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security/nss/lib/freebl/ecl/ecp_aff.c@6474c204b198 (annotated)

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

Wed, 31 Dec 2014 06:09:35 +0100

author

Michael Schloh von Bennewitz <michael@schloh.com>

date

Wed, 31 Dec 2014 06:09:35 +0100

changeset 0

6474c204b198

permissions

-rw-r--r--

Cloned upstream origin tor-browser at tor-browser-31.3.0esr-4.5-1-build1
revision ID fc1c9ff7c1b2defdbc039f12214767608f46423f for hacking purpose.

michael@0	1	/* This Source Code Form is subject to the terms of the Mozilla Public
michael@0	2	* License, v. 2.0. If a copy of the MPL was not distributed with this
michael@0	3	* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
michael@0	4
michael@0	5	#include "ecp.h"
michael@0	6	#include "mplogic.h"
michael@0	7	#include <stdlib.h>
michael@0	8
michael@0	9	/* Checks if point P(px, py) is at infinity. Uses affine coordinates. */
michael@0	10	mp_err
michael@0	11	ec_GFp_pt_is_inf_aff(const mp_int *px, const mp_int *py)
michael@0	12	{
michael@0	13
michael@0	14	if ((mp_cmp_z(px) == 0) && (mp_cmp_z(py) == 0)) {
michael@0	15	return MP_YES;
michael@0	16	} else {
michael@0	17	return MP_NO;
michael@0	18	}
michael@0	19
michael@0	20	}
michael@0	21
michael@0	22	/* Sets P(px, py) to be the point at infinity. Uses affine coordinates. */
michael@0	23	mp_err
michael@0	24	ec_GFp_pt_set_inf_aff(mp_int *px, mp_int *py)
michael@0	25	{
michael@0	26	mp_zero(px);
michael@0	27	mp_zero(py);
michael@0	28	return MP_OKAY;
michael@0	29	}
michael@0	30
michael@0	31	/* Computes R = P + Q based on IEEE P1363 A.10.1. Elliptic curve points P,
michael@0	32	* Q, and R can all be identical. Uses affine coordinates. Assumes input
michael@0	33	* is already field-encoded using field_enc, and returns output that is
michael@0	34	* still field-encoded. */
michael@0	35	mp_err
michael@0	36	ec_GFp_pt_add_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
michael@0	37	const mp_int *qy, mp_int *rx, mp_int *ry,
michael@0	38	const ECGroup *group)
michael@0	39	{
michael@0	40	mp_err res = MP_OKAY;
michael@0	41	mp_int lambda, temp, tempx, tempy;
michael@0	42
michael@0	43	MP_DIGITS(&lambda) = 0;
michael@0	44	MP_DIGITS(&temp) = 0;
michael@0	45	MP_DIGITS(&tempx) = 0;
michael@0	46	MP_DIGITS(&tempy) = 0;
michael@0	47	MP_CHECKOK(mp_init(&lambda));
michael@0	48	MP_CHECKOK(mp_init(&temp));
michael@0	49	MP_CHECKOK(mp_init(&tempx));
michael@0	50	MP_CHECKOK(mp_init(&tempy));
michael@0	51	/* if P = inf, then R = Q */
michael@0	52	if (ec_GFp_pt_is_inf_aff(px, py) == 0) {
michael@0	53	MP_CHECKOK(mp_copy(qx, rx));
michael@0	54	MP_CHECKOK(mp_copy(qy, ry));
michael@0	55	res = MP_OKAY;
michael@0	56	goto CLEANUP;
michael@0	57	}
michael@0	58	/* if Q = inf, then R = P */
michael@0	59	if (ec_GFp_pt_is_inf_aff(qx, qy) == 0) {
michael@0	60	MP_CHECKOK(mp_copy(px, rx));
michael@0	61	MP_CHECKOK(mp_copy(py, ry));
michael@0	62	res = MP_OKAY;
michael@0	63	goto CLEANUP;
michael@0	64	}
michael@0	65	/* if px != qx, then lambda = (py-qy) / (px-qx) */
michael@0	66	if (mp_cmp(px, qx) != 0) {
michael@0	67	MP_CHECKOK(group->meth->field_sub(py, qy, &tempy, group->meth));
michael@0	68	MP_CHECKOK(group->meth->field_sub(px, qx, &tempx, group->meth));
michael@0	69	MP_CHECKOK(group->meth->
michael@0	70	field_div(&tempy, &tempx, &lambda, group->meth));
michael@0	71	} else {
michael@0	72	/* if py != qy or qy = 0, then R = inf */
michael@0	73	if (((mp_cmp(py, qy) != 0)) || (mp_cmp_z(qy) == 0)) {
