Rabin数字签名 Lamport 一次签名

Rabin数字签名 代码：

#include<stdio.h>#include<string.h>#include<stdlib.h>#include<time.h>#include<iostream>#include<string.h>#include<math.h>#include<algorithm>#include<random>using namespace std;const int S = 10;long long mult_mod(long long a, long long b, long long c){    a %= c;    b %= c;    long long ret = 0;    while (b)    {        if (b & 1) { ret += a; ret %= c; }        a <<= 1;        if (a >= c)a %= c;        b >>= 1;    }    return ret;}//计算 ret =  x^n %clong long pow_mod(long long x, long long n, long long mod)//x^n%c{    if (n == 1)return x%mod;    x %= mod;    long long tmp = x;    long long ret = 1;    while (n)    {        if (n & 1) ret = mult_mod(ret, tmp, mod);        tmp = mult_mod(tmp, tmp, mod);        n >>= 1;    }    return ret;}bool check(long long a, long long n, long long x, long long t){    long long ret = pow_mod(a, x, n);    long long last = ret;    for (int i = 1; i <= t; i++)    {        ret = mult_mod(ret, ret, n);        if (ret == 1 && last != 1 && last != n - 1) return true;//合数        last = ret;    }    if (ret != 1) return true;    return false;}bool Miller_Rabin(long long n)//Miller_Rabin算法判断素数{    if (n<2)return false;    if (n == 2)return true;    if ((n & 1) == 0) return false;//偶数    long long x = n - 1;    long long t = 0;    while ((x & 1) == 0) { x >>= 1; t++; }    for (int i = 0; i<S; i++)    {        long long a = rand() % (n - 1) + 1;        if (check(a, n, x, t))            return false;//合数    }    return true;}long long gcd(long long a, long long b){    if (a == 0)return 1;    if (a<0) return gcd(-a, b);    while (b)    {        long long t = a%b;        a = b;        b = t;    }    return a;}bool Legendre(int a, int p){    int tmp = pow(a, (p - 1) / 2);    if (tmp % p == 1)        return true;    else        return false;}int main(){    cout << "*******************************************" << endl;    cout << "测试数据假定 p = 7 q = 11 ，进行签名和验证" << endl;    cout << "*******************************************" << endl << endl << endl;    static uniform_int_distribution<unsigned> u(1000000, 1000000000);    static default_random_engine e(time(0));    long long p = 6, q = 6;    //随机产生素数p q    while (!Miller_Rabin(p))        p = u(e);    while (!Miller_Rabin(q))        q = u(e);    //cout << p << " " << q << endl;    long long n = p*q;    cout << "素数p,q生成完毕！" << endl;    p = 7;    q = 11;    //签名生成    cout << "请输入 m 进行签名:" << endl;    long long m;    cin >> m;    if (!(Legendre(m, p) && Legendre(m, q)))    {        while (!(Legendre(m, p) && Legendre(m, q)))            m = m - 1;    }    long long s = ((long long)sqrt(m)) % n;     //签名验证    cout << "请输入s进行签名验证:" << endl;    int ss;    cin >> ss;    if (m == ss*ss%n)        cout << "true 验证成功！" << endl;    else        cout << "false 验证失败！" << endl;    return 0;}

Lamport 一次签名：

#include <iostream>#include <stdio.h>#include <cmath>#include <string>using namespace std;int quickpow(int m, int n, int k){    int  b = 1;    while (n > 0)    {        if (n & 1)            b = (b*m) % k;        n = n >> 1;        m = (m*m) % k;    }    return b;}int main(){    int n, MOD;    cin >> n >> MOD;    int y10, y11, y20, y21, y30, y31;    cin>>y10>>y11>>y20>>y21>>y30>>y31;    int z10, z11, z20, z21, z30, z31;    //    z10 = quickpow(n, y10, MOD);    z11 = quickpow(n, y11, MOD);    z20 = quickpow(n, y20, MOD);    z21 = quickpow(n, y21, MOD);    z30 = quickpow(n, y30, MOD);    z31 = quickpow(n, y31, MOD);    //    string cl;    cin >> cl;    int len = cl.size();    int Sign[100];    if (cl[0] == '0')        Sign[0] = y30;    else         Sign[0] = y31;    if (cl[1] == '0')        Sign[1] = y20;    else        Sign[1] = y21;    if (cl[2] == '0')        Sign[2] = y10;    else        Sign[2] = y11;    int Sign_ans[100];    for (int i = 0; i < 3; i++)    {        Sign_ans[i] = quickpow(n, Sign[2-i],MOD);        cout << Sign_ans[i] << endl;    }    return 0;}