tomcrypt/ecc.c

/* Implements ECC over Z/pZ for curve y^2 = x^3 - 3x + b
 *
 * All curves taken from NIST recommendation paper of July 1999
 * Available at http://csrc.nist.gov/cryptval/dss.htm
 */

#include "mycrypt.h"

#ifdef MECC

/* This holds the key settings.  ***MUST*** be organized by size from smallest to largest. */
static const struct {
   int size;
   char *name, *prime, *B, *order, *Gx, *Gy;
} sets[] = {
#ifdef ECC160
{
   20,
   "ECC-160",
   /* prime */
   "G00000000000000000000000007",
   /* B */
   "1oUV2vOaSlWbxr6",
   /* order */
   "G0000000000004sCQUtDxaqDUN5",
   /* Gx */
   "jpqOf1BHus6Yd/pyhyVpP",
   /* Gy */
   "D/wykuuIFfr+vPyx7kQEPu8MixO",
},
#endif
#ifdef ECC192
{  
    24,
   "ECC-192",
   /* prime */
   "/////////////////////l//////////",

   /* B */
   "P2456UMSWESFf+chSYGmIVwutkp1Hhcn",

   /* order */
   "////////////////cTxuDXHhoR6qqYWn",

   /* Gx */
   "68se3h0maFPylo3hGw680FJ/2ls2/n0I",

   /* Gy */
   "1nahbV/8sdXZ417jQoJDrNFvTw4UUKWH"
},
#endif
#ifdef ECC224
{
   28,
   "ECC-224",

   /* prime */
   "400000000000000000000000000000000000BV",

   /* B */
   "21HkWGL2CxJIp",

   /* order */
   "4000000000000000000Kxnixk9t8MLzMiV264/",

   /* Gx */
   "jpqOf1BHus6Yd/pyhyVpP",
 
   /* Gy */
   "3FCtyo2yHA5SFjkCGbYxbOvNeChwS+j6wSIwck",
},
#endif
#ifdef ECC256
{
   32,
   "ECC-256",
   /* Prime */
   "F////y000010000000000000000////////////////",

   /* B */
   "5h6DTYgEfFdi+kzLNQOXhnb7GQmp5EmzZlEF3udqc1B",

   /* Order */
   "F////y00000//////////+yvlgjfnUUXFEvoiByOoLH",

   /* Gx */
   "6iNqVBXB497+BpcvMEaGF9t0ts1BUipeFIXEKNOcCAM",

   /* Gy */
   "4/ZGkB+6d+RZkVhIdmFdXOhpZDNQp5UpiksG6Wtlr7r"
}, 
#endif
#ifdef ECC384
{
   48,
   "ECC-384",
   /* prime */
   "//////////////////////////////////////////x/////00000000003/"
   "////",
   
   /* B */
   "ip4lf+8+v+IOZWLhu/Wj6HWTd6x+WK4I0nG8Zr0JXrh6LZcDYYxHdIg5oEtJ"
   "x2hl",
   
   /* Order */
   "////////////////////////////////nsDDWVGtBTzO6WsoIB2dUkpi6MhC"
   "nIbp",

   /* Gx and Gy */
   "geVA8hwB1JUEiSSUyo2jT6uTEsABfvkOMVT1u89KAZXL0l9TlrKfR3fKNZXo"
   "TWgt",
   
   "DXVUIfOcB6zTdfY/afBSAVZq7RqecXHywTen4xNmkC0AOB7E7Nw1dNf37NoG"
   "wWvV"
},
#endif
#ifdef ECC521
{
   65,
   "ECC-521",
   /* prime */ 
   "V///////////////////////////////////////////////////////////"
   "///////////////////////////",
 
   /* B */
   "56LFhbXZXoQ7vAQ8Q2sXK3kejfoMvcp5VEuj8cHZl49uLOPEL7iVfDx5bB0l"
   "JknlmSrSz+8FImqyUz57zHhK3y0",
 
   /* Order */ 
   "V//////////////////////////////////////////+b66XuE/BvPhVym1I"
   "FS9fT0xjScuYPn7hhjljnwHE6G9",

   /* Gx and Gy */
   "CQ5ZWQt10JfpPu+osOZbRH2d6I1EGK/jI7uAAzWQqqzkg5BNdVlvrae/Xt19"
   "wB/gDupIBF1XMf2c/b+VZ72vRrc",
   
