#include <iostream>
#include <cstdlib>
#include <ctime>
#include <cstring>
#include <stdio.h>
using namespace std;
//RSA算法所需参数
typedef struct RSA_PARAM_Tag
{
unsigned __int64 p, q; //两个素数，不参与加密解密运算
unsigned __int64 f; //f=(p-1)*(q-1)，不参与加密解密运算
unsigned __int64 n, e; //公匙，n=p*q，gcd(e,f)=1
unsigned __int64 d; //私匙，e*d=1 (mod f)，gcd(n,d)=1
unsigned __int64 s; //块长，满足2^s<=n的最大的s，即log2(n)
} RSA_PARAM;
//小素数表
const static long g_PrimeTable[]=
{
3,5,7,11,13,17,19,23,29,31,37,41,43,
47,53,59,61,67,71,73,79,83,89,97
};
const static long g_PrimeCount=sizeof(g_PrimeTable) / sizeof(long);const unsigned __int64 multiplier=12747293821;
const unsigned __int64 adder=1343545677842234541;//随机数类
class RandNumber
{
private:
unsigned __int64 randSeed;
public:
RandNumber(unsigned __int64 s=0);
unsigned __int64 Random(unsigned __int64 n);
};
RandNumber::RandNumber(unsigned __int64 s)
{
if(!s)
{
randSeed= (unsigned __int64)time(NULL);
}
else
{
randSeed=s;
}
}
unsigned __int64 RandNumber::Random(unsigned __int64 n)
{
randSeed=multiplier * randSeed + adder;
return randSeed % n;
}static RandNumber g_Rnd;
//模乘运算，返回值 x=a*b mod n
inline unsigned __int64 MulMod(unsigned __int64 a, unsigned __int64 b, unsigned __int64 n)
{
return a * b % n;
}
//模幂运算，返回值 x=base^pow mod n
unsigned __int64 PowMod(unsigned __int64 &base, unsigned __int64 &pow, unsigned __int64 &n)
{
unsigned __int64 a=base, b=pow, c=1;
while(b)
{
while(!(b & 1))
{
b>>=1; //函数看起来可以处理64位的整数，但由于这里已经造成了溢出，因此实际处理范围没有64位
a=MulMod(a, a, n);
} b--; //这里也会溢出，若把64位整数拆为两个32位整数不知是否可以解决这个问题。
c=MulMod(a, c, n);
} return c;
}
/*
Rabin-Miller素数测试，通过测试返回1，否则返回0。
n是待测素数。
*/
long RabinMillerKnl(unsigned __int64 &n)
{
unsigned __int64 b, m, j, v, i;
m=n - 1;
j=0; //计算出m、j，使得n-1=m*2^j，其中m是正奇数，j是非负整数
while(!(m & 1))
{
++j;
m>>=1;
} //随机取一个b，2<=b<n-1
b=2 + g_Rnd.Random(n - 3); //算v=b^m mod n
v=PowMod(b, m, n); //如果v==1，通过测试
if(v == 1)
{
return 1;
} //令i=1
i=1; //v=n-1，通过测试
while(v != n - 1)
{
//i==l，非素数，结束
if(i == j)
{
return 0;
}
unsigned long long xxx;
int xxxx = 2;
xxx = xxxx;
v = PowMod(v, xxx, n);
++i; //循环到5
} return 1;
}
/*
Rabin-Miller素数测试，循环调用核心loop次
全部通过返回1，否则返回0
*/
long RabinMiller(unsigned __int64 &n, long loop)
{
//用小素数筛选一次，提高效率
for(long i=0; i < g_PrimeCount; i++)
{
if(n % g_PrimeTable[i] == 0)
{
return 0;
}
} //循环调用Rabin-Miller测试loop次，使得非素数通过测试的概率降为(1/4)^loop
for(long i=0; i < loop; i++)
{
if(!RabinMillerKnl(n))
{
return 0;
}
} return 1;
}/*
随机生成一个bits位(二进制位)的素数，最多32位
*/
unsigned __int64 RandomPrime(char bits)
{
unsigned __int64 base;
do
{
base= (unsigned long)1 << (bits - 1); //保证最高位是1
base+=g_Rnd.Random(base); //再加上一个随机数
base|=1; //保证最低位是1，即保证是奇数
} while(!RabinMiller(base, 30)); //进行拉宾－米勒测试30次
