c实现d大数rsa算法

RSA算法是一种公钥密码算法，其主要原理是基于大素数分解的困难性，实现加解密过程中涉及到大数运算。下面是一个使用C语言实现大数RSA算法的示例代码：

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <time.h>
#include <math.h>
#include <ctype.h>

#define MAX_DIGIT 1024

typedef struct {
   int digits[MAX_DIGIT];
   int size;
} BigNum;

void initBigNum(BigNum *num) {
   int i;
   for (i = 0; i < MAX_DIGIT; i++) {
      num->digits[i] = 0;
   }
   num->size = 0;
}

void printBigNum(BigNum *num) {
   int i;
   for (i = num->size - 1; i >= 0; i--) {
      printf("%d", num->digits[i]);
   }
   printf("\n");
}

void setBigNum(BigNum *num, char *str) {
   int len, i, j;
   initBigNum(num);
   len = strlen(str);
   for (i = len - 1, j = 0; i >= 0; i--, j++) {
      num->digits[j] = str[i] - '0';
   }
   num->size = len;
}

void copyBigNum(BigNum *dest, BigNum *src) {
   int i;
   for (i = 0; i < src->size; i++) {
      dest->digits[i] = src->digits[i];
   }
   dest->size = src->size;
}

void addBigNum(BigNum *result, BigNum *num1, BigNum *num2) {
   int i, carry = 0, sum;
   initBigNum(result);
   for (i = 0; i < num1->size || i < num2->size; i++) {
      sum = num1->digits[i] + num2->digits[i] + carry;
      result->digits[i] = sum % 10;
      carry = sum / 10;
      result->size++;
   }
   if (carry) {
      result->digits[result->size++] = carry;
   }
}

void subBigNum(BigNum *result, BigNum *num1, BigNum *num2) {
   int i, borrow = 0, diff;
   initBigNum(result);
   for (i = 0; i < num1->size || i < num2->size; i++) {
      diff = num1->digits[i] - borrow - num2->digits[i];
      if (diff < 0) {
         borrow = 1;
         diff += 10;
      }
      else {
         borrow = 0;
      }
      result->digits[i] = diff;
      result->size++;
   }
   while (result->size > 1 && result->digits[result->size - 1] == 0) {
      result->size--;
   }
}

void mulBigNum(BigNum *result, BigNum *num1, BigNum *num2) {
   int i, j, carry = 0, product;
   initBigNum(result);
   for (i = 0; i < num1->size; i++) {
      carry = 0;
      for (j = 0; j < num2->size; j++) {
         product = num1->digits[i] * num2->digits[j] + carry + result->digits[i + j];
         result->digits[i + j] = product % 10;
         carry = product / 10;
      }
      if (carry) {
         result->digits[i + j] = carry;
      }
   }
   result->size = i + j;
   while (result->size > 1 && result->digits[result->size - 1] == 0) {
      result->size--;
   }
}

void divBigNum(BigNum *quotient, BigNum *dividend, BigNum *divisor) {
   int i, j;
   BigNum temp, remainder;
   initBigNum(quotient);
   copyBigNum(&temp, dividend);
   while (temp.size >= divisor->size) {
      initBigNum(&remainder);
      remainder.size = temp.size;
      for (i = 0; i < temp.size; i++) {
         remainder.digits[i] = temp.digits[i];
      }
      remainder.size = temp.size;
      for (i = 0; i < temp.size - divisor->size; i++) {
         remainder.digits[i + divisor->size] = remainder.digits[i];
      }
      remainder.size += divisor->size;
      for (i = 0; i < divisor->size; i++) {
         remainder.digits[i] = 0;
      }
      while (remainder.size > 1 && remainder.digits[remainder.size - 1] == 0) {
         remainder.size--;
      }
      for (j = 9; j >= 0; j--) {
         setBigNum(divisor, "0");
         divisor->digits[0] = j;
         mulBigNum(&temp, divisor, quotient);
         if (compareBigNum(&temp, &remainder) <= 0) {
            break;
         }
      }
      setBigNum(divisor, "0");
      divisor->digits[0] = j;
      mulBigNum(quotient, divisor, quotient);
      subBigNum(&temp, &remainder, divisor);
      copyBigNum(&remainder, &temp);
      copyBigNum(&temp, &quotient);
      initBigNum(quotient);
      for (i = remainder.size - 1; i >= 0; i--) {
         quotient->digits[i] = temp.digits[i + remainder.size - divisor->size];
         quotient->size++;
      }
      while (quotient->size > 1 && quotient->digits[quotient->size - 1] == 0) {
         quotient->size--;
      }
   }
   copyBigNum(quotient, &temp);
   while (quotient->size > 1 && quotient->digits[quotient->size - 1] == 0) {
      quotient->size--;
   }
}

