簡述

SM2是非對稱加密算法

它是基于橢圓曲線密碼的公鑰密碼算法標(biāo)準(zhǔn)，其秘鑰長度256bit，包含數(shù)字簽名、密鑰交換和公鑰加密，用于替換RSA/DH/ECDSA/ECDH等國際算法。可以滿足電子認(rèn)證服務(wù)系統(tǒng)等應(yīng)用需求，由國家密碼管理局于2010年12月17號發(fā)布。

SM2采用的是ECC 256位的一種，其安全強(qiáng)度比RSA 2048位高，且運(yùn)算速度快于RSA。隨著密碼技術(shù)和計(jì)算技術(shù)的發(fā)展，目前常用的1024位RSA算法面臨嚴(yán)重的安全威脅，我們國家密碼管理部門經(jīng)過研究，決定采用SM2橢圓曲線算法替換RSA算法。SM2算法在安全性、性能上都具有優(yōu)勢。

基礎(chǔ)知識：橢圓曲線知識點(diǎn)、SM3算法

獲取公私鑰：

橢圓曲線方程：$y^2=x^3+ax+b\mathrm{m}\mathrm{o}\mathrm{d}p$

$確認(rèn)a、b、p，確認(rèn)曲線。$

$選擇一個(gè)點(diǎn)P(x_g,y_g)為基點(diǎn)。$

$對曲線做切線、x對稱點(diǎn)運(yùn)行。次數(shù)為d,運(yùn)算倍點(diǎn)為Q$

$d為私鑰,Q為公鑰$

密鑰對的生成:

$產(chǎn)生隨機(jī)整數(shù)d[1,n?2]$

$G為基點(diǎn)，計(jì)算點(diǎn)P=(xP,yP)=[d]G;$

$密鑰對為:(d,P)其中，d為私鑰，P為公鑰$

一個(gè)很典型的例子：

a = 0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC b = 0x28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93 p = 0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF x_g = 0x32c4ae2c1f1981195f9904466a39c9948fe30bbff2660be1715a4589334c74c7 y_g = 0xbc3736a2f4f6779c59bdcee36b692153d0a9877cc62a474002df32e52139f0a0 n = 0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123

SM簽名

$M$為待簽名消息，數(shù)字簽名結(jié)果為$(r,s)$ ，用戶密鑰對$(d,P)$。

實(shí)現(xiàn)步驟：

$e=hash(M)?獲取消息散列值$

$產(chǎn)生隨機(jī)數(shù)k?以便即使是同一個(gè)消息，每次簽名出來的結(jié)果不同。$

$使用隨機(jī)數(shù)，計(jì)算橢圓曲線點(diǎn)(x_1,y_1)=[k]G$

$r=(e+x1)\mathrm{m}\mathrm{o}\mathrm{d}n?判斷：r=0或者r+k=n,繼續(xù)第2步。$

$s=((1+d{)}^{?1}?(k?r?d))\mathrm{m}\mathrm{o}\mathrm{d}n,若s=0，繼續(xù)第2步$

$r,s為簽名信息。$

SM驗(yàn)簽

$M$為明文，$(r,s)$為簽名結(jié)果,用戶公鑰$P$

實(shí)現(xiàn)步驟：

$e=hash(M)$

$t=(r+s)\mathrm{m}\mathrm{o}\mathrm{d}n$

$(x,y)=[s]G+[t]P$

$R=(e+x)\mathrm{m}\mathrm{o}\mathrm{d}n$

$計(jì)算R是否等于r$

$[s]G$ +$[t]P$的結(jié)果可以推導(dǎo)出等于$[k]G$。

驗(yàn)證原理

$[s]G+[t]P??=sG+(r+s)P$
$=sG+(r+s)dG$
$=sG+sd?G+rd?G$
$=(1+d?)sG+rd?G$
$=(1+d?)(1+d{)}^{?1}(k?rd)G+rdG$
$=(k?rd?)G+rd?G$
$=kG?rdG+rdG$
$=kG=(x1?,y1?)?$

