The ElGamal encryption is a symmetric key encryption algorithm for private-key cryptography which is based on the public key exchange and provides an additional layer of security by asymmetrically encrypting keys previously used for asymmetric message encryption. It can be defined over any cyclic group G. Its security depends upon the difficulty of a certain problem in G related to computing discrete logarithms.
ElGamal encryption consists of three components: the key generator, the encryption algorithm, and the decryption algorithm. These operations are out of scope of this article. We suggest to go through very simple explanation given on Wikipedia for detailed explanation.
Following is the implementation of ElGamal encryption algorithm in C. The program expects an input file plain.txt which contains the plain text and generates an output file results.txt which contains our decrypted text. The program also generates two intermediary files – cipher1.txt and cipher2.txt.
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#include <stdio.h> #include <stdlib.h> #include <ctype.h> #include <math.h> int e1, e2; int p, d; int C1, C2; FILE *out1, *out2; int gcd(int a, int b) { int q, r1, r2, r; if (a > b) { r1 = a; r2 = b; } else { r1 = b; r2 = a; } while (r2 > 0) { q = r1 / r2; r = r1 - q * r2; r1 = r2; r2 = r; } return r1; } int PrimarityTest(int a, int i) { int n = i - 1; int k = 0; int m, T; while (n % 2 == 0) { k++; n = n / 2; } m = n; T = FindT(a, m, i); if (T == 1 || T == i - 1) return 1; for (int j = 0; j < k; j++) { T = FindT(T, 2, i); if (T == 1) return 0; if (T == i - 1) return 1; } return 0; } int PrimitiveRoot(int p) { int flag; for (int a = 2; a < p; a++) { flag = 1; for (int i = 1; i < p; i++) { if (FindT(a, i, p) == 1 && i < p - 1) { flag = 0; } else if (flag && FindT(a, i, p) == 1 && i == p - 1) { return a; } } } } int KeyGeneration() { do { do p = rand() + 256; while (p % 2 == 0); } while (!PrimarityTest(2, p)); p = 107; e1 = 2; do { d = rand() % (p - 2) + 1; // 1 <= d <= p-2 } while (gcd(d, p) != 1); d = 67; e2 = FindT(e1, d, p); } int FindT(int a, int m, int n) { int r; int y = 1; while (m > 0) { r = m % 2; FastExponention(r, n, &y, &a); m = m / 2; } return y; } int FastExponention(int bit, int n, int* y, int* a) { if (bit == 1) *y = (*y * (*a)) % n; *a = (*a) * (*a) % n; } int Encryption(int Plaintext) { out1 = fopen("cipher1.txt", "a+"); out2 = fopen("cipher2.txt", "a+"); int r; do { r = rand() % (p - 1) + 1; // 1 < r < p } while (gcd(r, p) != 1); C1 = FindT(e1, r, p); C2 = FindT(e2, r, p) * Plaintext % p; fprintf(out1, "%d ", C1); fprintf(out2, "%d ", C2); fclose(out1); fclose(out2); } int Decryption(int C1, int C2) { FILE* out = fopen("result.txt", "a+"); int decipher = C2 * FindT(C1, p - 1 - d, p) % p; fprintf(out, "%c", decipher); fclose(out); } int main() { FILE *out, *inp; // destroy contents of these files (from previous runs, if any) out = fopen("result.txt", "w+"); fclose(out); out = fopen("cipher1.txt", "w+"); fclose(out); out = fopen("cipher2.txt", "w+"); fclose(out); KeyGeneration(); inp = fopen("plain.txt", "r+"); if (inp == NULL) { printf("Error opening Source File.\n"); exit(1); } while (1) { char ch = getc(inp); if (ch == EOF) break; // M < p Encryption(toascii(ch)); } fclose(inp); fclose(out); FILE *inp1, *inp2; inp1 = fopen("cipher1.txt", "r"); inp2 = fopen("cipher2.txt", "r"); int C1, C2; while (1) { int ret = fscanf(inp1, "%d", &C1); fscanf(inp2, "%d", &C2); if (ret == -1) break; Decryption(C1, C2); } fclose(inp1); fclose(inp2); return 0; } |
Above program is tested in Windows environment using Code::Blocks 16.01.
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