of file
diff --git a/go_test/cert/pkpub.txt b/go_test/cert/pkpub.txt
new file mode 100644
index 0000000..462ddf4
--- /dev/null
+++ b/go_test/cert/pkpub.txt
@@ -0,0 +1 @@
+7196e9722d561a0fea21485fc16140096cc9b88f7174aec7508f14a7b85b61ba299292c726367bbcbf8f00b977849164bf9d3fd6260e55dd6498517bc0dec541
\ No newline at end of file
diff --git a/go_test/cert/prikey.txt b/go_test/cert/prikey.txt
new file mode 100644
index 0000000..101ec7b
--- /dev/null
+++ b/go_test/cert/prikey.txt
@@ -0,0 +1 @@
+6d0770e05a3ce79a32e2aea78fcda3bcb4054b86df8369e50a5ab4b7e26f1d38
\ No newline at end of file
diff --git a/go_test/cert/pubkey.txt b/go_test/cert/pubkey.txt
new file mode 100644
index 0000000..77a951d
--- /dev/null
+++ b/go_test/cert/pubkey.txt
@@ -0,0 +1 @@
+226383fbed07e3841affd83f7681f90602ad08e57bd27d6cad9a666d81b8b7ef17672b52cbc215c51d308299a1b640d6c0229bf761364cca3eae31d16c13da29
\ No newline at end of file
diff --git a/go_test/go.mod b/go_test/go.mod
new file mode 100644
index 0000000..e26fe90
--- /dev/null
+++ b/go_test/go.mod
@@ -0,0 +1,3 @@
+module example.com/m/v2
+
+go 1.20
diff --git a/go_test/gofunc.go b/go_test/gofunc.go
new file mode 100644
index 0000000..29fe98c
--- /dev/null
+++ b/go_test/gofunc.go
@@ -0,0 +1,293 @@
+package main
+
+import (
+	"crypto/elliptic"
+	"crypto/rand"
+	"crypto/sha256"
+	"errors"
+	"fmt"
+	"math/big"
+	"os"
+	"path/filepath"
+)
+
+func hash1(curve elliptic.Curve, ID []byte, Qx, Qy, PKx, PKy *big.Int) *big.Int {
+	// 创建 SHA-256 散列器
+	h := sha256.New()
+
+	// 更新散列器以包含字符串 ID 的内容
+	h.Write(ID)
+
+	// 更新散列器以包含点 Q 的坐标信息
+	h.Write(Qx.Bytes())
+	h.Write(Qy.Bytes())
+
+	// 更新散列器以包含公钥 PK_pub 的坐标信息
+	h.Write(PKx.Bytes())
+	h.Write(PKy.Bytes())
+
+	// 计算 SHA-256 散列值
+	hash := h.Sum(nil)
+
+	// 将散列值转换为大整数
+	hBig := new(big.Int).SetBytes(hash)
+
+	// 对大整数 hBig 进行幂运算，幂为 1，模数为 n
+	hBig.Mod(hBig, curve.Params().N)
+
+	return hBig
+}
+
+func hash2(curve elliptic.Curve, ID []byte, Xx, Xy *big.Int) *big.Int {
+	// 计算 hash 值 H_2(ID, X)
+	hash := sha256.New()
+
+	hash.Write(ID)
+
+	hash.Write(Xx.Bytes())
+	hash.Write(Xy.Bytes())
+
+	// 计算 SHA-256 散列值
+	h2 := hash.Sum(nil)
+
+	// 转换为大整数
+	h2Big := new(big.Int).SetBytes(h2)
+
+	// 对大整数 h2Big 进行幂运算，幂为 1，模数为 n
+	h2Big.Mod(h2Big, curve.Params().N)
+
+	return h2Big
+}
+
+func hash3(curve elliptic.Curve, ID, msg []byte, Qx, Qy, Ux, Uy, PKx, PKy *big.Int) *big.Int {
