RetroZilla/security/nss/lib/freebl/ecl/ec2_proj.c
2015-10-20 23:03:22 -04:00

370 lines
12 KiB
C

/*
* ***** BEGIN LICENSE BLOCK *****
* Version: MPL 1.1/GPL 2.0/LGPL 2.1
*
* The contents of this file are subject to the Mozilla Public License Version
* 1.1 (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* Software distributed under the License is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
* for the specific language governing rights and limitations under the
* License.
*
* The Original Code is the elliptic curve math library for binary polynomial field curves.
*
* The Initial Developer of the Original Code is
* Sun Microsystems, Inc.
* Portions created by the Initial Developer are Copyright (C) 2003
* the Initial Developer. All Rights Reserved.
*
* Contributor(s):
* Sheueling Chang-Shantz <sheueling.chang@sun.com>,
* Stephen Fung <fungstep@hotmail.com>, and
* Douglas Stebila <douglas@stebila.ca>, Sun Microsystems Laboratories.
*
* Alternatively, the contents of this file may be used under the terms of
* either the GNU General Public License Version 2 or later (the "GPL"), or
* the GNU Lesser General Public License Version 2.1 or later (the "LGPL"),
* in which case the provisions of the GPL or the LGPL are applicable instead
* of those above. If you wish to allow use of your version of this file only
* under the terms of either the GPL or the LGPL, and not to allow others to
* use your version of this file under the terms of the MPL, indicate your
* decision by deleting the provisions above and replace them with the notice
* and other provisions required by the GPL or the LGPL. If you do not delete
* the provisions above, a recipient may use your version of this file under
* the terms of any one of the MPL, the GPL or the LGPL.
*
* ***** END LICENSE BLOCK ***** */
#include "ec2.h"
#include "mplogic.h"
#include "mp_gf2m.h"
#include <stdlib.h>
#ifdef ECL_DEBUG
#include <assert.h>
#endif
/* by default, these routines are unused and thus don't need to be compiled */
#ifdef ECL_ENABLE_GF2M_PROJ
/* Converts a point P(px, py) from affine coordinates to projective
* coordinates R(rx, ry, rz). Assumes input is already field-encoded using
* field_enc, and returns output that is still field-encoded. */
mp_err
ec_GF2m_pt_aff2proj(const mp_int *px, const mp_int *py, mp_int *rx,
mp_int *ry, mp_int *rz, const ECGroup *group)
{
mp_err res = MP_OKAY;
MP_CHECKOK(mp_copy(px, rx));
MP_CHECKOK(mp_copy(py, ry));
MP_CHECKOK(mp_set_int(rz, 1));
if (group->meth->field_enc) {
MP_CHECKOK(group->meth->field_enc(rz, rz, group->meth));
}
CLEANUP:
return res;
}
/* Converts a point P(px, py, pz) from projective coordinates to affine
* coordinates R(rx, ry). P and R can share x and y coordinates. Assumes
* input is already field-encoded using field_enc, and returns output that
* is still field-encoded. */
mp_err
ec_GF2m_pt_proj2aff(const mp_int *px, const mp_int *py, const mp_int *pz,
mp_int *rx, mp_int *ry, const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int z1, z2;
MP_DIGITS(&z1) = 0;
MP_DIGITS(&z2) = 0;
MP_CHECKOK(mp_init(&z1));
MP_CHECKOK(mp_init(&z2));
/* if point at infinity, then set point at infinity and exit */
if (ec_GF2m_pt_is_inf_proj(px, py, pz) == MP_YES) {
MP_CHECKOK(ec_GF2m_pt_set_inf_aff(rx, ry));
goto CLEANUP;
}
/* transform (px, py, pz) into (px / pz, py / pz^2) */
if (mp_cmp_d(pz, 1) == 0) {
MP_CHECKOK(mp_copy(px, rx));
MP_CHECKOK(mp_copy(py, ry));
} else {
MP_CHECKOK(group->meth->field_div(NULL, pz, &z1, group->meth));
MP_CHECKOK(group->meth->field_sqr(&z1, &z2, group->meth));
MP_CHECKOK(group->meth->field_mul(px, &z1, rx, group->meth));
MP_CHECKOK(group->meth->field_mul(py, &z2, ry, group->meth));
}
CLEANUP:
mp_clear(&z1);
mp_clear(&z2);
return res;
}
/* Checks if point P(px, py, pz) is at infinity. Uses projective
* coordinates. */
mp_err
ec_GF2m_pt_is_inf_proj(const mp_int *px, const mp_int *py,
const mp_int *pz)
{
return mp_cmp_z(pz);
}
/* Sets P(px, py, pz) to be the point at infinity. Uses projective
* coordinates. */
mp_err
ec_GF2m_pt_set_inf_proj(mp_int *px, mp_int *py, mp_int *pz)
{
mp_zero(pz);
return MP_OKAY;
}
/* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
* (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical.
