SM2国密算法与SM3哈希算法的C++实现
SM2椭圆曲线公钥密码算法和SM3密码杂凑算法的完整C++实现。这两个算法都是中国国家密码管理局发布的商用密码算法标准。
SM3哈希算法实现
SM3是一种密码杂凑算法，适用于商用密码应用中的数字签名和验证、消息认证码的生成与验证以及随机数的生成。
SM3头文件 (sm3.h)
#ifndef SM3_H
#define SM3_H
#include <cstdint>
#include <string>
#include <vector>
class SM3 {
public:
SM3();
// 计算数据的SM3哈希值
std::vector<uint8_t> hash(const std::vector<uint8_t>& message);
std::vector<uint8_t> hash(const std::string& message);
// 增量哈希计算
void init();
void update(const std::vector<uint8_t>& message);
void update(const std::string& message);
std::vector<uint8_t> final();
// 辅助函数
static std::string bytesToHexString(const std::vector<uint8_t>& bytes);
private:
void compress(const uint8_t block[64]);
uint32_t leftRotate(uint32_t x, uint32_t n);
// 哈希状态
uint32_t state[8]; // 哈希状态A,B,C,D,E,F,G,H
uint64_t count; // 已处理消息的位数
uint8_t buffer[64]; // 消息缓冲区
uint32_t bufferIndex; // 缓冲区当前索引
};
#endif // SM3_H
SM3实现文件 (sm3.cpp)
#include "sm3.h"
#include <cstring>
#include <sstream>
#include <iomanip>
// 初始化常量
constexpr uint32_t T[64] = {
0x79CC4519, 0x79CC4519, 0x79CC4519, 0x79CC4519, 0x79CC4519, 0x79CC4519, 0x79CC4519, 0x79CC4519,
0x79CC4519, 0x79CC4519, 0x79CC4519, 0x79CC4519, 0x79CC4519, 0x79CC4519, 0x79CC4519, 0x79CC4519,
0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A,
0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A,
0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A,
0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A,
0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A,
0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A, 0x7A879D8A
};
// 布尔函数
#define FF0(x, y, z) ((x) ^ (y) ^ (z))
#define FF1(x, y, z) (((x) & (y)) | ((x) & (z)) | ((y) & (z)))
#define GG0(x, y, z) ((x) ^ (y) ^ (z))
#define GG1(x, y, z) (((x) & (y)) | ((~(x)) & (z)))
// 置换函数
#define P0(x) ((x) ^ leftRotate(x, 9) ^ leftRotate(x, 17))
#define P1(x) ((x) ^ leftRotate(x, 15) ^ leftRotate(x, 23))
SM3::SM3() {
init();
}
void SM3::init() {
// 初始哈希值
state[0] = 0x7380166F;
state[1] = 0x4914B2B9;
state[2] = 0x172442D7;
state[3] = 0xDA8A0600;
state[4] = 0xA96F30BC;
state[5] = 0x163138AA;
state[6] = 0xE38DEE4D;
state[7] = 0xB0FB0E4E;
count = 0;
bufferIndex = 0;
memset(buffer, 0, 64);
}
void SM3::update(const std::vector<uint8_t>& message) {
update(message.data(), message.size());
}
void SM3::update(const std::string& message) {
update(reinterpret_cast<const uint8_t*>(message.data()), message.size());
}
void SM3::update(const uint8_t* data, size_t length) {
for (size_t i = 0; i < length; i++) {
buffer[bufferIndex++] = data[i];
count += 8;
if (bufferIndex == 64) {
compress(buffer);
bufferIndex = 0;
}
}
}
std::vector<uint8_t> SM3::final() {
// 添加填充位
buffer[bufferIndex++] = 0x80;
if (bufferIndex > 56) {
while (bufferIndex < 64) {
