1 /***********************************************************************
2 * Copyright (c) 2013, 2014 Pieter Wuille *
3 * Distributed under the MIT software license, see the accompanying *
4 * file COPYING or https://www.opensource.org/licenses/mit-license.php.*
5 ***********************************************************************/
6
7 #ifndef SECP256K1_GROUP_IMPL_H
8 #define SECP256K1_GROUP_IMPL_H
9
10 #include "field.h"
11 #include "group.h"
12
13 /* These exhaustive group test orders and generators are chosen such that:
14 * - The field size is equal to that of secp256k1, so field code is the same.
15 * - The curve equation is of the form y^2=x^3+B for some constant B.
16 * - The subgroup has a generator 2*P, where P.x=1.
17 * - The subgroup has size less than 1000 to permit exhaustive testing.
18 * - The subgroup admits an endomorphism of the form lambda*(x,y) == (beta*x,y).
19 *
20 * These parameters are generated using sage/gen_exhaustive_groups.sage.
21 */
22 #if defined(EXHAUSTIVE_TEST_ORDER)
23 # if EXHAUSTIVE_TEST_ORDER == 13
24 static const rustsecp256k1_v0_4_1_ge rustsecp256k1_v0_4_1_ge_const_g = SECP256K1_GE_CONST(
25 0xc3459c3d, 0x35326167, 0xcd86cce8, 0x07a2417f,
26 0x5b8bd567, 0xde8538ee, 0x0d507b0c, 0xd128f5bb,
27 0x8e467fec, 0xcd30000a, 0x6cc1184e, 0x25d382c2,
28 0xa2f4494e, 0x2fbe9abc, 0x8b64abac, 0xd005fb24
29 );
30 static const rustsecp256k1_v0_4_1_fe rustsecp256k1_v0_4_1_fe_const_b = SECP256K1_FE_CONST(
31 0x3d3486b2, 0x159a9ca5, 0xc75638be, 0xb23a69bc,
32 0x946a45ab, 0x24801247, 0xb4ed2b8e, 0x26b6a417
33 );
34 # elif EXHAUSTIVE_TEST_ORDER == 199
35 static const rustsecp256k1_v0_4_1_ge rustsecp256k1_v0_4_1_ge_const_g = SECP256K1_GE_CONST(
36 0x226e653f, 0xc8df7744, 0x9bacbf12, 0x7d1dcbf9,
37 0x87f05b2a, 0xe7edbd28, 0x1f564575, 0xc48dcf18,
38 0xa13872c2, 0xe933bb17, 0x5d9ffd5b, 0xb5b6e10c,
39 0x57fe3c00, 0xbaaaa15a, 0xe003ec3e, 0x9c269bae
40 );
41 static const rustsecp256k1_v0_4_1_fe rustsecp256k1_v0_4_1_fe_const_b = SECP256K1_FE_CONST(
42 0x2cca28fa, 0xfc614b80, 0x2a3db42b, 0x00ba00b1,
43 0xbea8d943, 0xdace9ab2, 0x9536daea, 0x0074defb
44 );
45 # else
46 # error No known generator for the specified exhaustive test group order.
47 # endif
48 #else
49 /** Generator for secp256k1, value 'g' defined in
50 * "Standards for Efficient Cryptography" (SEC2) 2.7.1.
