RSA算法的C语言实现

LegendSaber

     想要实现RSA算法，就需要使用Miller-Rabin概率素性检验算法和扩展Euclid算法
以下是Miller-Rabin概率素性检验算法的实现

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#include <cstdio> #include <stack> #include <cmath>   using namespace std;   typedef unsigned long long int ll;   bool isPrime(ll a, ll n);   int main() {         bool bIsPrime = true;         double p = 0;         ll s = 0, n = 0, a = 0, i = 0;                   printf("请输入概率p和要检测的素数n:");         scanf("%lf %d", &p, &n);                   s = log(1 / (1 - p)) / log(2);                   for (i = 1; i <= s && i < n; i++)         {                 if (!isPrime(i, n))        bIsPrime = false;         }                   if (bIsPrime) printf("%ld is a prime\n", n);         else printf("%ld is not a prime\n", n);         return 0;        }   bool isPrime(ll a, ll n) {         ll tmp = n - 1;         ll d = 1;         stack<ll> s;         ll x = 0;                   while (tmp)         {                 s.push(tmp % 2);                 tmp /= 2;         }           while (!s.empty())         {                 x = d;                 d = (d * d) % n;                 if (d == 1 && x != 1 && x != n - 1) return false;                 if (s.top() == 1) d = (d * a) % n;                 s.pop();         }                   if (d != 1) return false;         return true; }

接着是扩展Euclid的算法实现

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#include <cstdio> #include <stack> #include <cmath>   using namespace std;   typedef unsigned long long int ll;   bool isPrime(ll a, ll n);   int main() {         bool bIsPrime = true;         double p = 0;         ll s = 0, n = 0, a = 0, i = 0;                   printf("请输入概率p和要检测的素数n:");         scanf("%lf %d", &p, &n);                   s = log(1 / (1 - p)) / log(2);                   for (i = 1; i <= s && i < n; i++)         {                 if (!isPrime(i, n))        bIsPrime = false;         }                   if (bIsPrime) printf("%ld is a prime\n", n);         else printf("%ld is not a prime\n", n);         return 0;        }   bool isPrime(ll a, ll n) {         ll tmp = n - 1;         ll d = 1;         stack<ll> s;         ll x = 0;                   while (tmp)         {                 s.push(tmp % 2);                 tmp /= 2;         }           while (!s.empty())         {                 x = d;                 d = (d * d) % n;                 if (d == 1 && x != 1 && x != n - 1) return false;                 if (s.top() == 1) d = (d * a) % n;                 s.pop();         }                   if (d != 1) return false;         return true; }

最后给出RSA算法的实现

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#include <cstdio> #include <stack> #include <cmath> #include <cstdlib>   using namespace std;   typedef unsigned long long int ll;   bool isPrime(ll a, ll n);        //判断是否为素数 ll ex_gcd(ll a, ll b, ll &x1, ll &y1);        //扩展欧几里得算法 ll quick_cal(ll a, ll b, ll n);        //快速指数算法 ll getRandomNumber();        //用来随机选取两个素数 ll gcd(ll a, ll b);   int main() {         ll m = 1900, c = 0;         ll p = 0, q = 0, n = 0, d = 0, n_1 = 0;         ll x = 0, y = 0, e = 0;                   p = getRandomNumber();           q = getRandomNumber();                   n = p * q;         n_1 = (p - 1) * (q - 1);                   for (int i = 2; i < n_1; i++)         {                 if (gcd(n_1, i) == 1 && ex_gcd(i, n_1, x, y) == 1 && x < n_1)                 {                         e = i;                         d = x;                 }         }                   printf("RSA加密前的数据:%ld\n", m);         c = quick_cal(m, e, n);         printf("RSA加密后的数据:%ld\n", c);         m = quick_cal(c, d, n);         printf("RSA解密后的数据:%ld\n", m);                   return 0; }   ll quick_cal(ll a, ll b, ll n) {         ll d = 1;         ll tmp = b;         stack<ll> s;                   while (tmp)         {                 s.push(tmp % 2);                 tmp /= 2;         }                   while (!s.empty())         {                 d = (d * d) % n;                 if (s.top() == 1) d = (d * a) % n;                 s.pop();         }                   return d; }   ll getRandomNumber() {         ll number = rand() % 1000;                   while (number < 100 || !isPrime(95, number)) number = rand() % 1000;                   return number; }   ll ex_gcd(ll a, ll b, ll &x1, ll &y1) {         if (b == 0)         {                 x1 = 1;                 y1 = 0;                                   return a;         }                   ll x2, y2;         ll d = ex_gcd(b, a % b, x2, y2);                   x1 = y2;         y1 = x2 - (a / b) * y2;                   return d; }    bool isPrime(ll a, ll n) {         ll tmp = n - 1;         ll d = 1;         stack<ll> s;         ll x = 0;                   while (tmp)         {                 s.push(tmp % 2);                 tmp /= 2;         }           while (!s.empty())         {                 x = d;                 d = (d * d) % n;                 if (d == 1 && x != 1 && x != n - 1) return false;                 if (s.top() == 1) d = (d * a) % n;                 s.pop();         }                   if (d != 1) return false;         return true; }   ll gcd(ll a, ll b) {         return b == 0 ? a : gcd(b, a % b); }

运行结果如下

flyingdancex

现在实际应用基本都用openssl，不过学习和研究算法还得自己动手

daishen

看着，想着，好容易，实现却好难，