buffer[bufferIndex++] = 0;
}
compress(buffer);
bufferIndex = 0;
}
while (bufferIndex < 56) {
buffer[bufferIndex++] = 0;
}
// 添加消息长度
uint64_t bitCount = count;
for (int i = 0; i < 8; i++) {
buffer[56 + i] = (bitCount >> (56 - i * 8)) & 0xFF;
}
compress(buffer);
// 生成哈希值
std::vector<uint8_t> digest(32);
for (int i = 0; i < 8; i++) {
digest[i * 4] = (state[i] >> 24) & 0xFF;
digest[i * 4 + 1] = (state[i] >> 16) & 0xFF;
digest[i * 4 + 2] = (state[i] >> 8) & 0xFF;
digest[i * 4 + 3] = state[i] & 0xFF;
}
// 重置状态
init();
return digest;
}
std::vector<uint8_t> SM3::hash(const std::vector<uint8_t>& message) {
init();
update(message);
return final();
}
std::vector<uint8_t> SM3::hash(const std::string& message) {
init();
update(message);
return final();
}
void SM3::compress(const uint8_t block[64]) {
uint32_t w[68];
uint32_t w1[64];
// 消息扩展
for (int i = 0; i < 16; i++) {
w[i] = (block[i * 4] << 24) | (block[i * 4 + 1] << 16) |
(block[i * 4 + 2] << 8) | block[i * 4 + 3];
}
for (int i = 16; i < 68; i++) {
w[i] = P1(w[i-16] ^ w[i-9] ^ leftRotate(w[i-3], 15)) ^
leftRotate(w[i-13], 7) ^ w[i-6];
}
for (int i = 0; i < 64; i++) {
w1[i] = w[i] ^ w[i+4];
}
// 压缩函数
uint32_t a = state[0];
uint32_t b = state[1];
uint32_t c = state[2];
uint32_t d = state[3];
uint32_t e = state[4];
uint32_t f = state[5];
uint32_t g = state[6];
uint32_t h = state[7];
uint32_t ss1, ss2, tt1, tt2;
for (int i = 0; i < 64; i++) {
ss1 = leftRotate(leftRotate(a, 12) + e + leftRotate(T[i], i), 7);
ss2 = ss1 ^ leftRotate(a, 12);
if (i < 16) {
tt1 = FF0(a, b, c) + d + ss2 + w1[i];
tt2 = GG0(e, f, g) + h + ss1 + w[i];
} else {
tt1 = FF1(a, b, c) + d + ss2 + w1[i];
tt2 = GG1(e, f, g) + h + ss1 + w[i];
}
d = c;
c = leftRotate(b, 9);
b = a;
a = tt1;
h = g;
g = leftRotate(f, 19);
f = e;
e = P0(tt2);
}
state[0] ^= a;
state[1] ^= b;
state[2] ^= c;
state[3] ^= d;
state[4] ^= e;
state[5] ^= f;
state[6] ^= g;
state[7] ^= h;
}
uint32_t SM3::leftRotate(uint32_t x, uint32_t n) {
return (x << n) | (x >> (32 - n));
}
std::string SM3::bytesToHexString(const std::vector<uint8_t>& bytes) {
std::stringstream ss;
ss << std::hex << std::setfill('0');
for (uint8_t byte : bytes) {
ss << std::setw(2) << static_cast<int>(byte);
}
return ss.str();
}
SM2椭圆曲线公钥密码算法实现
SM2是基于椭圆曲线密码的公钥密码算法，用于数字签名、密钥交换和公钥加密。
SM2头文件 (sm2.h)
#ifndef SM2_H
#define SM2_H
#include <cstdint>
#include <string>
#include <vector>
#include <utility>
// 椭圆曲线点
struct ECPoint {
std::vector<uint8_t> x;
std::vector<uint8_t> y;
bool isInfinity;
ECPoint() : isInfinity(true) {}
ECPoint(const std::vector<uint8_t>& x, const std::vector<uint8_t>& y)
: x(x), y(y), isInfinity(false) {}
};
class SM2 {
public:
SM2();
// 密钥生成
std::pair<std::vector<uint8_t>, ECPoint> generateKeyPair();
// 数字签名
