/*
  Author:  Pate Williams (c) 1997

  Exercise 1.5
  "An Affine-Hill Cipher is the following
  modification of the Hill Cipher...Suppose
  Oscar has learned that the plaintext
  adisplayedequation
  is encrypted to give the ciphertext
  DSRMSIOPLXLJBZULLM
  and Oscar also knows m = 3. Compute the key."
  -Douglas R. Stinson-
  See "Cryptography: Theory and Practice" by
  Douglas R. Stinson page 42.
*/

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

long **create_square_matrix(long n)
{
  long i, **matrix = calloc(n, sizeof(long *));

  if (!matrix) {
    fprintf(stderr, "fatal error\ninsufficient memory\n");
    fprintf(stderr, "from create_matrix\n");
    exit(1);
  }
  for (i = 0; i < n; i++) {
    matrix[i] = calloc(n, sizeof(long));
    if (!matrix[i]) {
      fprintf(stderr, "fatal error\ninsufficient memory\n");
      fprintf(stderr, "from create_matrix\n");
      exit(1);
    }
  }
  return matrix;
}

void delete_square_matrix(long n, long **matrix)
{
  long i;

  for (i = 0; i < n; i++) free(matrix[i]);
  free(matrix);
}

void Euclid_extended(long a, long b, long *u,
                     long *v, long *d)
{
  long q, t1, t3, v1, v3;

  *u = 1, *d = a;
  if (b == 0) {
    *v = 0;
    return;
  }
  v1 = 0, v3 = b;
  #ifdef DEBUG
  printf("----------------------------------\n");
  printf(" q    t3   *u   *d   t1   v1   v3\n");
  printf("----------------------------------\n");
  #endif
  while (v3 != 0) {
    q = *d / v3;
    t3 = *d - q * v3;
    t1 = *u - q * v1;
    *u = v1, *d = v3;
    #ifdef DEBUG
    printf("%4ld %4ld %4ld ", q, t3, *u);
    printf("%4ld %4ld %4ld %4ld\n", *d, t1, v1, v3);
    #endif
    v1 = t1, v3 = t3;
  }
  *v = (*d - a * *u) / b;
  #ifdef DEBUG
  printf("----------------------------------\n");
  #endif
}

long inv(long number, long modulus)
{
  long d, u, v;

  Euclid_extended(number, modulus, &u, &v, &d);
  if (d == 1) return u;
  return 0;
}

void gaussian_elimination(long n, long p,
                          long *b, long *x,
                          long **m)
{
  int found;
  long *d = calloc(n, sizeof(long)), ck, dj;
  long i, j, k, l, sum, t;

  if (!d) {
    fprintf(stderr, "fatal error\ninsufficient memory\n");
    fprintf(stderr, "from gaussian_elimination\n");
    exit(1);
  }
  for (j = 0; j < n; j++) {
    found = 0, i = j;
    while (!found && i < n) {
      found = m[i][j] != 0 && inv(m[i][j], p) != 0;
      if (!found) i++;
    }
    if (!found) {
      fprintf(stderr, "fatal error\nnon-invertible matrix\n");
      fprintf(stderr, "from gaussian_elimination\n");
      fprintf(stderr, "j = %ld\n", j);
      for (k = 0; k < n; k++) {
        for (l = 0; l < n; l++)
          printf("%2ld ", m[k][l]);
        printf("\n");
      }
      exit(1);
    }
    if (i > j) {
      /* swap elements */
      for (l = j; l < n; l++)
        t = m[i][l], m[i][l] = m[j][l], m[j][l] = t;
      t = b[i], b[i] = b[j], b[j] = t;
    }
    dj = d[j] = inv(m[j][j], p);
    if (dj == 0) {
      fprintf(stderr, "fatal error\nnon-invertible element\n");
      fprintf(stderr, "from gaussian elimination\n");
      fprintf(stderr, "element %ld mod %ld\n", m[j][j], p);
      exit(1);
    }
    for (k = j + 1; k < n; k++) {
      ck = (dj * m[k][j]) % p;
      for (l = j + 1; l < n; l++) {
        m[k][l] = (m[k][l] - ck * m[j][l]) % p;
        if (m[k][l] < 0) m[k][l] += p;
      }
      b[k] = (b[k] - ck * b[j]) % p;
      if (b[k] < 0) b[k] += p;
    }
  }
  for (i = n - 1; i >= 0; i--) {
    sum = 0;
    for (j = i + 1; j < n; j++)
      sum += (m[i][j] * x[j]) % p;
    if (sum < 0) sum += p;
    x[i] = (d[i] * (b[i] - sum)) % p;
    if (x[i] < 0) x[i] += p;
  }
}

