/*
  Author:  Pate Williams (c) 1997

  Exercise 9.2
  "Suppose Alice is using the Schnorr Scheme where
  q = 1201, p = 122503, t = 10, and alpha = 11538.
  (a) Verify that alpha has order q in Z_p*.
  (b) Suppose that Alice's secret exponent is
      a = 357. Compute v.
  (c) Suppose that k = 868. Compute gamma.
  (d) Suppose that Bob issues the challenge r = 501.
      Compute Alice's response y.
  (e) Perform Bob's calculations to verify y."
  -Douglas R. Stinson-
  See "Cryptography: Theory and Practice" by
  Douglas R. Stinson pages 303-304.
*/

#include <stdio.h>
#include "lip.h"

int main(void)
{
  long alpha = 11538, p = 122503, q = 1201;
  long a = 357, k = 868, r = 501;
  verylong za = 0, zb = 0, zc = 0, zk = 0, zp = 0;
  verylong zq = 0, zr = 0, zv = 0, zy = 0;
  verylong zalpha = 0, zgamma = 0;

  zintoz(alpha, &zalpha);
  zintoz(a, &za);
  zintoz(k, &zk);
  zintoz(p, &zp);
  zintoz(q, &zq);
  zintoz(r, &zr);
  zexpmod(zalpha, zq, zp, &zb);
  printf("alpha = %ld\n", alpha);
  printf("p = %ld\n", p);
  printf("q = %ld\n", q);
  printf("a = %ld\n", a);
  printf("k = %ld\n", k);
  printf("r = %ld\n", r);
  printf("alpha ^ q mod p = ");
  zwriteln(zb);
  zcopy(za, &zb);
  znegate(&zb);
  zadd(zb, zq, &zc);
  zexpmod(zalpha, zc, zp, &zv);
  printf("v = ");
  zwriteln(zv);
  zexpmod(zalpha, zk, zp, &zgamma);
  printf("gamma = ");
  zwriteln(zgamma);
  zmulmod(za, zr, zq, &zb);
  zaddmod(zk, zb, zq, &zy);
  printf("y = ");
  zwriteln(zy);
  zexpmod(zalpha, zy, zp, &zb);
  zexpmod(zv, zr, zp, &zc);
  zmulmod(zb, zc, zp, &za);
  if (zcompare(za, zgamma) == 0)
    printf("y verified\n");
  else
    printf("y not verfied\n");
  zfree(&za);
  zfree(&zb);
  zfree(&zc);
  zfree(&zk);
  zfree(&zp);
  zfree(&zq);
  zfree(&zr);
  zfree(&zy);
  zfree(&zalpha);
  zfree(&zgamma);
  return 0;
}