michael@0	74	mp_zero(rx);
michael@0	75	mp_zero(ry);
michael@0	76	res = MP_OKAY;
michael@0	77	goto CLEANUP;
michael@0	78	}
michael@0	79	/* lambda = (3qx^2+a) / (2qy) */
michael@0	80	MP_CHECKOK(group->meth->field_sqr(qx, &tempx, group->meth));
michael@0	81	MP_CHECKOK(mp_set_int(&temp, 3));
michael@0	82	if (group->meth->field_enc) {
michael@0	83	MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
michael@0	84	}
michael@0	85	MP_CHECKOK(group->meth->
michael@0	86	field_mul(&tempx, &temp, &tempx, group->meth));
michael@0	87	MP_CHECKOK(group->meth->
michael@0	88	field_add(&tempx, &group->curvea, &tempx, group->meth));
michael@0	89	MP_CHECKOK(mp_set_int(&temp, 2));
michael@0	90	if (group->meth->field_enc) {
michael@0	91	MP_CHECKOK(group->meth->field_enc(&temp, &temp, group->meth));
michael@0	92	}
michael@0	93	MP_CHECKOK(group->meth->field_mul(qy, &temp, &tempy, group->meth));
michael@0	94	MP_CHECKOK(group->meth->
michael@0	95	field_div(&tempx, &tempy, &lambda, group->meth));
michael@0	96	}
michael@0	97	/* rx = lambda^2 - px - qx */
michael@0	98	MP_CHECKOK(group->meth->field_sqr(&lambda, &tempx, group->meth));
michael@0	99	MP_CHECKOK(group->meth->field_sub(&tempx, px, &tempx, group->meth));
michael@0	100	MP_CHECKOK(group->meth->field_sub(&tempx, qx, &tempx, group->meth));
michael@0	101	/* ry = (x1-x2) * lambda - y1 */
michael@0	102	MP_CHECKOK(group->meth->field_sub(qx, &tempx, &tempy, group->meth));
michael@0	103	MP_CHECKOK(group->meth->
michael@0	104	field_mul(&tempy, &lambda, &tempy, group->meth));
michael@0	105	MP_CHECKOK(group->meth->field_sub(&tempy, qy, &tempy, group->meth));
michael@0	106	MP_CHECKOK(mp_copy(&tempx, rx));
michael@0	107	MP_CHECKOK(mp_copy(&tempy, ry));
michael@0	108
michael@0	109	CLEANUP:
michael@0	110	mp_clear(&lambda);
michael@0	111	mp_clear(&temp);
michael@0	112	mp_clear(&tempx);
michael@0	113	mp_clear(&tempy);
michael@0	114	return res;
michael@0	115	}
michael@0	116
michael@0	117	/* Computes R = P - Q. Elliptic curve points P, Q, and R can all be
michael@0	118	* identical. Uses affine coordinates. Assumes input is already
michael@0	119	* field-encoded using field_enc, and returns output that is still
michael@0	120	* field-encoded. */
michael@0	121	mp_err
michael@0	122	ec_GFp_pt_sub_aff(const mp_int *px, const mp_int *py, const mp_int *qx,
michael@0	123	const mp_int *qy, mp_int *rx, mp_int *ry,
michael@0	124	const ECGroup *group)
michael@0	125	{
michael@0	126	mp_err res = MP_OKAY;
michael@0	127	mp_int nqy;
michael@0	128
michael@0	129	MP_DIGITS(&nqy) = 0;
michael@0	130	MP_CHECKOK(mp_init(&nqy));
michael@0	131	/* nqy = -qy */
michael@0	132	MP_CHECKOK(group->meth->field_neg(qy, &nqy, group->meth));
michael@0	133	res = group->point_add(px, py, qx, &nqy, rx, ry, group);
michael@0	134	CLEANUP:
michael@0	135	mp_clear(&nqy);
michael@0	136	return res;
michael@0	137	}
michael@0	138
michael@0	139	/* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
michael@0	140	* affine coordinates. Assumes input is already field-encoded using
michael@0	141	* field_enc, and returns output that is still field-encoded. */
michael@0	142	mp_err
michael@0	143	ec_GFp_pt_dbl_aff(const mp_int *px, const mp_int *py, mp_int *rx,
michael@0	144	mp_int *ry, const ECGroup *group)
michael@0	145	{
michael@0	146	return ec_GFp_pt_add_aff(px, py, px, py, rx, ry, group);
michael@0	147	}
michael@0	148
michael@0	149	/* by default, this routine is unused and thus doesn't need to be compiled */