SM加密

M為明文字符串

$獲取隨機(jī)數(shù)k$

$(x1,y1)=[k]G$

$S=[h]P?h為余因子$

$C1=(x2,y2)=[k]P$

$t=KDF(x2\parallel y2,klen)?klen為M的長度。KDF是sm2的密鑰派生函數(shù)$

$C2=M+t$

$C3=Hash(x2\parallel M\parallel y2)$

$C=C1\parallel C2\parallel C3$

SM解密

C為密文字符串,klen為密文中C2的長度

$C1=C里面獲取，驗(yàn)證C1是否滿足橢圓曲線。?C2長度確定，可以獲取C1內(nèi)容。$

$S=[h]C1，S為無窮點(diǎn)，退出。$

$(x2,y2)=[d]C1$

$t=KDF(m2\parallel y2,klen)$

$M=C2+t$

$u=Hash(x2\parallel M\parallel y2),u?==C3$

$M為明文$

代碼實(shí)現(xiàn)

首先，需要導(dǎo)入包gmssl

pip install gmssl

生成公私鑰算法
sm2utils.py

from random import SystemRandomclass CurveFp:def __init__(self, A, B, P, N, Gx, Gy, name):self.A = Aself.B = Bself.P = Pself.N = Nself.Gx = Gxself.Gy = Gyself.name = namesm2p256v1 = CurveFp(name="sm2p256v1",A=0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC,B=0x28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93,P=0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF,N=0xFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123,Gx=0x32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7,Gy=0xBC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0 )def multiply(a, n, N, A, P):return fromJacobian(jacobianMultiply(toJacobian(a), n, N, A, P), P)def add(a, b, A, P):return fromJacobian(jacobianAdd(toJacobian(a), toJacobian(b), A, P), P)def inv(a, n):if a == 0:return 0lm, hm = 1, 0low, high = a % n, nwhile low > 1:r = high//lownm, new = hm-lm*r, high-low*rlm, low, hm, high = nm, new, lm, lowreturn lm % ndef toJacobian(Xp_Yp):Xp, Yp = Xp_Ypreturn (Xp, Yp, 1)def fromJacobian(Xp_Yp_Zp, P):Xp, Yp, Zp = Xp_Yp_Zpz = inv(Zp, P)return ((Xp * z**2) % P, (Yp * z**3) % P)def jacobianDouble(Xp_Yp_Zp, A, P):Xp, Yp, Zp = Xp_Yp_Zpif not Yp:return (0, 0, 0)ysq = (Yp ** 2) % PS = (4 * Xp * ysq) % PM = (3 * Xp ** 2 + A * Zp ** 4) % Pnx = (M**2 - 2 * S) % Pny = (M * (S - nx) - 8 * ysq ** 2) % Pnz = (2 * Yp * Zp) % Preturn (nx, ny, nz)def jacobianAdd(Xp_Yp_Zp, Xq_Yq_Zq, A, P):Xp, Yp, Zp = Xp_Yp_ZpXq, Yq, Zq = Xq_Yq_Zqif not Yp:return (Xq, Yq, Zq)if not Yq:return (Xp, Yp, Zp)U1 = (Xp * Zq ** 2) % PU2 = (Xq * Zp ** 2) % PS1 = (Yp * Zq ** 3) % PS2 = (Yq * Zp ** 3) % Pif U1 == U2:if S1 != S2:return (0, 0, 1)return jacobianDouble((Xp, Yp, Zp), A, P)H = U2 - U1R = S2 - S1H2 = (H * H) % PH3 = (H * H2) % PU1H2 = (U1 * H2) % Pnx = (R ** 2 - H3 - 2 * U1H2) % Pny = (R * (U1H2 - nx) - S1 * H3) % Pnz = (H * Zp * Zq) % Preturn (nx, ny, nz)def jacobianMultiply(Xp_Yp_Zp, n, N, A, P):Xp, Yp, Zp = Xp_Yp_Zpif Yp == 0 or n == 0:return (0, 0, 1)if n == 1:return (Xp, Yp, Zp)if n < 0 or n >= N:return jacobianMultiply((Xp, Yp, Zp), n % N, N, A, P)if (n % 2) == 0:return jacobianDouble(jacobianMultiply((Xp, Yp, Zp), n // 2, N, A, P), A, P)if (n % 2) == 1:return jacobianAdd(jacobianDouble(jacobianMultiply((Xp, Yp, Zp), n // 2, N, A, P), A, P), (Xp, Yp, Zp), A, P)class PrivateKey:def __init__(self, curve=sm2p256v1, secret=None):self.curve = curveself.secret = secret or SystemRandom().randrange(1, curve.N)def publicKey(self):curve = self.curvexPublicKey, yPublicKey = multiply((curve.Gx, curve.Gy), self.secret, A=curve.A, P=curve.P, N=curve.N)return PublicKey(xPublicKey, yPublicKey, curve)def toString(self):return "{}".format(str(hex(self.secret))[2:].zfill(64))class PublicKey:def __init__(self, x, y, curve):self.x = xself.y = yself.curve = curvedef toString(self, compressed=True):return {True: str(hex(self.x))[2:],False: "{}{}".format(str(hex(self.x))[2:].zfill(64), str(hex(self.y))[2:].zfill(64))}.get(compressed)if __name__ == "__main__":priKey = PrivateKey()pubKey = priKey.publicKey()print(priKey.toString())print(pubKey.toString(compressed = False))