* Uses mixed projective-affine coordinates. Assumes input is already
* field-encoded using field_enc, and returns output that is still
* field-encoded. Uses equation (3) from Hankerson, Hernandez, Menezes.
* Software Implementation of Elliptic Curve Cryptography Over Binary
* Fields. */
mp_err
ec_GF2m_pt_add_proj(const mp_int *px, const mp_int *py, const mp_int *pz,
const mp_int *qx, const mp_int *qy, mp_int *rx,
mp_int *ry, mp_int *rz, const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int A, B, C, D, E, F, G;
/* If either P or Q is the point at infinity, then return the other
* point */
if (ec_GF2m_pt_is_inf_proj(px, py, pz) == MP_YES) {
return ec_GF2m_pt_aff2proj(qx, qy, rx, ry, rz, group);
}
if (ec_GF2m_pt_is_inf_aff(qx, qy) == MP_YES) {
MP_CHECKOK(mp_copy(px, rx));
MP_CHECKOK(mp_copy(py, ry));
return mp_copy(pz, rz);
}
MP_DIGITS(&A) = 0;
MP_DIGITS(&B) = 0;
MP_DIGITS(&C) = 0;
MP_DIGITS(&D) = 0;
MP_DIGITS(&E) = 0;
MP_DIGITS(&F) = 0;
MP_DIGITS(&G) = 0;
MP_CHECKOK(mp_init(&A));
MP_CHECKOK(mp_init(&B));
MP_CHECKOK(mp_init(&C));
MP_CHECKOK(mp_init(&D));
MP_CHECKOK(mp_init(&E));
MP_CHECKOK(mp_init(&F));
MP_CHECKOK(mp_init(&G));
/* D = pz^2 */
MP_CHECKOK(group->meth->field_sqr(pz, &D, group->meth));
/* A = qy * pz^2 + py */
MP_CHECKOK(group->meth->field_mul(qy, &D, &A, group->meth));
MP_CHECKOK(group->meth->field_add(&A, py, &A, group->meth));
/* B = qx * pz + px */
MP_CHECKOK(group->meth->field_mul(qx, pz, &B, group->meth));
MP_CHECKOK(group->meth->field_add(&B, px, &B, group->meth));
/* C = pz * B */
MP_CHECKOK(group->meth->field_mul(pz, &B, &C, group->meth));
/* D = B^2 * (C + a * pz^2) (using E as a temporary variable) */
MP_CHECKOK(group->meth->
field_mul(&group->curvea, &D, &D, group->meth));
MP_CHECKOK(group->meth->field_add(&C, &D, &D, group->meth));
MP_CHECKOK(group->meth->field_sqr(&B, &E, group->meth));
MP_CHECKOK(group->meth->field_mul(&E, &D, &D, group->meth));
/* rz = C^2 */
MP_CHECKOK(group->meth->field_sqr(&C, rz, group->meth));
/* E = A * C */
MP_CHECKOK(group->meth->field_mul(&A, &C, &E, group->meth));
/* rx = A^2 + D + E */
MP_CHECKOK(group->meth->field_sqr(&A, rx, group->meth));
MP_CHECKOK(group->meth->field_add(rx, &D, rx, group->meth));
MP_CHECKOK(group->meth->field_add(rx, &E, rx, group->meth));
/* F = rx + qx * rz */
MP_CHECKOK(group->meth->field_mul(qx, rz, &F, group->meth));
MP_CHECKOK(group->meth->field_add(rx, &F, &F, group->meth));