michael@0	150	#ifdef ECL_ENABLE_GFP_PT_MUL_AFF
michael@0	151	/* Computes R = nP based on IEEE P1363 A.10.3. Elliptic curve points P and
michael@0	152	* R can be identical. Uses affine coordinates. Assumes input is already
michael@0	153	* field-encoded using field_enc, and returns output that is still
michael@0	154	* field-encoded. */
michael@0	155	mp_err
michael@0	156	ec_GFp_pt_mul_aff(const mp_int *n, const mp_int *px, const mp_int *py,
michael@0	157	mp_int *rx, mp_int *ry, const ECGroup *group)
michael@0	158	{
michael@0	159	mp_err res = MP_OKAY;
michael@0	160	mp_int k, k3, qx, qy, sx, sy;
michael@0	161	int b1, b3, i, l;
michael@0	162
michael@0	163	MP_DIGITS(&k) = 0;
michael@0	164	MP_DIGITS(&k3) = 0;
michael@0	165	MP_DIGITS(&qx) = 0;
michael@0	166	MP_DIGITS(&qy) = 0;
michael@0	167	MP_DIGITS(&sx) = 0;
michael@0	168	MP_DIGITS(&sy) = 0;
michael@0	169	MP_CHECKOK(mp_init(&k));
michael@0	170	MP_CHECKOK(mp_init(&k3));
michael@0	171	MP_CHECKOK(mp_init(&qx));
michael@0	172	MP_CHECKOK(mp_init(&qy));
michael@0	173	MP_CHECKOK(mp_init(&sx));
michael@0	174	MP_CHECKOK(mp_init(&sy));
michael@0	175
michael@0	176	/* if n = 0 then r = inf */
michael@0	177	if (mp_cmp_z(n) == 0) {
michael@0	178	mp_zero(rx);
michael@0	179	mp_zero(ry);
michael@0	180	res = MP_OKAY;
michael@0	181	goto CLEANUP;
michael@0	182	}
michael@0	183	/* Q = P, k = n */
michael@0	184	MP_CHECKOK(mp_copy(px, &qx));
michael@0	185	MP_CHECKOK(mp_copy(py, &qy));
michael@0	186	MP_CHECKOK(mp_copy(n, &k));
michael@0	187	/* if n < 0 then Q = -Q, k = -k */
michael@0	188	if (mp_cmp_z(n) < 0) {
michael@0	189	MP_CHECKOK(group->meth->field_neg(&qy, &qy, group->meth));
michael@0	190	MP_CHECKOK(mp_neg(&k, &k));
michael@0	191	}
michael@0	192	#ifdef ECL_DEBUG /* basic double and add method */
michael@0	193	l = mpl_significant_bits(&k) - 1;
michael@0	194	MP_CHECKOK(mp_copy(&qx, &sx));
michael@0	195	MP_CHECKOK(mp_copy(&qy, &sy));
michael@0	196	for (i = l - 1; i >= 0; i--) {
michael@0	197	/* S = 2S */
michael@0	198	MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
michael@0	199	/* if k_i = 1, then S = S + Q */
michael@0	200	if (mpl_get_bit(&k, i) != 0) {
michael@0	201	MP_CHECKOK(group->
michael@0	202	point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
michael@0	203	}
michael@0	204	}
michael@0	205	#else /* double and add/subtract method from
michael@0	206	* standard */
michael@0	207	/* k3 = 3 * k */
michael@0	208	MP_CHECKOK(mp_set_int(&k3, 3));
michael@0	209	MP_CHECKOK(mp_mul(&k, &k3, &k3));
michael@0	210	/* S = Q */
michael@0	211	MP_CHECKOK(mp_copy(&qx, &sx));
michael@0	212	MP_CHECKOK(mp_copy(&qy, &sy));
michael@0	213	/* l = index of high order bit in binary representation of 3*k */
michael@0	214	l = mpl_significant_bits(&k3) - 1;
michael@0	215	/* for i = l-1 downto 1 */
michael@0	216	for (i = l - 1; i >= 1; i--) {
michael@0	217	/* S = 2S */
michael@0	218	MP_CHECKOK(group->point_dbl(&sx, &sy, &sx, &sy, group));
michael@0	219	b3 = MP_GET_BIT(&k3, i);
michael@0	220	b1 = MP_GET_BIT(&k, i);
michael@0	221	/* if k3_i = 1 and k_i = 0, then S = S + Q */
michael@0	222	if ((b3 == 1) && (b1 == 0)) {
michael@0	223	MP_CHECKOK(group->
michael@0	224	point_add(&sx, &sy, &qx, &qy, &sx, &sy, group));
michael@0	225	/* if k3_i = 0 and k_i = 1, then S = S - Q */
michael@0	226	} else if ((b3 == 0) && (b1 == 1)) {
michael@0	227	MP_CHECKOK(group->
michael@0	228	point_sub(&sx, &sy, &qx, &qy, &sx, &sy, group));
michael@0	229	}
michael@0	230	}