void inverse(long n, long p, long **m, long **X)
{
  int found;
  long d, i, j, k, l, sum, temp;
  long **B = create_square_matrix(n);
  long *c = calloc(n, sizeof(long));

  if (!c) {
    fprintf(stderr, "fatal error\ninsufficient memory\n");
    fprintf(stderr, "from inverse\n");
    exit(1);
  }
  for (i = 0; i < n; i++) B[i][i] = 1;
  for (j = 0; j < n; j++) {
    found = 0;
    for (i = j; i < n && !found;) {
      found = m[i][j] != 0 && inv(m[i][j], p) != 0;
      if (!found) i++;
    }
    if (!found) {
      fprintf(stderr, "fatal error\nnon-invertible matrix\n");
      fprintf(stderr, "from inverse\n", j);
      exit(1);
    }
    if (i > j) {
      for (l = j; l < n; l++) {
        temp = m[i][l];
        m[i][l] = m[j][l];
        m[j][l] = temp;
      }
      for (l = 0; l < n; l++) {
        temp = B[i][l];
        B[i][l] = B[j][l];
        B[j][l] = temp;
      }
    }
    d = inv(m[j][j], p);
    for (k = j + 1; k < n; k++) c[k] = (d * m[k][j]) % p;
    for (k = j + 1; k < n; k++) {
      for (l = j + 1; l < n; l++) {
        m[k][l] -= (c[k] * m[j][l]) % p;
        m[k][l] %= p;
        if (m[k][l] < 0) m[k][l] += p;
      }
    }
    for (k = j + 1; k < n; k++) {
      for (l = 0; l < n; l++) {
        B[k][l] -= (c[k] * B[j][l]) % p;
        B[k][l] %= p;
        if (B[k][l] < 0) B[k][l] += p;
      }
    }
  }
  for (i = n - 1; i >= 0; i--) {
    for (j = 0; j < n; j++) {
      sum = 0;
      for (k = i + 1; k < n; k++)
        sum += m[i][k] * X[k][j];
      X[i][j] = inv(m[i][i], p) * (B[i][j] - sum);
      X[i][j] %= p;
      if (X[i][j] < 0) X[i][j] += p;
    }
  }
  delete_square_matrix(n, B);
  free(c);
}

int main(void)
{
  char ciphertext[32] = "DSRMSIOPLXLJBZULLM";
  char plaintext[32] = "ADISPLAYEDEQUATION";
  long i, j, l = 0, n = 12, p = 26, b[12], x[12];
  long length = strlen(plaintext);
  long **K = create_square_matrix(n);
  long **k = create_square_matrix(n);