void modBigNum(BigNum *result, BigNum *num, BigNum *modulus) {
   BigNum quotient;
   divBigNum(&quotient, num, modulus);
   mulBigNum(result, modulus, &quotient);
   subBigNum(result, num, result);
}

int compareBigNum(BigNum *num1, BigNum *num2) {
   int i;
   if (num1->size > num2->size) {
      return 1;
   }
   if (num1->size < num2->size) {
      return -1;
   }
   for (i = num1->size - 1; i >= 0; i--) {
      if (num1->digits[i] > num2->digits[i]) {
         return 1;
      }
      if (num1->digits[i] < num2->digits[i]) {
         return -1;
      }
   }
   return 0;
}

void powModBigNum(BigNum *result, BigNum *base, BigNum *exponent, BigNum *modulus) {
   BigNum temp;
   initBigNum(result);
   result->digits[0] = 1;
   result->size = 1;
   while (exponent->size > 0) {
      if (exponent->digits[0] % 2 == 1) {
         mulBigNum(&temp, result, base);
         modBigNum(result, &temp, modulus);
      }
      divBigNum(exponent, exponent, modulus);
      mulBigNum(&temp, base, base);
      modBigNum(base, &temp, modulus);
   }
}

void generateBigPrime(BigNum *result, int numDigits) {
   int i;
   BigNum candidate;
   initBigNum(result);
   initBigNum(&candidate);
   while (1) {
      for (i = 0; i < numDigits; i++) {
         candidate.digits[i] = rand() % 10;
      }
      candidate.digits[numDigits - 1] |= 1;
      candidate.size = numDigits;
      if (isPrime(&candidate)) {
         copyBigNum(result, &candidate);
         return;
      }
   }
}

int isPrime(BigNum *num) {
   int i;
   BigNum a, quotient, remainder, testNum;
   setBigNum(&testNum, "2");
   if (compareBigNum(num, &testNum) <= 0) {
      return 1;
   }
   if (num->digits[0] % 2 == 0) {
      return 0;
   }
   setBigNum(&testNum, "1");
   for (i = 0; i < 20; i++) {
      generateBigNum(&a, num->size - 1);
      if (compareBigNum(&a, &testNum) == 0) {
         a.digits[0] = 2;
      }
      if (compareBigNum(&a, num) >= 0) {
         a.digits[0] = num->digits[0] - 2;
      }
      powModBigNum(&remainder, &a, num, num);
      if (compareBigNum(&remainder, &testNum) != 0) {
         return 0;
      }
   }
   return 1;
}

void generateBigRSA(BigNum *p, BigNum *q, BigNum *n, BigNum *e, BigNum *d) {
   int numDigits = 256;
   BigNum phi, temp;
   initBigNum(p);
   initBigNum(q);
   initBigNum(n);
   initBigNum(e);
   initBigNum(d);
   generateBigPrime(p, numDigits);
   generateBigPrime(q, numDigits);
   mulBigNum(n, p, q);
   subBigNum(&temp, p, &temp);
   subBigNum(&phi, q, &temp);
   setBigNum(e, "65537");
   divBigNum(d, &temp, e);
   powModBigNum(&temp, e, d, &phi);
}

void encryptRSA(BigNum *ciphertext, BigNum *message, BigNum *e, BigNum *n) {
   powModBigNum(ciphertext, message, e, n);
}

void decryptRSA(BigNum *plaintext, BigNum *ciphertext, BigNum *d, BigNum *n) {
   powModBigNum(plaintext, ciphertext, d, n);
}

int main() {
   BigNum p, q, n, e, d, plaintext, ciphertext, decryptedtext;
   char message[] = "Hello World!";
   srand(time(NULL));
   setBigNum(&plaintext, message);
   generateBigRSA(&p, &q, &n, &e, &d);
   printf("p = ");
   printBigNum(&p);
   printf("q = ");
   printBigNum(&q);
   printf("n = ");
   printBigNum(&n);
   printf("e = ");
   printBigNum(&e);
   printf("d = ");
   printBigNum(&d);
   encryptRSA(&ciphertext, &plaintext, &e, &n);
   printf("Ciphertext: ");
   printBigNum(&ciphertext);
   decryptRSA(&decryptedtext, &ciphertext, &d, &n);
   printf("Plaintext: ");
   printBigNum(&decryptedtext);
   return 0;
}

该示例代码实现了大数加、减、乘、除、取模、比较、幂模等基本操作，以及生成大素数、生成RSA公私钥、加密解密等操作。其中，大数操作采用数组实现，支持高精度计算。RSA算法的具体实现过程，包括生成公私钥、加密解密等，都是基于大数操作实现的。