国密SM2算法的java和nodejs实现

转至 http://mp.weixin.qq.com/s/nboZAvg1qYiJIEun6yF2aQ

国密即国家密码局认定的国产密码算法，即商用密码。包括对称加密（SM1），非对称加密(SM2) , 信息摘要(SM3). 本文介绍SM2

SM2 基于 ECC实现。.国家密码局推荐ECC曲线是256位，相当于比特币的secp256k1.
SM2 数学计算过程可以参考国家密码局官网的公布文档
本文介绍SM2 签名验签的java和nodejs的实现

ECC 算法依赖两个重要的数学运算 1，大数运算，2，椭圆乘法运算。
Java 中天生有BigInteger类，椭圆乘法运算可以借助于开源的java加密库：bouncycastle ，gradle 工程添加依赖：
compile ‘org.bouncycastle:bcprov-jdk15on:1.55’
下面就贴代码吧

public class SM2
{//测试参数
// public static final String[] ecc_param = {
//     "8542D69E4C044F18E8B92435BF6FF7DE457283915C45517D722EDB8B08F1DFC3",
//     "787968B4FA32C3FD2417842E73BBFEFF2F3C848B6831D7E0EC65228B3937E498",
//     "63E4C6D3B23B0C849CF84241484BFE48F61D59A5B16BA06E6E12D1DA27C5249A",
//     "8542D69E4C044F18E8B92435BF6FF7DD297720630485628D5AE74EE7C32E79B7",
//     "421DEBD61B62EAB6746434EBC3CC315E32220B3BADD50BDC4C4E6C147FEDD43D",
//     "0680512BCBB42C07D47349D2153B70C4E5D7FDFCBFA36EA1A85841B9E46E09A2"
// };//正式参数public static String[] ecc_param = { "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF","FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC","28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93","FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123","32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7","BC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0"};public static SM2 Instance() {return new SM2();}public final BigInteger ecc_p;public final BigInteger ecc_a;public final BigInteger ecc_b;public final BigInteger ecc_n;public final BigInteger ecc_gx;public final BigInteger ecc_gy;public final ECCurve ecc_curve;public final ECPoint ecc_point_g;public final ECDomainParameters ecc_bc_spec;public final ECKeyPairGenerator ecc_key_pair_generator;public final ECFieldElement ecc_gx_fieldelement;public final ECFieldElement ecc_gy_fieldelement;public SM2() {this.ecc_p = new BigInteger(ecc_param[0], 16);this.ecc_a = new BigInteger(ecc_param[1], 16);this.ecc_b = new BigInteger(ecc_param[2], 16);this.ecc_n = new BigInteger(ecc_param[3], 16);this.ecc_gx = new BigInteger(ecc_param[4], 16);this.ecc_gy = new BigInteger(ecc_param[5], 16);this.ecc_gx_fieldelement = new Fp(this.ecc_p, this.ecc_gx);this.ecc_gy_fieldelement = new Fp(this.ecc_p, this.ecc_gy);this.ecc_curve = new ECCurve.Fp(this.ecc_p, this.ecc_a, this.ecc_b);this.ecc_point_g = new ECPoint.Fp(this.ecc_curve, this.ecc_gx_fieldelement, this.ecc_gy_fieldelement);this.ecc_bc_spec = new ECDomainParameters(this.ecc_curve, this.ecc_point_g, this.ecc_n);ECKeyGenerationParameters ecc_ecgenparam;ecc_ecgenparam = new ECKeyGenerationParameters(this.ecc_bc_spec, new SecureRandom());this.ecc_key_pair_generator = new ECKeyPairGenerator();this.ecc_key_pair_generator.init(ecc_ecgenparam);}
}
签名代码片段：public static BigInteger[] Sm2Sign(byte[] md, AsymmetricCipherKeyPair keypair) {SM3Digest sm3 = new SM3Digest();ECPublicKeyParameters ecpub = (ECPublicKeyParameters) keypair.getPublic();byte[] hashData = new byte[32];sm3.update(md, 0, md.length);sm3.doFinal(hashData, 0);// eBigInteger e = new BigInteger(1, hashData);// kBigInteger k = null;ECPoint kp = null;BigInteger r = null;BigInteger s = null;BigInteger userD = null;BigInteger ecc_n = null;do {do {ECPrivateKeyParameters ecpriv = (ECPrivateKeyParameters) keypair.getPrivate();k = ecpriv.getD();kp = ecpub.getQ();ecc_n = ecpriv.getParameters().getN();userD = ecpriv.getD();// r = (e+x) mod nr = e.add(kp.getX().toBigInteger());r = r.mod(ecc_n);}while (r.equals(BigInteger.ZERO) || r.add(k).equals(ecc_n));//s=  (((1 + dA)~-1)  *  (k - r*da )) mod nBigInteger da_1 = userD.add(BigInteger.ONE);da_1 = da_1.modInverse(ecc_n);// ss = r.multiply(userD);s = k.subtract(s).mod(ecc_n);s = da_1.multiply(s).mod(ecc_n);}while (s.equals(BigInteger.ZERO));return new BigInteger[]{r, s};}签验代码片段：public static boolean Sm2verify(byte[] md, BigInteger r, BigInteger s, AsymmetricCipherKeyPair keypair) {SM3Digest sm3 = new SM3Digest();ECPublicKeyParameters ecpub = (ECPublicKeyParameters) keypair.getPublic();byte[] hashData = new byte[32];sm3.update(md, 0, md.length);sm3.doFinal(hashData, 0);// eBigInteger e = new BigInteger(1, hashData);// kECPoint k;ECPoint G = null;ECPoint Pa = null;BigInteger t = null;BigInteger R = null;BigInteger ecc_n = null;Pa = ecpub.getQ();G = ecpub.getParameters().getG();ecc_n = ecpub.getParameters().getN();if(r.equals(BigInteger.ONE)  || r.equals(ecc_n)) {return false;}if(s.equals(BigInteger.ONE)  || s.equals(ecc_n)) {return false;}t = r.add(s).mod(ecc_n);if (t.equals(BigInteger.ZERO)) {return false;}//k(x,y) = s*G + t*Pak = G.multiply(s).add(Pa.multiply(t));//R = (e+k.x) mod nR = e.add(k.getX().toBigInteger()).mod(ecc_n);//R == r  trueif (R.equals(r)) return true;return false;}