/* G = rx + qy * rz */
MP_CHECKOK(group->meth->field_mul(qy, rz, &G, group->meth));
MP_CHECKOK(group->meth->field_add(rx, &G, &G, group->meth));
/* ry = E * F + rz * G (using G as a temporary variable) */
MP_CHECKOK(group->meth->field_mul(rz, &G, &G, group->meth));
MP_CHECKOK(group->meth->field_mul(&E, &F, ry, group->meth));
MP_CHECKOK(group->meth->field_add(ry, &G, ry, group->meth));
CLEANUP:
mp_clear(&A);
mp_clear(&B);
mp_clear(&C);
mp_clear(&D);
mp_clear(&E);
mp_clear(&F);
mp_clear(&G);
return res;
}
/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
* projective coordinates.
*
* Assumes input is already field-encoded using field_enc, and returns
* output that is still field-encoded.
*
* Uses equation (3) from Hankerson, Hernandez, Menezes. Software
* Implementation of Elliptic Curve Cryptography Over Binary Fields.
*/
mp_err
ec_GF2m_pt_dbl_proj(const mp_int *px, const mp_int *py, const mp_int *pz,
mp_int *rx, mp_int *ry, mp_int *rz,
const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int t0, t1;
if (ec_GF2m_pt_is_inf_proj(px, py, pz) == MP_YES) {
return ec_GF2m_pt_set_inf_proj(rx, ry, rz);
}
MP_DIGITS(&t0) = 0;
MP_DIGITS(&t1) = 0;
MP_CHECKOK(mp_init(&t0));
MP_CHECKOK(mp_init(&t1));
/* t0 = px^2 */
/* t1 = pz^2 */
MP_CHECKOK(group->meth->field_sqr(px, &t0, group->meth));
MP_CHECKOK(group->meth->field_sqr(pz, &t1, group->meth));
/* rz = px^2 * pz^2 */
MP_CHECKOK(group->meth->field_mul(&t0, &t1, rz, group->meth));
/* t0 = px^4 */
/* t1 = b * pz^4 */
MP_CHECKOK(group->meth->field_sqr(&t0, &t0, group->meth));
MP_CHECKOK(group->meth->field_sqr(&t1, &t1, group->meth));
MP_CHECKOK(group->meth->
field_mul(&group->curveb, &t1, &t1, group->meth));
/* rx = px^4 + b * pz^4 */
MP_CHECKOK(group->meth->field_add(&t0, &t1, rx, group->meth));
/* ry = b * pz^4 * rz + rx * (a * rz + py^2 + b * pz^4) */
MP_CHECKOK(group->meth->field_sqr(py, ry, group->meth));
MP_CHECKOK(group->meth->field_add(ry, &t1, ry, group->meth));
/* t0 = a * rz */
MP_CHECKOK(group->meth->
field_mul(&group->curvea, rz, &t0, group->meth));
MP_CHECKOK(group->meth->field_add(&t0, ry, ry, group->meth));
MP_CHECKOK(group->meth->field_mul(rx, ry, ry, group->meth));
/* t1 = b * pz^4 * rz */
MP_CHECKOK(group->meth->field_mul(&t1, rz, &t1, group->meth));
MP_CHECKOK(group->meth->field_add(&t1, ry, ry, group->meth));
CLEANUP:
mp_clear(&t0);
mp_clear(&t1);
return res;
}
/* Computes R = nP where R is (rx, ry) and P is (px, py). The parameters