   "HWvAMfucZl015oANxGiVHlPcFL4ILURH6WNhxqN9pvcB9VkSfbUz2P0nL2v0"
   "J+j1s4rF726edB2G8Y+b7QVqMPG",
},
#endif
{
   0,
   NULL, NULL, NULL, NULL, NULL, NULL
}
};

#if 0

/* you plug in a prime and B value and it finds a pseudo-random base point */
void ecc_find_base(void)
{
   static char *prime = "26959946667150639794667015087019630673637144422540572481103610249951";
   static char *order = "26959946667150639794667015087019637467111563745054605861463538557247";
   static char *b     = "9538957348957353489587";
   mp_int pp, p, r, B, tmp1, tmp2, tx, ty, x, y;
   char buf[4096];
   int i;

   mp_init_multi(&tx, &ty, &x, &y, &p, &pp, &r, &B, &tmp1, &tmp2, NULL);
   mp_read_radix(&p, prime, 10);
   mp_read_radix(&r, order, 10);
   mp_read_radix(&B, b, 10);

   /* get (p+1)/4 */
   mp_add_d(&p, 1, &pp);
   mp_div_2(&pp, &pp);
   mp_div_2(&pp, &pp);

   buf[0] = 0;
   do {
      printf("."); fflush(stdout);
      /* make a random value of x */
      for (i = 0; i < 16; i++) buf[i+1] = rand() & 255;
      mp_read_raw(&x, buf, 17);
      mp_copy(&x, &tx);

      /* now compute x^3 - 3x + b */
      mp_expt_d(&x, 3, &tmp1);
      mp_mul_d(&x, 3, &tmp2);
      mp_sub(&tmp1, &tmp2, &tmp1);
      mp_add(&tmp1, &B, &tmp1);
      mp_mod(&tmp1, &p, &tmp1);

      /* now compute sqrt via x^((p+1)/4) */
      mp_exptmod(&tmp1, &pp, &p, &tmp2);
      mp_copy(&tmp2, &ty);

      /* now square it */
      mp_sqrmod(&tmp2, &p, &tmp2);

      /* tmp2 should equal tmp1 */
   } while (mp_cmp(&tmp1, &tmp2)); 

   /* now output values in way that libtomcrypt wants */
   mp_todecimal(&p, buf);
   printf("\n\np==%s\n", buf);
   mp_tohex(&B, buf);
   printf("b==%s\n", buf);
   mp_todecimal(&r, buf);
   printf("r==%s\n", buf);
   mp_tohex(&tx, buf);
   printf("Gx==%s\n", buf);
   mp_tohex(&ty, buf);
   printf("Gy==%s\n", buf);

   mp_clear_multi(&tx, &ty, &x, &y, &p, &pp, &r, &B, &tmp1, &tmp2, NULL);
}

#endif

static int is_valid_idx(int n)
{
   int x;

   for (x = 0; sets[x].size != 0; x++);
   if ((n < 0) || (n >= x)) {
      return 0;
   }
   return 1;
}

static ecc_point *new_point(void)
{
   ecc_point *p;
   p = XMALLOC(sizeof(ecc_point));
   if (p == NULL) {
      return NULL;
   }
   if (mp_init_multi(&p->x, &p->y, NULL) != MP_OKAY) {
      XFREE(p);
      return NULL;
   }
   return p;
}

static void del_point(ecc_point *p)
{
   mp_clear_multi(&p->x, &p->y, NULL);
   XFREE(p);
}


/* double a point R = 2P, R can be P*/
static int dbl_point(ecc_point *P, ecc_point *R, mp_int *modulus)
{
   mp_int s, tmp, tmpx;
   int res;

   if (mp_init_multi(&s, &tmp, &tmpx, NULL) != MP_OKAY) { 
      return CRYPT_MEM;
   }

   /* s = (3Xp^2 + a) / (2Yp) */
   if (mp_mul_2(&P->y, &tmp) != MP_OKAY)                   { goto error; } /* tmp = 2*y */
   if (mp_invmod(&tmp, modulus, &tmp) != MP_OKAY)          { goto error; } /* tmp = 1/tmp mod modulus */
   if (mp_sqr(&P->x, &s) != MP_OKAY)                       { goto error; } /* s = x^2  */
   if (mp_mul_d(&s,(mp_digit)3, &s) != MP_OKAY)            { goto error; } /* s = 3*(x^2) */
   if (mp_sub_d(&s,(mp_digit)3, &s) != MP_OKAY)            { goto error; } /* s = 3*(x^2) - 3 */
   if (mp_mulmod(&s, &tmp, modulus, &s) != MP_OKAY)        { goto error; } /* s = tmp * s mod modulus */