+	// 创建 SHA-256 散列器
+	h := sha256.New()
+
+	// 更新散列器以包含字符串 ID 的内容
+	h.Write(ID)
+
+	// 更新散列器以包含字符串 msg 的内容
+	h.Write(msg)
+
+	// 更新散列器以包含点 Q 的坐标信息
+	h.Write(Qx.Bytes())
+	h.Write(Qy.Bytes())
+
+	// 更新散列器以包含点 U 的坐标信息
+	h.Write(Ux.Bytes())
+	h.Write(Uy.Bytes())
+
+	// 更新散列器以包含公钥 PK_pub 的坐标信息
+	h.Write(PKx.Bytes())
+	h.Write(PKy.Bytes())
+
+	// 计算 SHA-256 散列值
+	hash := h.Sum(nil)
+
+	// 将散列值转换为大整数
+	hBig := new(big.Int).SetBytes(hash)
+	hBig.Mod(hBig, curve.Params().N)
+
+	return hBig
+}
+
+func equal(lx, ly, rx, ry *big.Int) error {
+	if lx.Cmp(rx) == 0 && ly.Cmp(ry) == 0 {
+		return nil
+	}
+	return errors.New("point compare failed ")
+
+}
+
+func genKGCKey(curve elliptic.Curve) (*big.Int, *big.Int, *big.Int) {
+	// 随机生成 msk
+	msk, _ := rand.Int(rand.Reader, curve.Params().N)
+	PKx, PKy := curve.ScalarBaseMult(msk.Bytes())
+	return PKx, PKy, msk
+}
+
+func genSecret(curve elliptic.Curve) (*big.Int, *big.Int, *big.Int) {
+	// 随机生成 x
+	x, _ := rand.Int(rand.Reader, curve.Params().N)
+	Xx, Xy := curve.ScalarBaseMult(x.Bytes())
+	return Xx, Xy, x
+}
+
+func genPartialKey(curve elliptic.Curve, ID []byte, msk, Xx, Xy, PKx, PKy *big.Int) (*big.Int, *big.Int, *big.Int) {
+	// 随机生成 r
+	r, _ := rand.Int(rand.Reader, curve.Params().N)
+	Rx, Ry := curve.ScalarBaseMult(r.Bytes())
+
+	//计算h2的hash值
+	h2Big := hash2(curve, ID, Xx, Xy)
+
+	//计算 h2Big * X
+	tx, ty := curve.ScalarMult(Xx, Xy, h2Big.Bytes())
+
+	//计算 Q = R + h2 * X
+	Qx, Qy := curve.Add(Rx, Ry, tx, ty)
+
+	//计算hash1的值
+	h1Big := hash1(curve, ID, Qx, Qy, PKx, PKy)
+
+	//计算 d = r + msk * h1 mod n
+	temp := new(big.Int).Mul(msk, h1Big)
+	d := new(big.Int).Add(r, temp)
+	d.Mod(d, curve.Params().N)
+	return d, Qx, Qy
+
+}
+
+func VerifyEquation(curve elliptic.Curve, ID []byte, d, Qx, Qy, Xx, Xy, PKx, PKy *big.Int) error {
+	//计算等式左值 + h2 * X
+	lx, ly := curve.ScalarBaseMult(d.Bytes())
+	h2Big := hash2(curve, ID, Xx, Xy)
+	h2Xx, h2Xy := curve.ScalarMult(Xx, Xy, h2Big.Bytes())
+	lx, ly = curve.Add(lx, ly, h2Xx, h2Xy)
+
+	//计算 Q  + h1 * PK(t)
+	h1Big := hash1(curve, ID, Qx, Qy, PKx, PKy)
+	tx, ty := curve.ScalarMult(PKx, PKy, h1Big.Bytes())
+
+	rx, ry := curve.Add(Qx, Qy, tx, ty)
+
+	err := equal(lx, ly, rx, ry)
+	if err != nil {
+		return err
+	}
+
+	return nil
+}
+