  printf("plaintext:  %s\n", plaintext);
  printf("ciphertext: %s\n", ciphertext);
  for (i = 0; i < length; i++) {
    ciphertext[i] -= (char) 'A';
    plaintext[i]  -= (char) 'A';
  }
  K[0][0] = plaintext[0];
  K[0][3] = plaintext[1];
  K[0][6] = plaintext[2];
  K[0][9] = 1;
  K[1][1] = plaintext[0];
  K[1][4] = plaintext[1];
  K[1][7] = plaintext[2];
  K[1][10] = 1;
  K[2][2] = plaintext[0];
  K[2][5] = plaintext[1];
  K[2][8] = plaintext[2];
  K[2][11] = 1;
  K[3][0] = plaintext[6];
  K[3][3] = plaintext[7];
  K[3][6] = plaintext[8];
  K[3][9] = 1;
  K[4][1] = plaintext[6];
  K[4][4] = plaintext[7];
  K[4][7] = plaintext[8];
  K[4][10] = 1;
  K[5][2] = plaintext[6];
  K[5][5] = plaintext[7];
  K[5][8] = plaintext[8];
  K[5][11] = 1;
  K[6][0] = plaintext[9];
  K[6][3] = plaintext[10];
  K[6][6] = plaintext[11];
  K[6][9] = 1;
  K[7][1] = plaintext[9];
  K[7][4] = plaintext[10];
  K[7][7] = plaintext[11];
  K[7][10] = 1;
  K[8][2] = plaintext[9];
  K[8][5] = plaintext[10];
  K[8][8] = plaintext[11];
  K[8][11] = 1;
  K[9][0] = plaintext[15];
  K[9][3] = plaintext[16];
  K[9][6] = plaintext[17];
  K[9][9] = 1;
  K[10][1] = plaintext[15];
  K[10][4] = plaintext[16];
  K[10][7] = plaintext[17];
  K[10][10] = 1;
  K[11][2] = plaintext[15];
  K[11][5] = plaintext[16];
  K[11][8] = plaintext[17];
  K[11][11] = 1;
  b[0] = ciphertext[0];
  b[1] = ciphertext[1];
  b[2] = ciphertext[2];
  b[3] = ciphertext[6];
  b[4] = ciphertext[7];
  b[5] = ciphertext[8];
  b[6] = ciphertext[9];
  b[7] = ciphertext[10];
  b[8] = ciphertext[11];
  b[9] = ciphertext[15];
  b[10] = ciphertext[16];
  b[11] = ciphertext[17];
  gaussian_elimination(n, p, b, x, K);
  for (i = 0; i < 3; i++)
    for (j = 0; j < 3; j++)
      K[i][j] = x[l++];
  for (i = 0; i < 3; i++)
    b[i] = x[9 + i];
  printf("the key matrix is:\n");
  for (i = 0; i < 3; i++) {
    for (j = 0; j < 3; j++)
      printf("%2ld ", K[i][j]);
    printf("\n");
  }
  printf("the b vector is:\n");
  for (i = 0; i < 3; i++)
    printf("%2ld\n", b[i]);
  for (i = 0; i < length / 3; i++) {
    x[0] = K[0][0] * plaintext[3 * i]
         + K[1][0] * plaintext[3 * i + 1]
         + K[2][0] * plaintext[3 * i + 2]
         + b[0];
    x[1] = K[0][1] * plaintext[3 * i]
         + K[1][1] * plaintext[3 * i + 1]
         + K[2][1] * plaintext[3 * i + 2]
         + b[1];
    x[2] = K[0][2] * plaintext[3 * i]
         + K[1][2] * plaintext[3 * i + 1]
         + K[2][2] * plaintext[3 * i + 2]
         + b[2];
    x[0] %= p;
    x[1] %= p;
    x[2] %= p;
    if (x[0] != ciphertext[3 * i] ||
        x[1] != ciphertext[3 * i + 1] ||
        x[2] != ciphertext[3 * i + 2])
      printf("i = %ld no solution for m = 3\n", i);
  }
  inverse(3, p, K, k);
  printf("the inverse key matrix is:\n");
  for (i = 0; i < 3; i++) {
    for (j = 0; j < 3; j++)
      printf("%2ld ", k[i][j]);
    printf("\n");
  }
  delete_square_matrix(n, k);
  delete_square_matrix(n, K);
  return 0;
}