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Side by Side Diff: nss/lib/freebl/ecl/ecp_jm.c

Issue 2078763002: Delete bundled copy of NSS and replace with README. (Closed) Base URL: https://chromium.googlesource.com/chromium/deps/nss@master
Patch Set: Delete bundled copy of NSS and replace with README. Created 4 years, 6 months ago
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1 /* This Source Code Form is subject to the terms of the Mozilla Public
2 * License, v. 2.0. If a copy of the MPL was not distributed with this
3 * file, You can obtain one at http://mozilla.org/MPL/2.0/. */
4
5 #include "ecp.h"
6 #include "ecl-priv.h"
7 #include "mplogic.h"
8 #include <stdlib.h>
9
10 #define MAX_SCRATCH 6
11
12 /* Computes R = 2P. Elliptic curve points P and R can be identical. Uses
13 * Modified Jacobian coordinates.
14 *
15 * Assumes input is already field-encoded using field_enc, and returns
16 * output that is still field-encoded.
17 *
18 */
19 static mp_err
20 ec_GFp_pt_dbl_jm(const mp_int *px, const mp_int *py, const mp_int *pz,
21 const mp_int *paz4, mp_int *rx, mp_int *ry, mp_ int *rz,
22 mp_int *raz4, mp_int scratch[], const ECGroup * group)
23 {
24 mp_err res = MP_OKAY;
25 mp_int *t0, *t1, *M, *S;
26
27 t0 = &scratch[0];
28 t1 = &scratch[1];
29 M = &scratch[2];
30 S = &scratch[3];
31
32 #if MAX_SCRATCH < 4
33 #error "Scratch array defined too small "
34 #endif
35
36 /* Check for point at infinity */
37 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
38 /* Set r = pt at infinity by setting rz = 0 */
39
40 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, rz));
41 goto CLEANUP;
42 }
43
44 /* M = 3 (px^2) + a*(pz^4) */
45 MP_CHECKOK(group->meth->field_sqr(px, t0, group->meth));
46 MP_CHECKOK(group->meth->field_add(t0, t0, M, group->meth));
47 MP_CHECKOK(group->meth->field_add(t0, M, t0, group->meth));
48 MP_CHECKOK(group->meth->field_add(t0, paz4, M, group->meth));
49
50 /* rz = 2 * py * pz */
51 MP_CHECKOK(group->meth->field_mul(py, pz, S, group->meth));
52 MP_CHECKOK(group->meth->field_add(S, S, rz, group->meth));
53
54 /* t0 = 2y^2 , t1 = 8y^4 */
55 MP_CHECKOK(group->meth->field_sqr(py, t0, group->meth));
56 MP_CHECKOK(group->meth->field_add(t0, t0, t0, group->meth));
57 MP_CHECKOK(group->meth->field_sqr(t0, t1, group->meth));
58 MP_CHECKOK(group->meth->field_add(t1, t1, t1, group->meth));
59
60 /* S = 4 * px * py^2 = 2 * px * t0 */
61 MP_CHECKOK(group->meth->field_mul(px, t0, S, group->meth));
62 MP_CHECKOK(group->meth->field_add(S, S, S, group->meth));
63
64
65 /* rx = M^2 - 2S */
66 MP_CHECKOK(group->meth->field_sqr(M, rx, group->meth));
67 MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
68 MP_CHECKOK(group->meth->field_sub(rx, S, rx, group->meth));
69
70 /* ry = M * (S - rx) - t1 */
71 MP_CHECKOK(group->meth->field_sub(S, rx, S, group->meth));
72 MP_CHECKOK(group->meth->field_mul(S, M, ry, group->meth));
73 MP_CHECKOK(group->meth->field_sub(ry, t1, ry, group->meth));
74
75 /* ra*z^4 = 2*t1*(apz4) */
76 MP_CHECKOK(group->meth->field_mul(paz4, t1, raz4, group->meth));
77 MP_CHECKOK(group->meth->field_add(raz4, raz4, raz4, group->meth));
78
79
80 CLEANUP:
81 return res;
82 }
83
84 /* Computes R = P + Q where R is (rx, ry, rz), P is (px, py, pz) and Q is
85 * (qx, qy, 1). Elliptic curve points P, Q, and R can all be identical.
