密碼學---RSA密碼的C++實現

//RSA密碼
/*理解算法最重要，最好自己動手實現試試看，可以使用MFC寫一個簡單的交互界面*/

#include <iostream>
#include <cstdlib>
#include <ctime>
#include <cstring>
using namespace std;
//RSA算法所需參數
typedef struct  RSA_PARAM_Tag
{
    unsigned __int64    p, q;   //兩個素數，不參與加密解密運算
    unsigned __int64    f;      //f=(p-1)*(q-1)，不參與加密解密運算
    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;      //塊長，滿足2^s<=n的最大的s，即log2(n)
} RSA_PARAM;
//小素數表
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;//隨機數類
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;

//模乘運算，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;
}

//模冪運算，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;            //a=a * a % n;    //函數看起來可以處理64位的整數，但由於這里a*a在a>=2^32時已經造成了溢出，因此實際處理范圍沒有64位
            a=MulMod(a, a, n);
        }        b--;        //c=a * c % n;        //這里也會溢出，若把64位整數拆為兩個32位整數不知是否可以解決這個問題。
        c=MulMod(a, c, n);
    }    return c;
}
/*
Rabin-Miller素數測試，通過測試返回1，否則返回0。
n是待測素數。
*/
long RabinMillerKnl(unsigned __int64 &n)
{
    unsigned __int64    b, m, j, v, i;
    m=n - 1;
    j=0;    //計算出m、j，使得n-1=m*2^j，其中m是正奇數，j是非負整數
    while(!(m & 1))
    {
        ++j;
        m>>=1;
    }    //隨機取一個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，通過測試
    if(v == 1)
    {
        return 1;
    }    //令i=1
    i=1;    //v=n-1，通過測試
    while(v != n - 1)
    {
        //i==l，非素數，結束
        if(i == j)
        {
            return 0;
        }        //v=v^2 mod n，i=i+1
        unsigned long long xxx;
        int xxxx = 2;
        xxx = xxxx;
        v = PowMod(v, xxx, n);
        ++i;        //循環到5
    }    return 1;
}
/*
Rabin-Miller素數測試，循環調用核心loop次
全部通過返回1，否則返回0
*/
long RabinMiller(unsigned __int64 &n, long loop)
{
    //用小素數篩選一次，提高效率
    for(long i=0; i < g_PrimeCount; i++)
    {
        if(n % g_PrimeTable[i] == 0)
        {
            return 0;
        }
    }    //循環調用Rabin-Miller測試loop次，使得非素數通過測試的概率降為(1/4)^loop
    for(long i=0; i < loop; i++)
    {
        if(!RabinMillerKnl(n))
        {
            return 0;
        }
    }    return 1;
}/*
隨機生成一個bits位(二進制位)的素數，最多32位
*/
unsigned __int64 RandomPrime(char bits)
{
    unsigned __int64    base;
    do
    {
        base= (unsigned long)1 << (bits - 1);   //保證最高位是1
        base+=g_Rnd.Random(base);               //再加上一個隨機數
        base|=1;    //保證最低位是1，即保證是奇數
    } while(!RabinMiller(base, 30));    //進行拉賓－米勒測試30次
    return base;    //全部通過認為是素數
}/*
歐幾里得法求最大公約數
*/
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;   //兩數相等，最大公約數就是本身
    }
    else
    {
        while(b)    //輾轉相除法，gcd(a,b)=gcd(b,a-qb)
        {
            a=a % b;
            t=a;
            a=b;
            b=t;
        }        return a;
    }
}/*
Stein法求最大公約數
*/
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;           //兩數相等，最大公約數就是本身
    }
    else
    {
        while((!(a & 1)) && (!(b & 1)))
        {
            r<<=1;          //a、b為偶數時，gcd(a,b)=2*gcd(a/2,b/2)
            a>>=1;
            b>>=1;
        }        if(!(a & 1))
        {
            t=a;            //a為偶數，交換a，b
            a=b;
            b=t;
        }        do
        {
            while(!(b & 1))
            {
                b>>=1;      //b為偶數，a為奇數時，gcd(b,a)=gcd(b/2,a)
            }            if(b < a)
            {
                t=a;        //b小於a，交換a，b
                a=b;
                b=t;
            }            b=(b - a) >> 1; //b、a都是奇數，gcd(b,a)=gcd((b-a)/2,a)
        } while(b);
        return r * a;
    }
}/*
已知a、b，求x，滿足a*x =1 (mod b)
相當於求解a*x-b*y=1的最小整數解
*/
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;
}/*
隨機產生一個RSA加密參數
*/
RSA_PARAM RsaGetParam(void)
{
    RSA_PARAM           Rsa={ 0 };
    unsigned __int64    t;
    Rsa.p=RandomPrime(16);          //隨機生成兩個素數
    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);  //小於2^16，65536=2^16
        Rsa.e|=1;                   //保證最低位是1，即保證是奇數，因f一定是偶數，要互素，只能是奇數
    } 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;
}/*
拉賓－米勒測試
*/
void TestRM(void)
{
    unsigned long   k=0;
    cout << "拉賓－米勒測試\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 << "請輸入待加密的內容（支持字母、漢字、以及其他符號和下划線）：\n";
    RSA_PARAM           r;
    string in_1;
    //char  pSrc[123];
/*    char *pSrc;
    getline(cin, in_1);
    getline(cin, in_1);*/
//    char pSrc[100];
    fflush(stdin);
    char pSrc[100];
    scanf("%[^\n]s",pSrc);
    //scanf("%[^\n]s",pSrc);
    //puts(pSrc);
    //fflush(stdin);
//    pSrc = const_cast<char *>(in_1.data());

    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<<q<<"&&&&&\n";//=================
    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);
        cout << hex << pEnc[i] << " ";
    }    
    cout << "\n\n";
    
    cout << "Decode:\n";
    for (unsigned long i = 0; i < n; i++)
    {
        pDec[i] = PowMod(pEnc[i], r.d, r.n);
        cout << hex << (unsigned long)pDec[i] << " ";
    }    
    cout << "\n\n";
    
    cout << "解密后的文檔：\n";
    cout << (char *)pDec << endl;
}/* */
int main(void)
{
    cout << "Start~!\n\n";
    char inorder;
    /*cin >> inorder;
    fflush(stdin);
    if (inorder == '1')
        TestRSA();
    //    TestRSA();*/
    cout << "如果想進行下一個加密過程，請輸入n鍵，退出請輸入q鍵：\n\n";
    while (cin >> inorder && inorder == 'n')
    {
        system("cls");
        TestRSA();
        cout << "如果想進行下一個加密過程，請輸入n鍵，退出請輸入q鍵：\n\n";
    }
    if (inorder == 'q')
        cout << "謝謝使用~！下次再見 > . < ~\n";
    return 0;
}