return base; //全部通过认为是素数
}/*
欧几里得法求最大公约数
*/
unsigned __int64 EuclidGcd(unsigned __int64 &p, unsigned __int64 &q)
{
unsigned __int64 a=p > q ? p : q;
unsigned __int64 b=p < q ? p : q;
unsigned __int64 t;
if(p == q)
{
return p; //两数相等，最大公约数就是本身
}
else
{
while(b) //辗转相除法，gcd(a,b)=gcd(b,a-qb)
{
a=a % b;
t=a;
a=b;
b=t;
} return a;
}
}/*
Stein法求最大公约数
*/
unsigned __int64 SteinGcd(unsigned __int64 &p, unsigned __int64 &q)
{
unsigned __int64 a=p > q ? p : q;
unsigned __int64 b=p < q ? p : q;
unsigned __int64 t, r=1;
if(p == q)
{
return p; //两数相等，最大公约数就是本身
}
else
{
while((!(a & 1)) && (!(b & 1)))
{
r<<=1; //a、b为偶数时，gcd(a,b)=2*gcd(a/2,b/2)
a>>=1;
b>>=1;
} if(!(a & 1))
{
t=a; //a为偶数，交换a，b
a=b;
b=t;
} do
{
while(!(b & 1))
{
b>>=1; //b为偶数，a为奇数时，gcd(b,a)=gcd(b/2,a)
} if(b < a)
{
t=a; //b小于a，交换a，b
a=b;
b=t;
} b=(b - a) >> 1; //b、a都是奇数，gcd(b,a)=gcd((b-a)/2,a)
} while(b);
return r * a;
}
}/*
已知a、b，求x，满足a*x =1 (mod b)
相当于求解a*x-b*y=1的最小整数解
*/
unsigned __int64 Euclid(unsigned __int64 &a, unsigned __int64 &b)
{
unsigned __int64 m, e, i, j, x, y;
long xx, yy;
m=b;e=a;x=0;y=1;xx=1;yy=1;
while(e)
{
i=m / e;j=m % e;
m=e;e=j;j=y;y*=i;
if(xx == yy)
{
if(x > y)
y=x - y;
else{
y-=x;
yy=0;
}
}
else
{
y+=x;
xx=1 - xx;
yy=1 - yy;
} x=j;
}
if(xx == 0)
x=b - x;
return x;
}/*
随机产生一个RSA加密参数
*/
RSA_PARAM RsaGetParam(void)
{
RSA_PARAM Rsa={ 0 };
unsigned __int64 t;
Rsa.p=RandomPrime(16); //随机生成两个素数
Rsa.q=RandomPrime(16);
Rsa.n=Rsa.p * Rsa.q;
Rsa.f=(Rsa.p - 1) * (Rsa.q - 1);
do
{
Rsa.e=g_Rnd.Random(65536); //小于2^16，65536=2^16
Rsa.e|=1; //保证最低位是1，即保证是奇数，因f一定是偶数，要互素，只能是奇数
} while(SteinGcd(Rsa.e, Rsa.f) != 1);
Rsa.d=Euclid(Rsa.e, Rsa.f);
Rsa.s=0;
t=Rsa.n >> 1;
while(t)
{
Rsa.s++; //s=log2(n)
t>>=1;
}
return Rsa;
}/*
拉宾－米勒测试
*/
void TestRM(void)
{
unsigned long k=0;
cout << "拉宾－米勒测试\n" << endl;
for(unsigned __int64 i=4197900001; i < 4198000000; i+=2)
{
if(RabinMiller(i, 30))
{
k++;
cout << i << endl;
}
} cout << "Total: " << k << endl;
}/*
RSA加密解密
*/
void TestRSA(void)
{
cout << "请输入待加密的内容（支持字母、汉字、以及其他符号和下划线）：\n";
RSA_PARAM r;
string in_1;
fflush(stdin);
char pSrc[100];
scanf("%[^\n]s",pSrc);
const unsigned long n = sizeof(pSrc);
unsigned char *q, pDec[n];
unsigned __int64 pEnc[n];
r = RsaGetParam();
cout << "---------------------------------\n";
cout << "p=" << r.p << endl;
cout << "q=" << r.q << endl;
cout << "f=(p-1)*(q-1)=" << r.f << endl;
cout << "n=p*q=" << r.n << endl;
cout << "e=" << r.e << endl;
cout << "d=" << r.d << endl;
cout << "s=" << r.s << endl;
cout << "---------------------------------\n";
q = (unsigned char*)pSrc;
cout << "Encode:\n";
for (unsigned long i = 0; i < n; i++)
{
unsigned long long xxx;
int xxxx = q[i];
xxx = xxxx;
pEnc[i] = PowMod(xxx, r.e, r.n);