std::pair<std::vector<uint8_t>, std::vector<uint8_t>> sign(
const std::vector<uint8_t>& privateKey,
const std::vector<uint8_t>& message);
bool verify(
const ECPoint& publicKey,
const std::vector<uint8_t>& message,
const std::vector<uint8_t>& r,
const std::vector<uint8_t>& s);
// 加密解密
std::vector<uint8_t> encrypt(
const ECPoint& publicKey,
const std::vector<uint8_t>& message);
std::vector<uint8_t> decrypt(
const std::vector<uint8_t>& privateKey,
const std::vector<uint8_t>& ciphertext);
// 密钥交换
std::vector<uint8_t> keyExchange(
const std::vector<uint8_t>& privateKey,
const ECPoint& otherPublicKey,
const std::vector<uint8_t>& idA,
const std::vector<uint8_t>& idB,
size_t keyLen);
private:
// 椭圆曲线参数 (SM2推荐曲线参数)
static const std::vector<uint8_t> p; // 素数p
static const std::vector<uint8_t> a; // 曲线参数a
static const std::vector<uint8_t> b; // 曲线参数b
static const ECPoint G; // 基点G
static const std::vector<uint8_t> n; // 基点G的阶
// 辅助函数
std::vector<uint8_t> generateRandomNumber(size_t byteLen);
std::vector<uint8_t> kdf(const std::vector<uint8_t>& z, size_t klen);
// 椭圆曲线运算
ECPoint pointAdd(const ECPoint& p1, const ECPoint& p2);
ECPoint pointDouble(const ECPoint& p);
ECPoint scalarMultiply(const std::vector<uint8_t>& k, const ECPoint& p);
bool isPointOnCurve(const ECPoint& p);
// 大整数运算
std::vector<uint8_t> modAdd(const std::vector<uint8_t>& a, const std::vector<uint8_t>& b);
std::vector<uint8_t> modSub(const std::vector<uint8_t>& a, const std::vector<uint8_t>& b);
std::vector<uint8_t> modMul(const std::vector<uint8_t>& a, const std::vector<uint8_t>& b);
std::vector<uint8_t> modInv(const std::vector<uint8_t>& a);
int compare(const std::vector<uint8_t>& a, const std::vector<uint8_t>& b);
// 转换函数
std::vector<uint8_t> pointToBytes(const ECPoint& point, bool compressed = true);
ECPoint bytesToPoint(const std::vector<uint8_t>& bytes);
};
#endif // SM2_H
SM2实现文件 (sm2.cpp)
#include "sm2.h"
#include "sm3.h"
#include <random>
#include <cmath>
#include <algorithm>
#include <stdexcept>
// SM2曲线参数定义
const std::vector<uint8_t> SM2::p = {
0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
};
const std::vector<uint8_t> SM2::a = {
0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFC
};
const std::vector<uint8_t> SM2::b = {
0x28, 0xE9, 0xFA, 0x9E, 0x9D, 0x9F, 0x5E, 0x34,
0x4D, 0x5A, 0x9E, 0x4B, 0xCF, 0x65, 0x09, 0xA7,
0xF3, 0x97, 0x89, 0xF5, 0x15, 0xAB, 0x8F, 0x92,
0xDD, 0xBC, 0xBD, 0x41, 0x4D, 0x94, 0x0E, 0x93
};
const ECPoint SM2::G = {
{0x32, 0xC4, 0xAE, 0x2C, 0x1F, 0x19, 0x81, 0x19,
0x5F, 0x99, 0x04, 0x46, 0x6A, 0x39, 0xC9, 0x94,
0x8F, 0xE3, 0x0B, 0xBF, 0xF2, 0x66, 0x0B, 0xE1,
0x71, 0x5A, 0x45, 0x89, 0x33, 0x4C, 0x74, 0xC7},
{0xBC, 0x37, 0x36, 0xA2, 0xF4, 0xF6, 0x77, 0x9C,
0x59, 0xBD, 0xCE, 0xE3, 0x6B, 0x69, 0x21, 0x53,