   /* Xr = s^2 - 2Xp */
   if (mp_sqr(&s,  &tmpx) != MP_OKAY)                      { goto error; } /* tmpx = s^2  */
   if (mp_sub(&tmpx, &P->x, &tmpx) != MP_OKAY)             { goto error; } /* tmpx = tmpx - x */
   if (mp_submod(&tmpx, &P->x, modulus, &tmpx) != MP_OKAY) { goto error; } /* tmpx = tmpx - x mod modulus */

   /* Yr = -Yp + s(Xp - Xr)  */
   if (mp_sub(&P->x, &tmpx, &tmp) != MP_OKAY)              { goto error; } /* tmp = x - tmpx */
   if (mp_mul(&tmp, &s, &tmp) != MP_OKAY)                  { goto error; } /* tmp = tmp * s */
   if (mp_submod(&tmp, &P->y, modulus, &R->y) != MP_OKAY)  { goto error; } /* y = tmp - y mod modulus */
   if (mp_copy(&tmpx, &R->x) != MP_OKAY)                   { goto error; } /* x = tmpx */

   res = CRYPT_OK;
   goto done;
error:
   res = CRYPT_MEM;
done:
   mp_clear_multi(&tmpx, &tmp, &s, NULL);
   return res;
}

/* add two different points over Z/pZ, R = P + Q, note R can equal either P or Q */
static int add_point(ecc_point *P, ecc_point *Q, ecc_point *R, mp_int *modulus)
{
   mp_int s, tmp, tmpx;
   int res;

   if (mp_init(&tmp) != MP_OKAY) { 
      return CRYPT_MEM;
   }

   /* is P==Q or P==-Q? */
   if (mp_neg(&Q->y, &tmp) != MP_OKAY || mp_mod(&tmp, modulus, &tmp) != MP_OKAY) {
      mp_clear(&tmp);
      return CRYPT_MEM;
   }
   
   if (mp_cmp(&P->x, &Q->x) == MP_EQ)
      if (mp_cmp(&P->y, &Q->y) == MP_EQ || mp_cmp(&P->y, &tmp) == MP_EQ) {
         mp_clear(&tmp);
         return dbl_point(P, R, modulus);
      }

   if (mp_init_multi(&tmpx, &s, NULL) != MP_OKAY) { 
      mp_clear(&tmp);
      return CRYPT_MEM;
   }

   /* get s = (Yp - Yq)/(Xp-Xq) mod p */
   if (mp_submod(&P->x, &Q->x, modulus, &tmp) != MP_OKAY)     { goto error; } /* tmp = Px - Qx mod modulus */
   if (mp_invmod(&tmp, modulus, &tmp) != MP_OKAY)             { goto error; } /* tmp = 1/tmp mod modulus */
   if (mp_sub(&P->y, &Q->y, &s) != MP_OKAY)                   { goto error; } /* s = Py - Qy mod modulus */
   if (mp_mulmod(&s, &tmp, modulus, &s) != MP_OKAY)           { goto error; } /* s = s * tmp mod modulus */

   /* Xr = s^2 - Xp - Xq */
   if (mp_sqrmod(&s, modulus, &tmp) != MP_OKAY)               { goto error; } /* tmp = s^2 mod modulus */
   if (mp_sub(&tmp, &P->x, &tmp) != MP_OKAY)                  { goto error; } /* tmp = tmp - Px */
   if (mp_sub(&tmp, &Q->x, &tmpx) != MP_OKAY)                 { goto error; } /* tmpx = tmp - Qx */

