ge25519_unpack.c

#include "fe25519.h"
#include "ge25519.h"

/* d */
static const fe25519 ecd = {{929955233495203, 466365720129213, 1662059464998953, 2033849074728123, 1442794654840575}};
/* sqrt(-1) */
static const fe25519 sqrtm1 = {{1718705420411056, 234908883556509, 2233514472574048, 2117202627021982, 765476049583133}};

/* return 0 on success, -1 otherwise */
int ge25519_unpack_vartime(ge25519_p3 *r, const unsigned char p[32])
{
  fe25519 t, chk, num, den, den2, den4, den6;
  unsigned char par = p[31] >> 7;

  fe25519_setint(&r->z,1);
  fe25519_unpack(&r->y, p); 
  fe25519_square(&num, &r->y); /* x = y^2 */
  fe25519_mul(&den, &num, &ecd); /* den = dy^2 */
  fe25519_sub(&num, &num, &r->z); /* x = y^2-1 */
  fe25519_add(&den, &r->z, &den); /* den = dy^2+1 */

  /* Computation of sqrt(num/den)
     1.: computation of num^((p-5)/8)*den^((7p-35)/8) = (num*den^7)^((p-5)/8)
  */
  fe25519_square(&den2, &den);
  fe25519_square(&den4, &den2);
  fe25519_mul(&den6, &den4, &den2);
  fe25519_mul(&t, &den6, &num);
  fe25519_mul(&t, &t, &den);

  fe25519_pow2523(&t, &t);
  /* 2. computation of r->x = t * num * den^3
  */
  fe25519_mul(&t, &t, &num);
  fe25519_mul(&t, &t, &den);
  fe25519_mul(&t, &t, &den);
  fe25519_mul(&r->x, &t, &den);

  /* 3. Check whether sqrt computation gave correct result, multiply by sqrt(-1) if not:
  */
  fe25519_square(&chk, &r->x);
  fe25519_mul(&chk, &chk, &den);
  if (!fe25519_iseq_vartime(&chk, &num))
    fe25519_mul(&r->x, &r->x, &sqrtm1);

  /* 4. Now we have one of the two square roots, except if input was not a square
  */
  fe25519_square(&chk, &r->x);
  fe25519_mul(&chk, &chk, &den);
  if (!fe25519_iseq_vartime(&chk, &num))
    return -1;

  /* 5. Choose the desired square root according to parity:
  */
  if(fe25519_getparity(&r->x) != par)
    fe25519_neg(&r->x, &r->x);

  fe25519_mul(&r->t, &r->x, &r->y);
  return 0;
}