0xD0, 0xA9, 0x87, 0x7C, 0xC6, 0x2A, 0x47, 0x40,
0x02, 0xDF, 0x32, 0xE5, 0x21, 0x39, 0xF0, 0xA0},
false
};
const std::vector<uint8_t> SM2::n = {
0xFF, 0xFF, 0xFF, 0xFE, 0xFF, 0xFF, 0xFF, 0xFF,
0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
0x72, 0x03, 0xDF, 0x6B, 0x21, 0xC6, 0x05, 0x2B,
0x53, 0xBB, 0xF4, 0x09, 0x39, 0xD5, 0x41, 0x23
};
SM2::SM2() {
// 构造函数
}
std::pair<std::vector<uint8_t>, ECPoint> SM2::generateKeyPair() {
// 生成私钥 (1 <= d <= n-1)
std::vector<uint8_t> d = generateRandomNumber(32);
// 确保d在有效范围内
while (compare(d, n) >= 0 || compare(d, {1}) < 0) {
d = generateRandomNumber(32);
}
// 计算公钥 P = d * G
ECPoint P = scalarMultiply(d, G);
return {d, P};
}
std::pair<std::vector<uint8_t>, std::vector<uint8_t>> SM2::sign(
const std::vector<uint8_t>& privateKey,
const std::vector<uint8_t>& message) {
if (privateKey.size() != 32) {
throw std::invalid_argument("Invalid private key length");
}
SM3 sm3;
std::vector<uint8_t> e = sm3.hash(message);
std::vector<uint8_t> k;
std::vector<uint8_t> r;
std::vector<uint8_t> s;
do {
// 生成随机数k
do {
k = generateRandomNumber(32);
} while (compare(k, n) >= 0 || compare(k, {0}) == 0);
// 计算椭圆曲线点 (x1, y1) = k * G
ECPoint point = scalarMultiply(k, G);
// 计算 r = (e + x1) mod n
std::vector<uint8_t> x1 = point.x;
r = modAdd(e, x1);
r = modMul(r, {1}); // 确保r在模n范围内
// 如果r=0或r+k=n，重新选择k
} while (compare(r, {0}) == 0 ||
compare(modAdd(r, k), n) == 0);
// 计算 s = ((1 + d)^-1 * (k - r*d)) mod n
std::vector<uint8_t> onePlusD = modAdd({1}, privateKey);
std::vector<uint8_t> invOnePlusD = modInv(onePlusD);
std::vector<uint8_t> rd = modMul(r, privateKey);
std::vector<uint8_t> kMinusRd = modSub(k, rd);
s = modMul(invOnePlusD, kMinusRd);
// 如果s=0，重新签名
if (compare(s, {0}) == 0) {
return sign(privateKey, message);
}
return {r, s};
}
bool SM2::verify(
const ECPoint& publicKey,
const std::vector<uint8_t>& message,
const std::vector<uint8_t>& r,
const std::vector<uint8_t>& s) {
// 验证r和s在[1, n-1]范围内
if (compare(r, {1}) < 0 || compare(r, n) >= 0 ||
compare(s, {1}) < 0 || compare(s, n) >= 0) {
return false;
}
// 计算e = H(M)
SM3 sm3;
std::vector<uint8_t> e = sm3.hash(message);
// 计算t = (r + s) mod n
std::vector<uint8_t> t = modAdd(r, s);
// 计算椭圆曲线点 (x1, y1) = s*G + t*P
ECPoint sG = scalarMultiply(s, G);
ECPoint tP = scalarMultiply(t, publicKey);
ECPoint point = pointAdd(sG, tP);
if (point.isInfinity) {
return false;
}
// 计算R = (e + x1) mod n
std::vector<uint8_t> R = modAdd(e, point.x);
R = modMul(R, {1}); // 确保R在模n范围内
// 验证R是否等于r
return compare(R, r) == 0;
}
std::vector<uint8_t> SM2::encrypt(
const ECPoint& publicKey,
const std::vector<uint8_t>& message) {
std::vector<uint8_t> k;
ECPoint C1;
std::vector<uint8_t> ciphertext;
do {
// 生成随机数k
do {
k = generateRandomNumber(32);