* a, b and p are the elliptic curve coefficients and the prime that
* determines the field GF2m. Elliptic curve points P and R can be
* identical. Uses mixed projective-affine coordinates. Assumes input is
* already field-encoded using field_enc, and returns output that is still
* field-encoded. Uses 4-bit window method. */
mp_err
ec_GF2m_pt_mul_proj(const mp_int *n, const mp_int *px, const mp_int *py,
mp_int *rx, mp_int *ry, const ECGroup *group)
{
mp_err res = MP_OKAY;
mp_int precomp[16][2], rz;
mp_digit precomp_arr[ECL_MAX_FIELD_SIZE_DIGITS * 16 * 2], *t;
int i, ni, d;
ARGCHK(group != NULL, MP_BADARG);
ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
/* initialize precomputation table */
t = precomp_arr;
for (i = 0; i < 16; i++) {
/* x co-ord */
MP_SIGN(&precomp[i][0]) = MP_ZPOS;
MP_ALLOC(&precomp[i][0]) = ECL_MAX_FIELD_SIZE_DIGITS;
MP_USED(&precomp[i][0]) = 1;
*t = 0;
MP_DIGITS(&precomp[i][0]) = t;
t += ECL_MAX_FIELD_SIZE_DIGITS;
/* y co-ord */
MP_SIGN(&precomp[i][1]) = MP_ZPOS;
MP_ALLOC(&precomp[i][1]) = ECL_MAX_FIELD_SIZE_DIGITS;
MP_USED(&precomp[i][1]) = 1;
*t = 0;
MP_DIGITS(&precomp[i][1]) = t;
t += ECL_MAX_FIELD_SIZE_DIGITS;
}
/* fill precomputation table */
mp_zero(&precomp[0][0]);
mp_zero(&precomp[0][1]);
MP_CHECKOK(mp_copy(px, &precomp[1][0]));
MP_CHECKOK(mp_copy(py, &precomp[1][1]));
for (i = 2; i < 16; i++) {
MP_CHECKOK(group->
point_add(&precomp[1][0], &precomp[1][1],
&precomp[i - 1][0], &precomp[i - 1][1],
&precomp[i][0], &precomp[i][1], group));
}
d = (mpl_significant_bits(n) + 3) / 4;
/* R = inf */
MP_DIGITS(&rz) = 0;
MP_CHECKOK(mp_init(&rz));
MP_CHECKOK(ec_GF2m_pt_set_inf_proj(rx, ry, &rz));
for (i = d - 1; i >= 0; i--) {
/* compute window ni */
ni = MP_GET_BIT(n, 4 * i + 3);
ni <<= 1;
ni |= MP_GET_BIT(n, 4 * i + 2);
ni <<= 1;
ni |= MP_GET_BIT(n, 4 * i + 1);
ni <<= 1;
ni |= MP_GET_BIT(n, 4 * i);
/* R = 2^4 * R */
MP_CHECKOK(ec_GF2m_pt_dbl_proj(rx, ry, &rz, rx, ry, &rz, group));
MP_CHECKOK(ec_GF2m_pt_dbl_proj(rx, ry, &rz, rx, ry, &rz, group));
MP_CHECKOK(ec_GF2m_pt_dbl_proj(rx, ry, &rz, rx, ry, &rz, group));
MP_CHECKOK(ec_GF2m_pt_dbl_proj(rx, ry, &rz, rx, ry, &rz, group));
/* R = R + (ni * P) */
MP_CHECKOK(ec_GF2m_pt_add_proj
(rx, ry, &rz, &precomp[ni][0], &precomp[ni][1], rx, ry,
&rz, group));
}
/* convert result S to affine coordinates */
MP_CHECKOK(ec_GF2m_pt_proj2aff(rx, ry, &rz, rx, ry, group));
CLEANUP:
mp_clear(&rz);
return res;
}
#endif