231 lines
5.3 KiB
Go
231 lines
5.3 KiB
Go
package kgc
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import (
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"crypto/elliptic"
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"crypto/rand"
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"crypto/sha256"
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"errors"
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"fmt"
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"math/big"
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)
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func hash1(curve elliptic.Curve, ID []byte, Qx, Qy, PKx, PKy *big.Int) *big.Int {
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// 创建 SHA-256 散列器
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h := sha256.New()
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// 更新散列器以包含字符串 ID 的内容
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h.Write(ID)
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// 更新散列器以包含点 Q 的坐标信息
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h.Write(Qx.Bytes())
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h.Write(Qy.Bytes())
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// 更新散列器以包含公钥 PK_pub 的坐标信息
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h.Write(PKx.Bytes())
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h.Write(PKy.Bytes())
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// 计算 SHA-256 散列值
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hash := h.Sum(nil)
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// 将散列值转换为大整数
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hBig := new(big.Int).SetBytes(hash)
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// 对大整数 hBig 进行幂运算，幂为 1，模数为 n
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hBig.Mod(hBig, curve.Params().N)
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return hBig
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}
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func hash2(curve elliptic.Curve, ID []byte, Xx, Xy *big.Int) *big.Int {
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// 计算 hash 值 H_2(ID, X)
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hash := sha256.New()
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hash.Write(ID)
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hash.Write(Xx.Bytes())
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hash.Write(Xy.Bytes())
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// 计算 SHA-256 散列值
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h2 := hash.Sum(nil)
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// 转换为大整数
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h2Big := new(big.Int).SetBytes(h2)
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// 对大整数 h2Big 进行幂运算，幂为 1，模数为 n
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h2Big.Mod(h2Big, curve.Params().N)
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return h2Big
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}
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func hash3(curve elliptic.Curve, ID, msg []byte, Qx, Qy, Ux, Uy, PKx, PKy *big.Int) *big.Int {
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// 创建 SHA-256 散列器
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h := sha256.New()
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// 更新散列器以包含字符串 ID 的内容
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h.Write(ID)
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// 更新散列器以包含字符串 msg 的内容
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h.Write(msg)
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// 更新散列器以包含点 Q 的坐标信息
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h.Write(Qx.Bytes())
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h.Write(Qy.Bytes())
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// 更新散列器以包含点 U 的坐标信息
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h.Write(Ux.Bytes())
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h.Write(Uy.Bytes())
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// 更新散列器以包含公钥 PK_pub 的坐标信息
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h.Write(PKx.Bytes())
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h.Write(PKy.Bytes())
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// 计算 SHA-256 散列值
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hash := h.Sum(nil)
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// 将散列值转换为大整数
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hBig := new(big.Int).SetBytes(hash)
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hBig.Mod(hBig, curve.Params().N)
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return hBig
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}
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func equal(lx, ly, rx, ry *big.Int) error {
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if lx.Cmp(rx) == 0 && ly.Cmp(ry) == 0 {
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return nil
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}
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return errors.New("point compare failed ")
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}
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func genKGCKey(curve elliptic.Curve) (*big.Int, *big.Int, *big.Int) {
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// 随机生成 msk
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msk, _ := rand.Int(rand.Reader, curve.Params().N)
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PKx, PKy := curve.ScalarBaseMult(msk.Bytes())
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return PKx, PKy, msk
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}
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func genSecret(curve elliptic.Curve) (*big.Int, *big.Int, *big.Int) {
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// 随机生成 x
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x, _ := rand.Int(rand.Reader, curve.Params().N)
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Xx, Xy := curve.ScalarBaseMult(x.Bytes())
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return Xx, Xy, x
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}
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func genPartialKey(curve elliptic.Curve, ID []byte, msk, Xx, Xy, PKx, PKy *big.Int) (*big.Int, *big.Int, *big.Int) {
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// 随机生成 r
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r, _ := rand.Int(rand.Reader, curve.Params().N)
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Rx, Ry := curve.ScalarBaseMult(r.Bytes())
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//计算h2的hash值