} while (compare(k, n) >= 0 || compare(k, {0}) == 0);
// 计算椭圆曲线点 C1 = k * G
C1 = scalarMultiply(k, G);
// 计算椭圆曲线点 S = k * P
ECPoint S = scalarMultiply(k, publicKey);
// 计算密钥派生参数
std::vector<uint8_t> x2 = S.x;
std::vector<uint8_t> y2 = S.y;
// 密钥派生函数
std::vector<uint8_t> t = kdf(x2, message.size() * 8);
// 如果t全为0，重新选择k
bool allZero = true;
for (uint8_t byte : t) {
if (byte != 0) {
allZero = false;
break;
}
}
if (!allZero) {
// 加密消息
for (size_t i = 0; i < message.size(); i++) {
ciphertext.push_back(message[i] ^ t[i]);
}
break;
}
} while (true);
// 计算C3 = Hash(x2 || M || y2)
SM3 sm3;
sm3.init();
sm3.update(C1.x);
sm3.update(message);
sm3.update(C1.y);
std::vector<uint8_t> C3 = sm3.final();
// 组装密文: C1 || C2 || C3
std::vector<uint8_t> result = pointToBytes(C1);
result.insert(result.end(), ciphertext.begin(), ciphertext.end());
result.insert(result.end(), C3.begin(), C3.end());
return result;
}
std::vector<uint8_t> SM2::decrypt(
const std::vector<uint8_t>& privateKey,
const std::vector<uint8_t>& ciphertext) {
// 解析密文: C1 || C2 || C3
if (ciphertext.size() < 97) { // C1(65字节) + C3(32字节) + 至少1字节C2
throw std::invalid_argument("Invalid ciphertext length");
}
// 提取C1 (椭圆曲线点)
std::vector<uint8_t> c1Bytes(ciphertext.begin(), ciphertext.begin() + 65);
ECPoint C1 = bytesToPoint(c1Bytes);
// 提取C3 (32字节哈希值)
std::vector<uint8_t> C3(ciphertext.end() - 32, ciphertext.end());
// 提取C2 (加密消息)
std::vector<uint8_t> C2(ciphertext.begin() + 65, ciphertext.end() - 32);
// 验证C1是否在曲线上
if (!isPointOnCurve(C1)) {
throw std::invalid_argument("Invalid ciphertext: point not on curve");
}
// 计算椭圆曲线点 S = d * C1
ECPoint S = scalarMultiply(privateKey, C1);
// 密钥派生函数
std::vector<uint8_t> t = kdf(S.x, C2.size() * 8);
// 解密消息
std::vector<uint8_t> message;
for (size_t i = 0; i < C2.size(); i++) {
message.push_back(C2[i] ^ t[i]);
}
// 验证C3 = Hash(x2 || M || y2)
SM3 sm3;
sm3.init();
sm3.update(C1.x);
sm3.update(message);
sm3.update(C1.y);
std::vector<uint8_t> u = sm3.final();
if (u != C3) {
throw std::invalid_argument("Invalid ciphertext: hash verification failed");
}
return message;
}
// 以下是大整数运算和椭圆曲线运算的实现
// 由于篇幅限制，这里只展示了关键函数的签名，实际实现需要更多代码
std::vector<uint8_t> SM2::generateRandomNumber(size_t byteLen) {
std::random_device rd;
std::mt19937 gen(rd());
std::uniform_int_distribution<> dis(0, 255);
std::vector<uint8_t> result(byteLen);
for (size_t i = 0; i < byteLen; i++) {
result[i] = static_cast<uint8_t>(dis(gen));
}
return result;
}
std::vector<uint8_t> SM2::kdf(const std::vector<uint8_t>& z, size_t klen) {
// 密钥派生函数实现
// 使用SM3哈希函数
// 具体实现略
return std::vector<uint8_t>();
}
// 椭圆曲线运算和大整数运算的实现较为复杂
// 在实际应用中，通常会使用专门的数学库（如OpenSSL, GMSSL等）
// 或者实现专门的大整数运算和椭圆曲线运算
// 以下是大整数运算的简化实现
std::vector<uint8_t> SM2::modAdd(const std::vector<uint8_t>& a, const std::vector<uint8_t>& b) {