   /* Yr = -Yp + s(Xp - Xr) */
   if (mp_sub(&P->x, &tmpx, &tmp) != MP_OKAY)                 { goto error; } /* tmp = Px - tmpx */
   if (mp_mul(&tmp, &s, &tmp) != MP_OKAY)                     { goto error; } /* tmp = tmp * s */
   if (mp_submod(&tmp, &P->y, modulus, &R->y) != MP_OKAY)     { goto error; } /* Ry = tmp - Py mod modulus */
   if (mp_mod(&tmpx, modulus, &R->x) != MP_OKAY)              { goto error; } /* Rx = tmpx mod modulus */

   res = CRYPT_OK;
   goto done;
error:
   res = CRYPT_MEM;
done:
   mp_clear_multi(&s, &tmpx, &tmp, NULL);
   return res;
}

/* perform R = kG where k == integer and G == ecc_point */
static int ecc_mulmod(mp_int *k, ecc_point *G, ecc_point *R, mp_int *modulus)
{
   ecc_point *tG, *M[14];
   int i, j, z, res;
   mp_digit d;
   unsigned char bits[150], m, first;
   
   /* init M tab */
   for (i = 0; i < 14; i++) {
       M[i] = new_point();
       if (M[i] == NULL) {
          for (j = 0; j < i; j++) {
              del_point(M[j]);
          }
          return CRYPT_MEM;
       }
   }
   
   /* get bits of k */
   first = m = (unsigned char)0;
   for (z = i = 0; z < (int)USED(k); z++) {
       d = DIGIT(k, z);
       for (j = 0; j < (int)MP_DIGIT_BIT; j++) {
           first |= (d&1)<<(unsigned)(m++);
           if (m == (unsigned char)4) {
              bits[i++] = first;
              first = m = (unsigned char)0;
           }
           d >>= 1;
       }
   }
   
   /* residue of multiplicand [if any] */
   if (m) {
      bits[i++] = first;
   }

   /* make a copy of G incase R==G */
   tG = new_point();
   if (tG == NULL)                                          { goto error; }

   /* skip leading digits which are zero */   
   --i; while (i != 0 && bits[i] == (unsigned char)0) { --i; }
   
   if (i == 0) {
      res = CRYPT_INVALID_ARG;
      goto done;
   }
   
   /* now calc the M tab, note that there are only 14 spots, the normal M[0] is a no-op, and M[1] is the input
      point (saves ram)
   */
   
   /* M[0] now is 2*G */
   if (dbl_point(G, M[0], modulus) != CRYPT_OK)             { goto error; }
   for (j = 1; j < 14; j++) {
       if (add_point(M[j-1], G, M[j], modulus) != CRYPT_OK) { goto error; }
   }
  
   /* tG = G */
   if (mp_copy(&G->x, &tG->x) != MP_OKAY)                   { goto error; }
   if (mp_copy(&G->y, &tG->y) != MP_OKAY)                   { goto error; }

   /* set result M[bits[i]] */
   if (bits[i] == (unsigned char)1) {
     if (mp_copy(&G->x, &R->x) != MP_OKAY)                  { goto error; }
     if (mp_copy(&G->y, &R->y) != MP_OKAY)                  { goto error; }
   } else if (bits[i] >= (unsigned char)2) {
     if (mp_copy(&M[(int)bits[i]-2]->x, &R->x) != MP_OKAY)       { goto error; }
     if (mp_copy(&M[(int)bits[i]-2]->y, &R->y) != MP_OKAY)       { goto error; }
   }
   
   while (--i >= 0) {
       /* double */
       for (j = 0; j < 4; j++) {
          if (dbl_point(R, R, modulus) != CRYPT_OK)               { goto error; }
       }
       
       /* now based on the value of bits[i] we do ops */
       if (bits[i] == (unsigned char)0) {
          /* nop */
       } else if (bits[i] == (unsigned char)1) {
          /* add base point */
          if (add_point(R, tG, R, modulus) != CRYPT_OK)           { goto error; }
       } else {
          /* other case */
          if (add_point(R, M[(int)bits[i] - 2], R, modulus) != CRYPT_OK) { goto error; }
       }
   }
   
   res = CRYPT_OK; 
   goto done;
error:
   res = CRYPT_MEM;
done:
   del_point(tG);
   for (i = 0; i < 14; i++) {
       del_point(M[i]);
   }
#ifdef CLEAN_STACK
   zeromem(bits, sizeof(bits)); 
#endif
   return res;
}

int ecc_test(void)
{
   mp_int     modulus, order;
   ecc_point  *G, *GG;
   int i, res, primality;

   if (mp_init_multi(&modulus, &order, NULL) != MP_OKAY) { 
      return CRYPT_MEM;
   }