加解密算法
封裝類 sm2encryp.py

from gmssl import sm2 from base64 import b64encode, b64decode # sm2的公私鑰 SM2_PRIVATE_KEY = '00B9AB0B828FF68872F21A837FC303668428DEA11DCD1B24429D0C99E24EED83D5' SM2_PUBLIC_KEY = 'B9C9A6E04E9C91F7BA880429273747D7EF5DDEB0BB2FF6317EB00BEF331A83081A6994B8993F3F5D6EADDDB81872266C87C018FB4162F5AF347B483E24620207'sm2_crypt = sm2.CryptSM2(public_key=SM2_PUBLIC_KEY, private_key=SM2_PRIVATE_KEY)class sm2Encrypt:# 加密def encrypt(self, info):encode_info = sm2_crypt.encrypt(info.encode(encoding="utf-8"))encode_info = b64encode(encode_info).decode() # 將二進(jìn)制bytes通過base64編碼return encode_info# 解密def decrypt(self, info):decode_info = b64decode(info.encode()) # 通過base64解碼成二進(jìn)制bytesdecode_info = sm2_crypt.decrypt(decode_info).decode(encoding="utf-8")return decode_infoif __name__ == "__main__":origin_pwd = '123456'sm2 = sm2Encrypt()# 加密的密碼encrypy_pwd = sm2.encrypt(origin_pwd)print(encrypy_pwd)# 解密的密碼decrypt_pwd = sm2.decrypt(encrypy_pwd)print(decrypt_pwd)

當(dāng)跟sm2encryp.py在一個(gè)文件夾是可以直接引用它

from sm2encryp import sm2Encrypt pass_encrypt = sm2Encrypt() pwd = pass_encrypt.decrypt("H24OlVZgSTtevCW138O+C5PlZp8OiD920JnpVr7r9ndkGBWFZUVDD48iIVrZRnamgosV5910m9k0438WpIyi0guEt8F5inG7Y5A51whRfdPZ+qdvWVQxI857CBEzkb3h1bMp1ETQ") print(pwd)

參考

https://www.jianshu.com/p/efc43060e0aa
https://blog.csdn.net/u013137970/article/details/84573200
https://blog.csdn.net/u014651560/article/details/113744296

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