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h2Big := hash2(curve, ID, Xx, Xy)
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//计算 h2Big * X
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tx, ty := curve.ScalarMult(Xx, Xy, h2Big.Bytes())
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//计算 Q = R + h2 * X
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Qx, Qy := curve.Add(Rx, Ry, tx, ty)
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//计算hash1的值
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h1Big := hash1(curve, ID, Qx, Qy, PKx, PKy)
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//计算 d = r + msk * h1 mod n
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temp := new(big.Int).Mul(msk, h1Big)
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d := new(big.Int).Add(r, temp)
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d.Mod(d, curve.Params().N)
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return d, Qx, Qy
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}
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func VerifyEquation(curve elliptic.Curve, ID []byte, d, Qx, Qy, Xx, Xy, PKx, PKy *big.Int) error {
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//计算等式左值 + h2 * X
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lx, ly := curve.ScalarBaseMult(d.Bytes())
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h2Big := hash2(curve, ID, Xx, Xy)
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h2Xx, h2Xy := curve.ScalarMult(Xx, Xy, h2Big.Bytes())
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lx, ly = curve.Add(lx, ly, h2Xx, h2Xy)
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//计算 Q + h1 * PK(t)
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h1Big := hash1(curve, ID, Qx, Qy, PKx, PKy)
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tx, ty := curve.ScalarMult(PKx, PKy, h1Big.Bytes())
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rx, ry := curve.Add(Qx, Qy, tx, ty)
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err := equal(lx, ly, rx, ry)
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if err != nil {
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return err
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}
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return nil
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}
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func genPriKey(curve elliptic.Curve, ID []byte, x, d, Xx, Xy *big.Int) *big.Int {
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//计算h2Big
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h2Big := hash2(curve, ID, Xx, Xy)
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//计算s = d + h2Big * x
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temp := new(big.Int).Mul(h2Big, x)
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sUser := new(big.Int).Add(d, temp)
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//s = s mod n
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sUser = sUser.Mod(sUser, curve.Params().N)
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return sUser
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}
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func SignThumb(curve elliptic.Curve, ID, msg []byte, s, Qx, Qy, PKx, PKy *big.Int) (*big.Int, *big.Int, *big.Int) {
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// 生成小于素数 的随机数 u
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u, _ := rand.Int(rand.Reader, curve.Params().N)
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// 生成点U
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Ux, Uy := curve.ScalarMult(curve.Params().Gx, curve.Params().Gy, u.Bytes())
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if !curve.IsOnCurve(Ux, Uy) {
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fmt.Println("zhuyi ----------------------------------------------U不在曲线上！！！！")
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}
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//计算h3
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h3 := hash3(curve, ID, msg, Qx, Qy, Ux, Uy, PKx, PKy)
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// 计算 v = u + h3 * s mod n
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// 计算 tmp = sa * h_3_big
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tmp := new(big.Int).Mul(h3, s)
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// 计算 v = u + tmp
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v := new(big.Int).Add(u, tmp)
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// 计算 v = v mod N
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v.Mod(v, curve.Params().N)
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return Ux, Uy, v
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}
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func VerifyThumb(curve elliptic.Curve, ID, msg []byte, Qx, Qy, PKx, PKy, Ux, Uy, v *big.Int) error {
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//计算h1和h3
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h1Big := hash1(curve, ID, Qx, Qy, PKx, PKy)
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h3Big := hash3(curve, ID, msg, Qx, Qy, Ux, Uy, PKx, PKy)
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//验证等式 v*P = U + h_3(Q + h_1 * PK_pub)
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//等式左边
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lx, ly := curve.ScalarBaseMult(v.Bytes())
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// 计算 t = h_1_big * PK_pub
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tx, ty := curve.ScalarMult(PKx, PKy, h1Big.Bytes())
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// 计算 out = Q + t
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tx, ty = curve.Add(Qx, Qy, tx, ty)
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// 计算 t = h_3_big * t
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tx, ty = curve.ScalarMult(tx, ty, h3Big.Bytes())
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// 计算 t = U + tmp_p
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rx, ry := curve.Add(Ux, Uy, tx, ty)
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//比较等式左右两值是否相等
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err := equal(lx, ly, rx, ry)
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if err != nil {
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fmt.Println("invalid!")
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return err
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}
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//fmt.Println("valid!")
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return nil
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}
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