michael@0	231	#endif
michael@0	232	/* output S */
michael@0	233	MP_CHECKOK(mp_copy(&sx, rx));
michael@0	234	MP_CHECKOK(mp_copy(&sy, ry));
michael@0	235
michael@0	236	CLEANUP:
michael@0	237	mp_clear(&k);
michael@0	238	mp_clear(&k3);
michael@0	239	mp_clear(&qx);
michael@0	240	mp_clear(&qy);
michael@0	241	mp_clear(&sx);
michael@0	242	mp_clear(&sy);
michael@0	243	return res;
michael@0	244	}
michael@0	245	#endif
michael@0	246
michael@0	247	/* Validates a point on a GFp curve. */
michael@0	248	mp_err
michael@0	249	ec_GFp_validate_point(const mp_int *px, const mp_int *py, const ECGroup *group)
michael@0	250	{
michael@0	251	mp_err res = MP_NO;
michael@0	252	mp_int accl, accr, tmp, pxt, pyt;
michael@0	253
michael@0	254	MP_DIGITS(&accl) = 0;
michael@0	255	MP_DIGITS(&accr) = 0;
michael@0	256	MP_DIGITS(&tmp) = 0;
michael@0	257	MP_DIGITS(&pxt) = 0;
michael@0	258	MP_DIGITS(&pyt) = 0;
michael@0	259	MP_CHECKOK(mp_init(&accl));
michael@0	260	MP_CHECKOK(mp_init(&accr));
michael@0	261	MP_CHECKOK(mp_init(&tmp));
michael@0	262	MP_CHECKOK(mp_init(&pxt));
michael@0	263	MP_CHECKOK(mp_init(&pyt));
michael@0	264
michael@0	265	/* 1: Verify that publicValue is not the point at infinity */
michael@0	266	if (ec_GFp_pt_is_inf_aff(px, py) == MP_YES) {
michael@0	267	res = MP_NO;
michael@0	268	goto CLEANUP;
michael@0	269	}
michael@0	270	/* 2: Verify that the coordinates of publicValue are elements
michael@0	271	* of the field.
michael@0	272	*/
michael@0	273	if ((MP_SIGN(px) == MP_NEG) || (mp_cmp(px, &group->meth->irr) >= 0) ||
michael@0	274	(MP_SIGN(py) == MP_NEG) || (mp_cmp(py, &group->meth->irr) >= 0)) {
michael@0	275	res = MP_NO;
michael@0	276	goto CLEANUP;
michael@0	277	}
michael@0	278	/* 3: Verify that publicValue is on the curve. */
michael@0	279	if (group->meth->field_enc) {
michael@0	280	group->meth->field_enc(px, &pxt, group->meth);
michael@0	281	group->meth->field_enc(py, &pyt, group->meth);
michael@0	282	} else {
michael@0	283	mp_copy(px, &pxt);
michael@0	284	mp_copy(py, &pyt);
michael@0	285	}
michael@0	286	/* left-hand side: y^2 */
michael@0	287	MP_CHECKOK( group->meth->field_sqr(&pyt, &accl, group->meth) );
michael@0	288	/* right-hand side: x^3 + a*x + b = (x^2 + a)*x + b by Horner's rule */
michael@0	289	MP_CHECKOK( group->meth->field_sqr(&pxt, &tmp, group->meth) );
michael@0	290	MP_CHECKOK( group->meth->field_add(&tmp, &group->curvea, &tmp, group->meth) );
michael@0	291	MP_CHECKOK( group->meth->field_mul(&tmp, &pxt, &accr, group->meth) );
michael@0	292	MP_CHECKOK( group->meth->field_add(&accr, &group->curveb, &accr, group->meth) );
michael@0	293	/* check LHS - RHS == 0 */
michael@0	294	MP_CHECKOK( group->meth->field_sub(&accl, &accr, &accr, group->meth) );
michael@0	295	if (mp_cmp_z(&accr) != 0) {
michael@0	296	res = MP_NO;
michael@0	297	goto CLEANUP;
michael@0	298	}
michael@0	299	/* 4: Verify that the order of the curve times the publicValue
michael@0	300	* is the point at infinity.
michael@0	301	*/
michael@0	302	MP_CHECKOK( ECPoint_mul(group, &group->order, px, py, &pxt, &pyt) );
michael@0	303	if (ec_GFp_pt_is_inf_aff(&pxt, &pyt) != MP_YES) {
michael@0	304	res = MP_NO;
michael@0	305	goto CLEANUP;
michael@0	306	}
michael@0	307
michael@0	308	res = MP_YES;
michael@0	309
michael@0	310	CLEANUP:
michael@0	311	mp_clear(&accl);
michael@0	312	mp_clear(&accr);
michael@0	313	mp_clear(&tmp);
michael@0	314	mp_clear(&pxt);
michael@0	315	mp_clear(&pyt);
michael@0	316	return res;
michael@0	317	}