86 * Uses mixed Modified_Jacobian-affine coordinates. Assumes input is
87 * already field-encoded using field_enc, and returns output that is still
88 * field-encoded. */
89 static mp_err
90 ec_GFp_pt_add_jm_aff(const mp_int *px, const mp_int *py, const mp_int *pz,
91 const mp_int *paz4, const mp_int *qx,
92 const mp_int *qy, mp_int *rx, mp_int *r y, mp_int *rz,
93 mp_int *raz4, mp_int scratch[], const E CGroup *group)
94 {
95 mp_err res = MP_OKAY;
96 mp_int *A, *B, *C, *D, *C2, *C3;
97
98 A = &scratch[0];
99 B = &scratch[1];
100 C = &scratch[2];
101 D = &scratch[3];
102 C2 = &scratch[4];
103 C3 = &scratch[5];
104
105 #if MAX_SCRATCH < 6
106 #error "Scratch array defined too small "
107 #endif
108
109 /* If either P or Q is the point at infinity, then return the other
110 * point */
111 if (ec_GFp_pt_is_inf_jac(px, py, pz) == MP_YES) {
112 MP_CHECKOK(ec_GFp_pt_aff2jac(qx, qy, rx, ry, rz, group));
113 MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
114 MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
115 MP_CHECKOK(group->meth->
116 field_mul(raz4, &group->curvea, raz4, group-> meth));
117 goto CLEANUP;
118 }
119 if (ec_GFp_pt_is_inf_aff(qx, qy) == MP_YES) {
120 MP_CHECKOK(mp_copy(px, rx));
121 MP_CHECKOK(mp_copy(py, ry));
122 MP_CHECKOK(mp_copy(pz, rz));
123 MP_CHECKOK(mp_copy(paz4, raz4));
124 goto CLEANUP;
125 }
126
127 /* A = qx * pz^2, B = qy * pz^3 */
128 MP_CHECKOK(group->meth->field_sqr(pz, A, group->meth));
129 MP_CHECKOK(group->meth->field_mul(A, pz, B, group->meth));
130 MP_CHECKOK(group->meth->field_mul(A, qx, A, group->meth));
131 MP_CHECKOK(group->meth->field_mul(B, qy, B, group->meth));
132
133 /* C = A - px, D = B - py */
134 MP_CHECKOK(group->meth->field_sub(A, px, C, group->meth));
135 MP_CHECKOK(group->meth->field_sub(B, py, D, group->meth));
136
137 /* C2 = C^2, C3 = C^3 */
138 MP_CHECKOK(group->meth->field_sqr(C, C2, group->meth));
139 MP_CHECKOK(group->meth->field_mul(C, C2, C3, group->meth));
140
141 /* rz = pz * C */
142 MP_CHECKOK(group->meth->field_mul(pz, C, rz, group->meth));
143
144 /* C = px * C^2 */
145 MP_CHECKOK(group->meth->field_mul(px, C2, C, group->meth));
146 /* A = D^2 */
147 MP_CHECKOK(group->meth->field_sqr(D, A, group->meth));
148
149 /* rx = D^2 - (C^3 + 2 * (px * C^2)) */
150 MP_CHECKOK(group->meth->field_add(C, C, rx, group->meth));
151 MP_CHECKOK(group->meth->field_add(C3, rx, rx, group->meth));
152 MP_CHECKOK(group->meth->field_sub(A, rx, rx, group->meth));
153
154 /* C3 = py * C^3 */
155 MP_CHECKOK(group->meth->field_mul(py, C3, C3, group->meth));
156
157 /* ry = D * (px * C^2 - rx) - py * C^3 */
158 MP_CHECKOK(group->meth->field_sub(C, rx, ry, group->meth));
159 MP_CHECKOK(group->meth->field_mul(D, ry, ry, group->meth));
160 MP_CHECKOK(group->meth->field_sub(ry, C3, ry, group->meth));
161
162 /* raz4 = a * rz^4 */
163 MP_CHECKOK(group->meth->field_sqr(rz, raz4, group->meth));
164 MP_CHECKOK(group->meth->field_sqr(raz4, raz4, group->meth));
165 MP_CHECKOK(group->meth->
166 field_mul(raz4, &group->curvea, raz4, group->meth));
167 CLEANUP:
168 return res;
169 }
170
171 /* Computes R = nP where R is (rx, ry) and P is the base point. Elliptic
172 * curve points P and R can be identical. Uses mixed Modified-Jacobian
173 * co-ordinates for doubling and Chudnovsky Jacobian coordinates for
