Rabin数字签名 Lamport 一次签名

#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 %c
long 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;
}

#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;
}