   G   = new_point();
   if (G == NULL) { 
      mp_clear_multi(&modulus, &order, NULL);
      return CRYPT_MEM;
   }

   GG  = new_point();
   if (GG == NULL) { 
      mp_clear_multi(&modulus, &order, NULL);
      del_point(G);
      return CRYPT_MEM;
   }

   for (i = 0; sets[i].size; i++) {
       #if 0
          printf("Testing %d\n", sets[i].size);
       #endif
       if (mp_read_radix(&modulus, (unsigned char *)sets[i].prime, 64) != MP_OKAY)   { goto error; }
       if (mp_read_radix(&order, (unsigned char *)sets[i].order, 64) != MP_OKAY)     { goto error; }

       /* is prime actually prime? */
       if (is_prime(&modulus, &primality) != CRYPT_OK)           { goto error; }
       if (primality == 0) {
          res = CRYPT_FAIL_TESTVECTOR;
          goto done1;
       }
  
       /* is order prime ? */
       if (is_prime(&order, &primality) != CRYPT_OK)             { goto error; }
       if (primality == 0) {
          res = CRYPT_FAIL_TESTVECTOR;
          goto done1;
       }

       if (mp_read_radix(&G->x, (unsigned char *)sets[i].Gx, 64) != MP_OKAY) { goto error; }
       if (mp_read_radix(&G->y, (unsigned char *)sets[i].Gy, 64) != MP_OKAY) { goto error; }

       /* then we should have G == (order + 1)G */
       if (mp_add_d(&order, 1, &order) != MP_OKAY)                  { goto error; }
       if (ecc_mulmod(&order, G, GG, &modulus) != CRYPT_OK)         { goto error; }
       if (mp_cmp(&G->x, &GG->x) != 0 || mp_cmp(&G->y, &GG->y) != 0) {
          res = CRYPT_FAIL_TESTVECTOR;
          goto done1;
       }
   }
   res = CRYPT_OK;
   goto done1;
error:
   res = CRYPT_MEM;
done1:
   del_point(GG);
   del_point(G);
   mp_clear_multi(&order, &modulus, NULL);
   return res;
}

void ecc_sizes(int *low, int *high)
{
 int i;
 _ARGCHK(low != NULL);
 _ARGCHK(high != NULL);

 *low = INT_MAX;
 *high = 0;
 for (i = 0; sets[i].size != 0; i++) {
     if (sets[i].size < *low)  { 
        *low  = sets[i].size; 
     }
     if (sets[i].size > *high) { 
        *high = sets[i].size; 
     }
 }
}

int ecc_make_key(prng_state *prng, int wprng, int keysize, ecc_key *key)
{
   int x, res, err;
   ecc_point *base;
   mp_int prime;
   unsigned char buf[4096];

   _ARGCHK(key != NULL);

   /* good prng? */
   if ((err = prng_is_valid(wprng)) != CRYPT_OK) {
      return err;
   }

   /* find key size */
   for (x = 0; (keysize > sets[x].size) && (sets[x].size != 0); x++);
   keysize = sets[x].size;

   if (sets[x].size == 0) { 
      return CRYPT_INVALID_KEYSIZE;
   }
   key->idx = x;

   /* make up random string */
   if (prng_descriptor[wprng].read(buf, (unsigned long)keysize, prng) != (unsigned long)keysize) {
      return CRYPT_ERROR_READPRNG;
   }

   /* setup the key variables */
   if (mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->k, &prime, NULL) != MP_OKAY) { 
      return CRYPT_MEM;
   }
   base = new_point();
   if (base == NULL) {
      mp_clear_multi(&key->pubkey.x, &key->pubkey.y, &key->k, &prime, NULL);
      return CRYPT_MEM;
   }

   /* read in the specs for this key */
   if (mp_read_radix(&prime, (unsigned char *)sets[key->idx].prime, 64) != MP_OKAY)  { goto error; }
   if (mp_read_radix(&base->x, (unsigned char *)sets[key->idx].Gx, 64) != MP_OKAY)   { goto error; }
   if (mp_read_radix(&base->y, (unsigned char *)sets[key->idx].Gy, 64) != MP_OKAY)   { goto error; }
   if (mp_read_unsigned_bin(&key->k, (unsigned char *)buf, keysize) != MP_OKAY)      { goto error; }