174 * additions. Assumes input is already field-encoded using field_enc, and
175 * returns output that is still field-encoded. Uses 5-bit window NAF
176 * method (algorithm 11) for scalar-point multiplication from Brown,
177 * Hankerson, Lopez, Menezes. Software Implementation of the NIST Elliptic
178 * Curves Over Prime Fields. */
179 mp_err
180 ec_GFp_pt_mul_jm_wNAF(const mp_int *n, const mp_int *px, const mp_int *py,
181 mp_int *rx, mp_int *ry, const ECGroup *group)
182 {
183 mp_err res = MP_OKAY;
184 mp_int precomp[16][2], rz, tpx, tpy;
185 mp_int raz4;
186 mp_int scratch[MAX_SCRATCH];
187 signed char *naf = NULL;
188 int i, orderBitSize;
189
190 MP_DIGITS(&rz) = 0;
191 MP_DIGITS(&raz4) = 0;
192 MP_DIGITS(&tpx) = 0;
193 MP_DIGITS(&tpy) = 0;
194 for (i = 0; i < 16; i++) {
195 MP_DIGITS(&precomp[i][0]) = 0;
196 MP_DIGITS(&precomp[i][1]) = 0;
197 }
198 for (i = 0; i < MAX_SCRATCH; i++) {
199 MP_DIGITS(&scratch[i]) = 0;
200 }
201
202 ARGCHK(group != NULL, MP_BADARG);
203 ARGCHK((n != NULL) && (px != NULL) && (py != NULL), MP_BADARG);
204
205 /* initialize precomputation table */
206 MP_CHECKOK(mp_init(&tpx));
207 MP_CHECKOK(mp_init(&tpy));;
208 MP_CHECKOK(mp_init(&rz));
209 MP_CHECKOK(mp_init(&raz4));
210
211 for (i = 0; i < 16; i++) {
212 MP_CHECKOK(mp_init(&precomp[i][0]));
213 MP_CHECKOK(mp_init(&precomp[i][1]));
214 }
215 for (i = 0; i < MAX_SCRATCH; i++) {
216 MP_CHECKOK(mp_init(&scratch[i]));
217 }
218
219 /* Set out[8] = P */
220 MP_CHECKOK(mp_copy(px, &precomp[8][0]));
221 MP_CHECKOK(mp_copy(py, &precomp[8][1]));
222
223 /* Set (tpx, tpy) = 2P */
224 MP_CHECKOK(group->
225 point_dbl(&precomp[8][0], &precomp[8][1], &tpx, &tpy,
226 group));
227
228 /* Set 3P, 5P, ..., 15P */
229 for (i = 8; i < 15; i++) {
230 MP_CHECKOK(group->
231 point_add(&precomp[i][0], &precomp[i][1], &tp x, &tpy,
232 &precomp[i + 1][0], &pr ecomp[i + 1][1],
233 group));
234 }
235
236 /* Set -15P, -13P, ..., -P */
237 for (i = 0; i < 8; i++) {
238 MP_CHECKOK(mp_copy(&precomp[15 - i][0], &precomp[i][0]));
239 MP_CHECKOK(group->meth->
240 field_neg(&precomp[15 - i][1], &precomp[i][1] ,
241 group->meth));
242 }
243
244 /* R = inf */
245 MP_CHECKOK(ec_GFp_pt_set_inf_jac(rx, ry, &rz));
246
247 orderBitSize = mpl_significant_bits(&group->order);
248
249 /* Allocate memory for NAF */
250 naf = (signed char *) malloc(sizeof(signed char) * (orderBitSize + 1));
251 if (naf == NULL) {
252 res = MP_MEM;
253 goto CLEANUP;
254 }
255
256 /* Compute 5NAF */
257 ec_compute_wNAF(naf, orderBitSize, n, 5);
258
259 /* wNAF method */
260 for (i = orderBitSize; i >= 0; i--) {
261 /* R = 2R */
262 ec_GFp_pt_dbl_jm(rx, ry, &rz, &raz4, rx, ry, &rz,
263 &raz4, scratch, group);
264 if (naf[i] != 0) {
265 ec_GFp_pt_add_jm_aff(rx, ry, &rz, &raz4,
266 &precomp[(naf[i ] + 15) / 2][0],
267 &precomp[(naf[i ] + 15) / 2][1], rx, ry,
268 &rz, &raz4, scr atch, group);
269 }
270 }
271
272 /* convert result S to affine coordinates */
273 MP_CHECKOK(ec_GFp_pt_jac2aff(rx, ry, &rz, rx, ry, group));
274
275 CLEANUP:
276 for (i = 0; i < MAX_SCRATCH; i++) {
277 mp_clear(&scratch[i]);
278 }
279 for (i = 0; i < 16; i++) {
280 mp_clear(&precomp[i][0]);
281 mp_clear(&precomp[i][1]);
282 }
283 mp_clear(&tpx);
284 mp_clear(&tpy);
285 mp_clear(&rz);
286 mp_clear(&raz4);
287 free(naf);
288 return res;
289 }
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