The Tor Browser: security/nss/lib/freebl/ecl/ec2

security/nss/lib/freebl/ecl/ec2_proj.c@b8a032363ba2 (annotated)

security/nss/lib/freebl/ecl/ec2_proj.c

Thu, 22 Jan 2015 13:21:57 +0100

author: Michael Schloh von Bennewitz <michael@schloh.com>
date: Thu, 22 Jan 2015 13:21:57 +0100
branch: TOR_BUG_9701
changeset 15: b8a032363ba2
permissions: -rw-r--r--

Incorporate requested changes from Mozilla in review:
https://bugzilla.mozilla.org/show_bug.cgi?id=1123480#c6

 /* This Source Code Form is subject to the terms of the Mozilla Public
  * License, v. 2.0. If a copy of the MPL was not distributed with this
  * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
 #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

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security/nss/lib/freebl/ecl/ec2_proj.c@b8a032363ba2 (annotated)

security/nss/lib/freebl/ecl/ec2_proj.c