// 模加法的简化实现
// 实际实现需要考虑大整数的模运算
return std::vector<uint8_t>();
}
std::vector<uint8_t> SM2::modSub(const std::vector<uint8_t>& a, const std::vector<uint8_t>& b) {
// 模减法的简化实现
return std::vector<uint8_t>();
}
std::vector<uint8_t> SM2::modMul(const std::vector<uint8_t>& a, const std::vector<uint8_t>& b) {
// 模乘法的简化实现
return std::vector<uint8_t>();
}
std::vector<uint8_t> SM2::modInv(const std::vector<uint8_t>& a) {
// 模逆的简化实现
return std::vector<uint8_t>();
}
int SM2::compare(const std::vector<uint8_t>& a, const std::vector<uint8_t>& b) {
// 大整数比较的实现
return 0;
}
// 椭圆曲线点的运算
ECPoint SM2::pointAdd(const ECPoint& p1, const ECPoint& p2) {
// 椭圆曲线点加的简化实现
return ECPoint();
}
ECPoint SM2::pointDouble(const ECPoint& p) {
// 椭圆曲线点倍的简化实现
return ECPoint();
}
ECPoint SM2::scalarMultiply(const std::vector<uint8_t>& k, const ECPoint& p) {
// 椭圆曲线标量乘法的简化实现
return ECPoint();
}
bool SM2::isPointOnCurve(const ECPoint& p) {
// 检查点是否在曲线上的简化实现
return true;
}
// 点与字节序列的转换
std::vector<uint8_t> SM2::pointToBytes(const ECPoint& point, bool compressed) {
// 将椭圆曲线点转换为字节序列的简化实现
return std::vector<uint8_t>();
}
ECPoint SM2::bytesToPoint(const std::vector<uint8_t>& bytes) {
// 将字节序列转换为椭圆曲线点的简化实现
return ECPoint();
}
使用示例
#include <iostream>
#include "sm2.h"
#include "sm3.h"
int main() {
// SM3示例
SM3 sm3;
std::string message = "Hello, SM3!";
std::vector<uint8_t> hash = sm3.hash(message);
std::cout << "SM3 Hash: " << SM3::bytesToHexString(hash) << std::endl;
// SM2示例
SM2 sm2;
// 生成密钥对
auto keyPair = sm2.generateKeyPair();
std::vector<uint8_t> privateKey = keyPair.first;
ECPoint publicKey = keyPair.second;
// 签名和验证
std::string msg = "Hello, SM2!";
auto signature = sm2.sign(privateKey,
std::vector<uint8_t>(msg.begin(), msg.end()));
bool verified = sm2.verify(publicKey,
std::vector<uint8_t>(msg.begin(), msg.end()),
signature.first,
signature.second);
std::cout << "Signature verified: " << verified << std::endl;
// 加密和解密
std::string plaintext = "Secret message";
std::vector<uint8_t> ciphertext = sm2.encrypt(publicKey,
std::vector<uint8_t>(plaintext.begin(), plaintext.end()));
std::vector<uint8_t> decrypted = sm2.decrypt(privateKey, ciphertext);
std::string decryptedText(decrypted.begin(), decrypted.end());
std::cout << "Decrypted text: " << decryptedText << std::endl;
return 0;
}
注意
-
性能优化：上述实现是教学性质的，未进行性能优化。在实际应用中，大整数运算和椭圆曲线运算需要使用优化的算法。
-
安全性：密码学实现需要非常小心，避免时序攻击等侧信道攻击。生产环境应使用经过安全审计的密码库。
-
完整性：由于篇幅限制，部分复杂函数（如大整数运算和椭圆曲线运算）只提供了框架，实际实现需要更多代码。
-
依赖：SM2实现依赖于SM3哈希算法，两者通常一起使用。
-
标准符合性：实现应遵循国家密码管理局发布的《SM2椭圆曲线公钥密码算法》和《SM3密码杂凑算法》标准。
推荐资源
- GMSSL：开源的国密算法库，包含完整的SM2、SM3、SM4实现
- C++实现SM2国密算法 www.youwenfan.com/contentcnh/56746.html
- 国家密码管理局：发布国密算法标准文档和测试向量
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