The Hill cipher is a polygraphic substitution cipher based on linear algebra. It was the first polygraphic cipher in which it was practical to operate on more than three symbols at once.
This article do not cover algorithm behind the Hill cipher. We suggest to go through very simple explanation given on Wikipedia for detailed explanation on Encryption and Decryption.
Following is the implementation of the Hill cipher in C++ –
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#include <iostream> #include <string> using namespace std; #define M 3 int inverse(int b) { int inv; int q, r, r1 = 26, r2 = b, t, t1 = 0, t2 = 1; while (r2 > 0) { q = r1 / r2; r = r1 - q * r2; r1 = r2; r2 = r; t = t1 - q * t2; t1 = t2; t2 = t; } if (r1 == 1) { inv = t1; if (inv < 0) inv = inv + 26; return inv; } return -1; } void inverseMatrix(int key[][3], int inv[][3]) { int C[3][3]; // matrix for cofactors of matrix key[][] int A[3][3]; // matrix for adjoint of matrix C[][] C[0][0] = key[1][1] * key[2][2] - key[2][1] * key[1][2]; C[0][1] = -(key[1][0] * key[2][2] - key[2][0] * key[1][2]); C[0][2] = key[1][0] * key[2][1] - key[1][1] * key[2][0]; C[1][0] = -(key[0][1] * key[2][2] - key[2][1] * key[0][2]); C[1][1] = key[0][0] * key[2][2] - key[2][0] * key[0][2]; C[1][2] = -(key[0][0] * key[2][1] - key[2][0] * key[0][1]); C[2][0] = key[0][1] * key[1][2] - key[0][2] * key[1][1]; C[2][1] = -(key[0][0] * key[1][2] - key[1][0] * key[0][2]); C[2][2] = key[0][0] * key[1][1] - key[1][0] * key[0][1]; for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) { A[i][j] = C[j][i]; } } int det = key[0][0] * C[0][0] + key[0][1] * C[0][1] + key[0][2] * C[0][2]; if (det == 0 || det % 2 == 0 || det % 13 == 0) { printf("The text cannot be encrypted. Take valid key.\n"); exit(1); } int invs = inverse(det); for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) { inv[i][j] = A[i][j] * invs; } } printf("\nInverse of a Key-\n\n"); for (int i = 0; i < 3; i++) { for (int j = 0; j < 3; j++) { if (inv[i][j] >= 0) { inv[i][j] = inv[i][j] % 26; printf("%3d", inv[i][j]); } else { for (int x = 0;; x++) { if (x * 26 + inv[i][j] > 0) { inv[i][j] = x * 26 + inv[i][j]; break; } } printf("%3d", inv[i][j]); } } printf("\n"); } } string encrypt(string text, int key[][3]) { string c = ""; int k = 0; int input[3]; while (k < text.length()) { input[0] = text[k++] - 65; input[1] = text[k++] - 65; input[2] = text[k++] - 65; for (int i = 0; i < M; i++) { int cipher = 0; for (int j = 0; j < M; j++) { cipher += key[i][j] * input[j]; } c += (cipher % 26) + 65; } } return c; } string decrypt(string s, int inv[][3]) { string d = ""; int k = 0; int input[3]; while (k < s.length()) { input[0] = s[k++] - 65; input[1] = s[k++] - 65; input[2] = s[k++] - 65; for (int i = 0; i < M; i++) { int decipher = 0; for (int j = 0; j < M; j++) { decipher += inv[i][j] * input[j]; } d += (decipher % 26) + 65; } } return d; } int main() { int key[3][3] = { { 6, 24, 1 }, { 13, 16, 10 }, { 20, 17, 15 } }; string text = "ACTBEFOREDAWNZZ"; string c = encrypt(text, key); cout << "Corresponding cipher text is - " << c; int inv[3][3]; inverseMatrix(key, inv); cout << "\nCorresponding decrypted text is - " << decrypt(c, inv); return 0; } |
Output:
Corresponding cipher text is – POHDXHCAFOZABNU
Inverse of a Key-
8 5 10
21 8 21
21 12 8
Corresponding decrypted text is – ACTBEFOREDAWNZZ
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