+func genPriKey(curve elliptic.Curve, ID []byte, x, d, Xx, Xy *big.Int) *big.Int {
+	//计算h2Big
+	h2Big := hash2(curve, ID, Xx, Xy)
+
+	//计算s = d + h2Big * x
+	temp := new(big.Int).Mul(h2Big, x)
+	sUser := new(big.Int).Add(d, temp)
+
+	//s = s mod n
+	sUser = sUser.Mod(sUser, curve.Params().N)
+
+	return sUser
+}
+
+func SignThumb(curve elliptic.Curve, ID, msg []byte, s, Qx, Qy, PKx, PKy *big.Int) (*big.Int, *big.Int, *big.Int) {
+	// 生成小于素数 的随机数 u
+	u, _ := rand.Int(rand.Reader, curve.Params().N)
+
+	// 生成点U
+	Ux, Uy := curve.ScalarMult(curve.Params().Gx, curve.Params().Gy, u.Bytes())
+
+	//计算h3
+	h3 := hash3(curve, ID, msg, Qx, Qy, Ux, Uy, PKx, PKy)
+
+	// 计算 v = u + h3 * s mod n
+	// 计算 tmp = sa * h_3_big
+	tmp := new(big.Int).Mul(h3, s)
+
+	// 计算 v = u + tmp
+	v := new(big.Int).Add(u, tmp)
+
+	// 计算 v = v mod N
+	v.Mod(v, curve.Params().N)
+
+	return Ux, Uy, v
+}
+
+func VerifyThumb(curve elliptic.Curve, ID, msg []byte, Qx, Qy, PKx, PKy, Ux, Uy, v *big.Int) error {
+	//计算h1和h3
+	h1Big := hash1(curve, ID, Qx, Qy, PKx, PKy)
+	h3Big := hash3(curve, ID, msg, Qx, Qy, Ux, Uy, PKx, PKy)
+
+	//验证等式 v*P = U + h_3(Q + h_1 * PK_pub)
+	//等式左边
+	lx, ly := curve.ScalarBaseMult(v.Bytes())
+
+	// 计算 t = h_1_big * PK_pub
+	tx, ty := curve.ScalarMult(PKx, PKy, h1Big.Bytes())
+
+	// 计算 out = Q + t
+	tx, ty = curve.Add(Qx, Qy, tx, ty)
+
+	// 计算 t = h_3_big * t
+	tx, ty = curve.ScalarMult(tx, ty, h3Big.Bytes())
+
+	// 计算 t = U + tmp_p
+	rx, ry := curve.Add(Ux, Uy, tx, ty)
+
+	//比较等式左右两值是否相等
+	err := equal(lx, ly, rx, ry)
+	if err != nil {
+		fmt.Println("invalid!")
+		return err
+	}
+	fmt.Println("valid!")
+	return nil
+}
+
+func writeToFolder(directory, filename string, data []byte) error {
+	// 检查 cert 文件夹是否存在
+	if _, err := os.Stat(directory); os.IsNotExist(err) {
+		// 如果文件夹不存在，则创建它
+		err := os.Mkdir(directory, 0755)
+		if err != nil {
+			return fmt.Errorf("创建文件夹时出错: %v", err)
+		}
+	}
+
+	// 构造文件的完整路径
+	filePath := filepath.Join(directory, filename)
+
+	err := os.WriteFile(filePath, []byte(data), 0644)
+	if err != nil {
+		return fmt.Errorf("写入文件时出错: %v", err)
+	}
+	fmt.Println("字符串已成功写入文件:", filePath)
+	return nil
+}
+
+func mergeBigInts(bigInts ...*big.Int) []byte {
+	var mergedBytes []byte
+
+	for _, num := range bigInts {
+		numBytes := []byte(num.Text(16))
+		mergedBytes = append(mergedBytes, numBytes...)