   /* make the public key */
   if (ecc_mulmod(&key->k, base, &key->pubkey, &prime) != CRYPT_OK) { goto error; }
   key->type = PK_PRIVATE;
   
   /* shrink key */
   if (mp_shrink(&key->k) != MP_OKAY)          { goto error; }
   if (mp_shrink(&key->pubkey.x) != MP_OKAY)   { goto error; }
   if (mp_shrink(&key->pubkey.y) != MP_OKAY)   { goto error; }

   /* free up ram */
   res = CRYPT_OK;
   goto done;
error:
   res = CRYPT_MEM;
done:
   del_point(base);
   mp_clear(&prime);
#ifdef CLEAN_STACK
   zeromem(buf, sizeof(buf));
#endif
   return res;
}

void ecc_free(ecc_key *key)
{
   _ARGCHK(key != NULL);
   mp_clear_multi(&key->pubkey.x, &key->pubkey.y, &key->k, NULL);
}

static int compress_y_point(ecc_point *pt, int idx, int *result)
{
   mp_int tmp, tmp2, p;
   int res;

   _ARGCHK(pt != NULL);
   _ARGCHK(result != NULL);

   if (mp_init_multi(&tmp, &tmp2, &p, NULL) != MP_OKAY) {
      return CRYPT_MEM;
   }

   /* get x^3 - 3x + b */
   if (mp_read_radix(&p, (unsigned char *)sets[idx].B, 64) != MP_OKAY) { goto error; } /* p = B */
   if (mp_expt_d(&pt->x, 3, &tmp) != MP_OKAY)              { goto error; } /* tmp = pX^3  */
   if (mp_mul_d(&pt->x, 3, &tmp2) != MP_OKAY)              { goto error; } /* tmp2 = 3*pX^3 */
   if (mp_sub(&tmp, &tmp2, &tmp) != MP_OKAY)               { goto error; } /* tmp = tmp - tmp2 */
   if (mp_add(&tmp, &p, &tmp) != MP_OKAY)                  { goto error; } /* tmp = tmp + p */
   if (mp_read_radix(&p, (unsigned char *)sets[idx].prime, 64) != MP_OKAY)  { goto error; } /* p = prime */
   if (mp_mod(&tmp, &p, &tmp) != MP_OKAY)                  { goto error; } /* tmp = tmp mod p */

   /* now find square root */
   if (mp_add_d(&p, 1, &tmp2) != MP_OKAY)                  { goto error; } /* tmp2 = p + 1 */
   if (mp_div_2(&tmp2, &tmp2) != MP_OKAY)                  { goto error; } /* tmp2 = tmp2/2 */
   if (mp_div_2(&tmp2, &tmp2) != MP_OKAY)                  { goto error; } /* tmp2 = (p+1)/4 */
   if (mp_exptmod(&tmp, &tmp2, &p, &tmp) != MP_OKAY)       { goto error; } /* tmp  = (x^3 - 3x + b)^((p+1)/4) mod p */

   /* if tmp equals the y point give a 0, otherwise 1 */
   if (mp_cmp(&tmp, &pt->y) == 0) { 
      *result = 0;
   } else {
      *result = 1;
   }
   
   res = CRYPT_OK;
   goto done;
error:
   res = CRYPT_MEM;
done:
   mp_clear_multi(&p, &tmp, &tmp2, NULL);
   return res;
}

static int expand_y_point(ecc_point *pt, int idx, int result)
{
   mp_int tmp, tmp2, p;
   int res;

   _ARGCHK(pt != NULL);
 
   if (mp_init_multi(&tmp, &tmp2, &p, NULL) != MP_OKAY) {
      return CRYPT_MEM;
   }

   /* get x^3 - 3x + b */
   if (mp_read_radix(&p, (unsigned char *)sets[idx].B, 64) != MP_OKAY) { goto error; } /* p = B */
   if (mp_expt_d(&pt->x, 3, &tmp) != MP_OKAY)              { goto error; } /* tmp = pX^3 */
   if (mp_mul_d(&pt->x, 3, &tmp2) != MP_OKAY)              { goto error; } /* tmp2 = 3*pX^3 */
   if (mp_sub(&tmp, &tmp2, &tmp) != MP_OKAY)               { goto error; } /* tmp = tmp - tmp2 */
   if (mp_add(&tmp, &p, &tmp) != MP_OKAY)                  { goto error; } /* tmp = tmp + p */
   if (mp_read_radix(&p, (unsigned char *)sets[idx].prime, 64) != MP_OKAY)  { goto error; } /* p = prime */
   if (mp_mod(&tmp, &p, &tmp) != MP_OKAY)                  { goto error; } /* tmp = tmp mod p */

