C语言实现的RSA算法程序

#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;
}