+	}
+
+	return mergedBytes
+}
+
+func readFileFromDirectory(directory, filename string) ([]byte, error) {
+	// 构造文件的完整路径
+	filePath := filepath.Join(directory, filename)
+
+	// 读取文件内容
+	data, err := os.ReadFile(filePath)
+	if err != nil {
+		return nil, err
+	}
+
+	return data, nil
+}
+
+func BytesToBig(bytes []byte) *big.Int {
+	//不能直接转为big，转为字符串后用16进制解码
+	big := new(big.Int)
+	big.SetString(string(bytes), 16)
+	return big
+}
+
+func bytes_halve(slice []byte) ([]byte, []byte) {
+	length := len(slice)
+
+	// 计算每个部分的长度
+	halfLength := length / 2
+
+	// 切分切片
+	part1 := slice[:halfLength]
+	part2 := slice[halfLength:]
+
+	return part1, part2
+}
diff --git a/go_test/main.go b/go_test/main.go
new file mode 100644
index 0000000..bc926ff
--- /dev/null
+++ b/go_test/main.go
@@ -0,0 +1,79 @@
+package main
+
+import (
+	"crypto/elliptic"
+	"fmt"
+)
+
+func main() {
+
+	// 创建 P256 曲线
+	curve := elliptic.P256()
+
+	//初始化用户id 和消息
+	ID := []byte("1234567890111213141516171819202122232425")
+	msg := []byte("DDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD")
+
+	//生成KGC公私钥
+	PKx, PKy, msk := genKGCKey(curve)
+
+	//用户生成秘密值,后经过运算返回点
+	Xx, Xy, x := genSecret(curve)
+
+	//KGC生成用户的部分私钥d和全部公钥Q
+	d, Qx, Qy := genPartialKey(curve, ID, msk, Xx, Xy, PKx, PKy)
+
+	//用户验证生成的部分私钥和全部公钥是否有效
+	err := VerifyEquation(curve, ID, d, Qx, Qy, Xx, Xy, PKx, PKy)
+	if err != nil {
+		fmt.Println("KGC生成的私钥无效！！！")
+		return
+	}
+	fmt.Println("生成的私钥有效！")
+
+	//用户生成全部私钥
+	s := genPriKey(curve, ID, x, d, Xx, Xy)
+
+	//用户对消息签名
+	Ux, Uy, v := SignThumb(curve, ID, msg, s, Qx, Qy, PKx, PKy)
+
+	//接收方对消息进行验证
+	err = VerifyThumb(curve, ID, msg, Qx, Qy, PKx, PKy, Ux, Uy, v)
+	if err != nil {
+		fmt.Println("签名验证失败！")
+	}
+
+	//fmt.Printf("KGC基点为：\nP_x:%s\nP_y:%s\n", curve.Params().Gx, curve.Params().Gy)
+	//fmt.Printf("用户的公钥为：\nPK_pub_s:%x\nPK_pub_s:%x\n", PKx, PKy)
+
+	//fmt.Println(append([]byte(PKx.Text(16)), []byte(PKy.Text(16))...))
+
+	pubdata := mergeBigInts(Qx, Qy)
+	kgcpub := mergeBigInts(PKx, PKy)
+	pridata := mergeBigInts(s)
+
+	fmt.Printf("KGC公钥为：%s\n", kgcpub)
+	fmt.Printf("用户公钥为：%s\n", pubdata)
+	fmt.Printf("用户私钥为：%s\n", pridata)
+	//fmt.Printf("用户ID为：\nID:%s\n", ID)
+	writeToFolder("./cert", "pkpub.txt", kgcpub)
+	writeToFolder("./cert", "prikey.txt", pridata)
+	writeToFolder("./cert", "pubkey.txt", pubdata)
+
+	data, _ := readFileFromDirectory("./cert", "pubkey.txt")
+	fmt.Println(data)
+	dax, day := bytes_halve(data)
+
+	Dx := BytesToBig(dax)
+	Dy := BytesToBig(day)
+	fmt.Println(Dx, Dy)
+	onCurve := curve.IsOnCurve(Dx, Dy)
+
+	if onCurve {
+		fmt.Println("点在椭圆曲线上")
+	} else {
+		fmt.Println("点不在椭圆曲线上")
+	}
+
+	//return
+}