   /* now find square root */
   if (mp_add_d(&p, 1, &tmp2) != MP_OKAY)                  { goto error; } /* tmp2 = p + 1 */
   if (mp_div_2(&tmp2, &tmp2) != MP_OKAY)                  { goto error; } /* tmp2 = tmp2/2 */
   if (mp_div_2(&tmp2, &tmp2) != MP_OKAY)                  { goto error; } /* tmp2 = (p+1)/4 */
   if (mp_exptmod(&tmp, &tmp2, &p, &tmp) != MP_OKAY)       { goto error; } /* tmp  = (x^3 - 3x + b)^((p+1)/4) mod p */

   /* if result==0, then y==tmp, otherwise y==p-tmp */
   if (result == 0) {
      if (mp_copy(&tmp, &pt->y) != MP_OKAY) { goto error; }
   } else {
      if (mp_sub(&p, &tmp, &pt->y) != MP_OKAY) { goto error; }
   }
   
   res = CRYPT_OK;
   goto done;
error:
   res = CRYPT_MEM;
done:
   mp_clear_multi(&p, &tmp, &tmp2, NULL);
   return res;
}

#define OUTPUT_BIGNUM(num, buf2, y, z)         \
{                                              \
      z = (unsigned long)mp_unsigned_bin_size(num);  \
      STORE32L(z, buf2+y);                     \
      y += 4;                                  \
      (void)mp_to_unsigned_bin(num, buf2+y);   \
      y += z;                                  \
}


#define INPUT_BIGNUM(num, in, x, y)                              \
{                                                                \
     /* load value */                                            \
     if (y+4 > inlen) {                                          \
        err = CRYPT_INVALID_PACKET;                              \
        goto error;                                              \
     }                                                           \
     LOAD32L(x, in+y);                                           \
     y += 4;                                                     \
                                                                 \
     /* sanity check... */                                       \
     if (y+x > inlen) {                                          \
        err = CRYPT_INVALID_PACKET;                              \
        goto error;                                              \
     }                                                           \
                                                                 \
     /* load it */                                               \
     if (mp_read_unsigned_bin(num, (unsigned char *)in+y, (int)x) != MP_OKAY) {\
        err = CRYPT_MEM;                                       \
        goto error;                                              \
     }                                                           \
     y += x;                                                     \
     if (mp_shrink(num) != MP_OKAY) {                            \
        err = CRYPT_MEM;                                       \
        goto error;                                              \
     }                                                           \
}

int ecc_export(unsigned char *out, unsigned long *outlen, int type, ecc_key *key)
{
   unsigned long y, z;
   int res, err;
   unsigned char buf2[512];

   _ARGCHK(out != NULL);
   _ARGCHK(outlen != NULL);
   _ARGCHK(key != NULL);

   /* type valid? */
   if (key->type != PK_PRIVATE && type == PK_PRIVATE) { 
      return CRYPT_PK_TYPE_MISMATCH; 
   }

   /* output type and magic byte */
   y = PACKET_SIZE;
   buf2[y++] = (unsigned char)type;
   buf2[y++] = (unsigned char)sets[key->idx].size;

   /* output x coordinate */
   OUTPUT_BIGNUM(&(key->pubkey.x), buf2, y, z);

   /* compress y and output it  */
   if ((err = compress_y_point(&key->pubkey, key->idx, &res)) != CRYPT_OK) {
      return err;
   }
   buf2[y++] = (unsigned char)res;

   if (type == PK_PRIVATE) {
      OUTPUT_BIGNUM(&key->k, buf2, y, z);
   }

   /* check size */
   if (*outlen < y) { 
      return CRYPT_BUFFER_OVERFLOW;
   }

   /* store header */
   packet_store_header(buf2, PACKET_SECT_ECC, PACKET_SUB_KEY);

   memcpy(out, buf2, (size_t)y);
   *outlen = y;

