C语言实现的RSA算法程序
源程序来自Gethub的Simple implementation of the RSA algorithm。
程序中有关类型转换代码略做修改,并且已经能够编译运行。
程序如下:
#include <stdio.h> #include <stdlib.h> #include <time.h> #include <string.h> #define ACCURACY 5 #define SINGLE_MAX 10000 #define EXPONENT_MAX 1000 #define BUF_SIZE 1024 /** * Computes a^b mod c */ int modpow(long long a, long long b, int c) { int res = 1; while(b > 0) { /* Need long multiplication else this will overflow... */ if(b & 1) { res = (res * a) % c; } b = b >> 1; a = (a * a) % c; /* Same deal here */ } return res; } /** * Computes the Jacobi symbol, (a, n) */ int jacobi(int a, int n) { int twos, temp; int mult = 1; while(a > 1 && a != n) { a = a % n; if(a <= 1 || a == n) break; twos = 0; while(a % 2 == 0 && ++twos) a /= 2; /* Factor out multiples of 2 */ if(twos > 0 && twos % 2 == 1) mult *= (n % 8 == 1 || n % 8 == 7) * 2 - 1; if(a <= 1 || a == n) break; if(n % 4 != 1 && a % 4 != 1) mult *= -1; /* Coefficient for flipping */ temp = a; a = n; n = temp; } if(a == 0) return 0; else if(a == 1) return mult; else return 0; /* a == n => gcd(a, n) != 1 */ } /** * Check whether a is a Euler witness for n */ int solovayPrime(int a, int n) { int x = jacobi(a, n); if(x == -1) x = n - 1; return x != 0 && modpow(a, (n - 1)/2, n) == x; } /** * Test if n is probably prime, using accuracy of k (k solovay tests) */ int probablePrime(int n, int k) { if(n == 2) return 1; else if(n % 2 == 0 || n == 1) return 0; while(k-- > 0) { if(!solovayPrime(rand() % (n - 2) + 2, n)) return 0; } return 1; } /** * Find a random (probable) prime between 3 and n - 1, this distribution is * nowhere near uniform, see prime gaps */ int randPrime(int n) { int prime = rand() % n; n += n % 2; /* n needs to be even so modulo wrapping preserves oddness */ prime += 1 - prime % 2; while(1) { if(probablePrime(prime, ACCURACY)) return prime; prime = (prime + 2) % n; } } /** * Compute gcd(a, b) */ int gcd(int a, int b) { int temp; while(b != 0) { temp = b; b = a % b; a = temp; } return a; } /** * Find a random exponent x between 3 and n - 1 such that gcd(x, phi) = 1, * this distribution is similarly nowhere near uniform */ int randExponent(int phi, int n) { int e = rand() % n; while(1) { if(gcd(e, phi) == 1) return e; e = (e + 1) % n; if(e <= 2) e = 3; } } /** * Compute n^-1 mod m by extended euclidian method */ int inverse(int n, int modulus) { int a = n, b = modulus; int x = 0, y = 1, x0 = 1, y0 = 0, q, temp; while(b != 0) { q = a / b; temp = a % b; a = b; b = temp; temp = x; x = x0 - q * x; x0 = temp; temp = y; y = y0 - q * y; y0 = temp; } if(x0 < 0) x0 += modulus; return x0; } /** * Read the file fd into an array of bytes ready for encryption. * The array will be padded with zeros until it divides the number of * bytes encrypted per block. Returns the number of bytes read. */ int readFile(FILE* fd, char** buffer, int bytes) { int len = 0, cap = BUF_SIZE, r; char buf[BUF_SIZE]; *buffer = (char *)malloc(BUF_SIZE * sizeof(char)); while((r = fread(buf, sizeof(char), BUF_SIZE, fd)) > 0) { if(len + r >= cap) { cap *= 2; *buffer = (char *)realloc(*buffer, cap); } memcpy(&(*buffer)[len], buf, r); len += r; } /* Pad the last block with zeros to signal end of cryptogram. An additional block is added if there is no room */ if(len + bytes - len % bytes > cap) *buffer = (char *)realloc(*buffer, len + bytes - len % bytes); do { (*buffer)[len] = '\0'; len++; } while(len % bytes != 0); return len; } /** * Encode the message m using public exponent and modulus, c = m^e mod n */ int encode(int m, int e, int n) { return modpow(m, e, n); } /** * Decode cryptogram c using private exponent and public modulus, m = c^d mod n */ int decode(int c, int d, int n) { return modpow(c, d, n); } /** * Encode the message of given length, using the public key (exponent, modulus) * The resulting array will be of size len/bytes, each index being the encryption * of "bytes" consecutive characters, given by m = (m1 + m2*128 + m3*128^2 + ..), * encoded = m^exponent mod modulus */ int* encodeMessage(int len, int bytes, char* message, int exponent, int modulus) { int *encoded = (int *)malloc((len/bytes) * sizeof(int)); int x, i, j; for(i = 0; i < len; i += bytes) { x = 0; for(j = 0; j < bytes; j++) x += message[i + j] * (1 << (7 * j)); encoded[i/bytes] = encode(x, exponent, modulus); #ifndef MEASURE printf("%d ", encoded[i/bytes]); #endif } return encoded; } /** * Decode the cryptogram of given length, using the private key (exponent, modulus) * Each encrypted packet should represent "bytes" characters as per encodeMessage. * The returned message will be of size len * bytes. */ int* decodeMessage(int len, int bytes, int* cryptogram, int exponent, int modulus) { int *decoded = (int *)malloc(len * bytes * sizeof(int)); int x, i, j; for(i = 0; i < len; i++) { x = decode(cryptogram[i], exponent, modulus); for(j = 0; j < bytes; j++) { decoded[i*bytes + j] = (x >> (7 * j)) % 128; #ifndef MEASURE if(decoded[i*bytes + j] != '\0') printf("%c", decoded[i*bytes + j]); #endif } } return decoded; } /** * Main method to demostrate the system. Sets up primes p, q, and proceeds to encode and * decode the message given in "text.txt" */ int main(void) { int p, q, n, phi, e, d, bytes, len; int *encoded, *decoded; char *buffer; FILE *f; srand(time(NULL)); while(1) { p = randPrime(SINGLE_MAX); printf("Got first prime factor, p = %d ... ", p); getchar(); q = randPrime(SINGLE_MAX); printf("Got second prime factor, q = %d ... ", q); getchar(); n = p * q; printf("Got modulus, n = pq = %d ... ", n); if(n < 128) { printf("Modulus is less than 128, cannot encode single bytes. Trying again ... "); getchar(); } else break; } if(n >> 21) bytes = 3; else if(n >> 14) bytes = 2; else bytes = 1; getchar(); phi = (p - 1) * (q - 1); printf("Got totient, phi = %d ... ", phi); getchar(); e = randExponent(phi, EXPONENT_MAX); printf("Chose public exponent, e = %d\nPublic key is (%d, %d) ... ", e, e, n); getchar(); d = inverse(e, phi); printf("Calculated private exponent, d = %d\nPrivate key is (%d, %d) ... ", d, d, n); getchar(); printf("Opening file \"text.txt\" for reading\n"); f = fopen("text.txt", "r"); if(f == NULL) { printf("Failed to open file \"text.txt\". Does it exist?\n"); return EXIT_FAILURE; } len = readFile(f, &buffer, bytes); /* len will be a multiple of bytes, to send whole chunks */ fclose(f); printf("File \"text.txt\" read successfully, %d bytes read. Encoding byte stream in chunks of %d bytes ... ", len, bytes); getchar(); encoded = encodeMessage(len, bytes, buffer, e, n); printf("\nEncoding finished successfully ... "); getchar(); printf("Decoding encoded message ... "); getchar(); decoded = decodeMessage(len/bytes, bytes, encoded, d, n); printf("\nFinished RSA demonstration!\n"); free(encoded); free(decoded); free(buffer); return EXIT_SUCCESS; }