nodejs的实现方式
nodejs本身没有BigInteger的，但有牛人写了个BigInteger ，https://www.npmjs.com/package/biginteger
椭圆运算：https://github.com/cryptocoinjs/ecurve
有这两基本运算，就可以按国密局文档编写我们的SM2算法了
下面直接贴代码吧

var ecurve = require('ecurve');
var Point = ecurve.Point;
var BigInteger = require('bigi');
var Curve = ecurve.Curve;
var assert = require('assert')var SM2=getCurveSM2();
function getCurveSM2() {var curve = {p: "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFF",a: "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF00000000FFFFFFFFFFFFFFFC",b: "28E9FA9E9D9F5E344D5A9E4BCF6509A7F39789F515AB8F92DDBCBD414D940E93",n: "FFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFF7203DF6B21C6052B53BBF40939D54123",h: "01",Gx: "32C4AE2C1F1981195F9904466A39C9948FE30BBFF2660BE1715A4589334C74C7",Gy: "BC3736A2F4F6779C59BDCEE36B692153D0A9877CC62A474002DF32E52139F0A0"}if (!curve) return nullvar p = new BigInteger(curve.p, 16)var a = new BigInteger(curve.a, 16)var b = new BigInteger(curve.b, 16)var n = new BigInteger(curve.n, 16)var h = new BigInteger(curve.h, 16)var Gx = new BigInteger(curve.Gx, 16)var Gy = new BigInteger(curve.Gy, 16)return new Curve(p, a, b, Gx, Gy, n, h)
}function getQ(d) {var D =  BigInteger.fromBuffer(d);var G = SM2.Gvar Q = G.multiply(D);return Q;
}
function decodeFrom(buffer) {return Point.decodeFrom(SM2,buffer);
}function decodeFromXY(buffer) {var byteLength = Math.floor((SM2.p.bitLength() + 7) / 8)assert.equal(buffer.length, byteLength * 2, 'Invalid sequence length')var x = BigInteger.fromBuffer(buffer.slice(0, byteLength))var y = BigInteger.fromBuffer(buffer.slice(byteLength))var Q = Point.fromAffine(SM2, x, y)return Q;
}function sign(hash, d) {//var x = d.toBuffer(32)var e = BigInteger.fromBuffer(hash)var D =  BigInteger.fromBuffer(d);var n = SM2.nvar G = SM2.Gvar Q = G.multiply(D);var r, s;do {do {r = e.add(Q.affineX);r = r.mod(n);}while (r.equals(BigInteger.ZERO) || r.add(D).equals(n));//s=  (((1 + dA)~-1)  *  (k - r*da )) mod nvar da_1 = D.add(BigInteger.ONE);da_1 = da_1.modInverse(n);// ss = r.multiply(D);s = D.subtract(s).mod(n);s = da_1.multiply(s).mod(n);}while (s.equals(BigInteger.ZERO));return {r:r.toBuffer(),s:s.toBuffer()};
}
function verify (hash, signature, Q) {var n = SM2.nvar G = SM2.Gvar r = BigInteger.fromBuffer(signature.r);var s =  BigInteger.fromBuffer(signature.s);// 1.4.1 Enforce r and s are both integers in the interval [1, n − 1]if (r.signum() <= 0 || r.compareTo(n) >= 0) return falseif (s.signum() <= 0 || s.compareTo(n) >= 0) return false// 1.4.2 H = Hash(M), already done by the user// 1.4.3 e = Hvar e = BigInteger.fromBuffer(hash)var t;t = r.add(s).mod(n);if (t.equals(BigInteger.ZERO)) {return false;}//k(x,y) = s*G + t*Pavar k = G.multiply(s).add(Q.multiply(t));//R = (e+k.x) mod nR = e.add(k.affineX).mod(n);//R == r  trueif (R.equals(r)) return true;return false;}
module.exports = {Curve: SM2,Point:Point,decodeFrom:decodeFrom,decodeFromXY:decodeFromXY,getQ:getQ,sign: sign,verify: verify
}

以上代码只是代码片段，需要完整工程的同学可以关注订阅号索取源代码

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