   #ifdef CLEAN_STACK
       zeromem(buf2, sizeof(buf2));
   #endif
   return CRYPT_OK;
}

int ecc_import(const unsigned char *in, unsigned long inlen, ecc_key *key)
{
   unsigned long x, y, s;
   int err;

   _ARGCHK(in != NULL);
   _ARGCHK(key != NULL);

   /* check type */
   if ((err = packet_valid_header((unsigned char *)in, PACKET_SECT_ECC, PACKET_SUB_KEY)) != CRYPT_OK) { 
      return err;
   }
   
   if (2+PACKET_SIZE > inlen) {
      return CRYPT_INVALID_PACKET;
   }

   /* init key */
   if (mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->k, NULL) != MP_OKAY) {
      return CRYPT_MEM;
   }

   y = PACKET_SIZE;
   key->type = (int)in[y++];
   s = (unsigned long)in[y++];
   
   for (x = 0; (s > (unsigned long)sets[x].size) && (sets[x].size != 0); x++);
   if (sets[x].size == 0) { 
      err = CRYPT_INVALID_KEYSIZE;
      goto error;
   }
   key->idx = (int)x;

   /* type check both values */
   if ((key->type != PK_PUBLIC) && (key->type != PK_PRIVATE))  {
      err = CRYPT_INVALID_PACKET;
      goto error;
   }

   /* is the key idx valid? */
   if (is_valid_idx(key->idx) != 1) {
      err = CRYPT_INVALID_PACKET;
      goto error;
   }

   /* load x coordinate */
   INPUT_BIGNUM(&key->pubkey.x, in, x, y);
  
   /* load y */
   x = (unsigned long)in[y++];
   if ((err = expand_y_point(&key->pubkey, key->idx, (int)x)) != CRYPT_OK) { 
       goto error; 
   }

   if (key->type == PK_PRIVATE) {
      /* load private key */
      INPUT_BIGNUM(&key->k, in, x, y);
   }
   
   /* eliminate private key if public */
   if (key->type == PK_PUBLIC) {
      mp_clear(&key->k);
   }      
   
   return CRYPT_OK;
error:
   mp_clear_multi(&key->pubkey.x, &key->pubkey.y, &key->k, NULL);
   return err;
}

int ecc_shared_secret(ecc_key *private_key, ecc_key *public_key, 
                      unsigned char *out, unsigned long *outlen)
{
   unsigned long x, y;
   ecc_point *result;
   mp_int prime;
   int res, err;

   _ARGCHK(private_key != NULL);
   _ARGCHK(public_key != NULL);
   _ARGCHK(out != NULL);
   _ARGCHK(outlen != NULL);

   /* type valid? */
   if (private_key->type != PK_PRIVATE) {
      return CRYPT_PK_NOT_PRIVATE;
   }

   if (private_key->idx != public_key->idx) {
      return CRYPT_PK_TYPE_MISMATCH;
   }

   /* make new point */
   result = new_point();
   if (result == NULL) { 
      return CRYPT_MEM;
   }

   if (mp_init(&prime) != MP_OKAY) { 
      del_point(result);
      return CRYPT_MEM;
   }

   if (mp_read_radix(&prime, (unsigned char *)sets[private_key->idx].prime, 64) != MP_OKAY) { goto error; }
   if ((err = ecc_mulmod(&private_key->k, &public_key->pubkey, result, &prime)) != CRYPT_OK) { res = err; goto done1; }

   x = (unsigned long)mp_unsigned_bin_size(&result->x);
   y = (unsigned long)mp_unsigned_bin_size(&result->y);

   if (*outlen < (x+y)) {
      res = CRYPT_BUFFER_OVERFLOW;
      goto done1;
   }
   *outlen = x+y;
   (void)mp_to_unsigned_bin(&result->x, out);
   (void)mp_to_unsigned_bin(&result->y, out+x);

   res = CRYPT_OK;
   goto done1;
error:
   res = CRYPT_MEM;
done1:
   mp_clear(&prime);
   del_point(result);
   return res;
}

int ecc_get_size(ecc_key *key)
{
   _ARGCHK(key != NULL);
   if (is_valid_idx(key->idx))
      return sets[key->idx].size;
   else
      return INT_MAX; /* large value known to cause it to fail when passed to ecc_make_key() */
}

#include "ecc_sys.c"

#endif