51 */
52 static const rustsecp256k1_v0_4_1_ge rustsecp256k1_v0_4_1_ge_const_g = SECP256K1_GE_CONST(
53 0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,
54 0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL,
55 0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,
56 0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
57 );
58
59 static const rustsecp256k1_v0_4_1_fe rustsecp256k1_v0_4_1_fe_const_b = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 7);
60 #endif
61
rustsecp256k1_v0_4_1_ge_set_gej_zinv(rustsecp256k1_v0_4_1_ge * r,const rustsecp256k1_v0_4_1_gej * a,const rustsecp256k1_v0_4_1_fe * zi)62 static void rustsecp256k1_v0_4_1_ge_set_gej_zinv(rustsecp256k1_v0_4_1_ge *r, const rustsecp256k1_v0_4_1_gej *a, const rustsecp256k1_v0_4_1_fe *zi) {
63 rustsecp256k1_v0_4_1_fe zi2;
64 rustsecp256k1_v0_4_1_fe zi3;
65 rustsecp256k1_v0_4_1_fe_sqr(&zi2, zi);
66 rustsecp256k1_v0_4_1_fe_mul(&zi3, &zi2, zi);
67 rustsecp256k1_v0_4_1_fe_mul(&r->x, &a->x, &zi2);
68 rustsecp256k1_v0_4_1_fe_mul(&r->y, &a->y, &zi3);
69 r->infinity = a->infinity;
70 }
71
rustsecp256k1_v0_4_1_ge_set_xy(rustsecp256k1_v0_4_1_ge * r,const rustsecp256k1_v0_4_1_fe * x,const rustsecp256k1_v0_4_1_fe * y)72 static void rustsecp256k1_v0_4_1_ge_set_xy(rustsecp256k1_v0_4_1_ge *r, const rustsecp256k1_v0_4_1_fe *x, const rustsecp256k1_v0_4_1_fe *y) {
73 r->infinity = 0;
74 r->x = *x;
75 r->y = *y;
76 }
77
rustsecp256k1_v0_4_1_ge_is_infinity(const rustsecp256k1_v0_4_1_ge * a)78 static int rustsecp256k1_v0_4_1_ge_is_infinity(const rustsecp256k1_v0_4_1_ge *a) {
79 return a->infinity;
80 }
81
rustsecp256k1_v0_4_1_ge_neg(rustsecp256k1_v0_4_1_ge * r,const rustsecp256k1_v0_4_1_ge * a)82 static void rustsecp256k1_v0_4_1_ge_neg(rustsecp256k1_v0_4_1_ge *r, const rustsecp256k1_v0_4_1_ge *a) {
83 *r = *a;
84 rustsecp256k1_v0_4_1_fe_normalize_weak(&r->y);
85 rustsecp256k1_v0_4_1_fe_negate(&r->y, &r->y, 1);
86 }
87
rustsecp256k1_v0_4_1_ge_set_gej(rustsecp256k1_v0_4_1_ge * r,rustsecp256k1_v0_4_1_gej * a)88 static void rustsecp256k1_v0_4_1_ge_set_gej(rustsecp256k1_v0_4_1_ge *r, rustsecp256k1_v0_4_1_gej *a) {
89 rustsecp256k1_v0_4_1_fe z2, z3;
90 r->infinity = a->infinity;
91 rustsecp256k1_v0_4_1_fe_inv(&a->z, &a->z);
92 rustsecp256k1_v0_4_1_fe_sqr(&z2, &a->z);
93 rustsecp256k1_v0_4_1_fe_mul(&z3, &a->z, &z2);
94 rustsecp256k1_v0_4_1_fe_mul(&a->x, &a->x, &z2);
95 rustsecp256k1_v0_4_1_fe_mul(&a->y, &a->y, &z3);
96 rustsecp256k1_v0_4_1_fe_set_int(&a->z, 1);
97 r->x = a->x;
98 r->y = a->y;
99 }
100
rustsecp256k1_v0_4_1_ge_set_gej_var(rustsecp256k1_v0_4_1_ge * r,rustsecp256k1_v0_4_1_gej * a)101 static void rustsecp256k1_v0_4_1_ge_set_gej_var(rustsecp256k1_v0_4_1_ge *r, rustsecp256k1_v0_4_1_gej *a) {
102 rustsecp256k1_v0_4_1_fe z2, z3;
103 if (a->infinity) {
104 rustsecp256k1_v0_4_1_ge_set_infinity(r);
105 return;
106 }
107 rustsecp256k1_v0_4_1_fe_inv_var(&a->z, &a->z);
108 rustsecp256k1_v0_4_1_fe_sqr(&z2, &a->z);
109 rustsecp256k1_v0_4_1_fe_mul(&z3, &a->z, &z2);
110 rustsecp256k1_v0_4_1_fe_mul(&a->x, &a->x, &z2);
111 rustsecp256k1_v0_4_1_fe_mul(&a->y, &a->y, &z3);
112 rustsecp256k1_v0_4_1_fe_set_int(&a->z, 1);
113 rustsecp256k1_v0_4_1_ge_set_xy(r, &a->x, &a->y);
114 }
115
rustsecp256k1_v0_4_1_ge_set_all_gej_var(rustsecp256k1_v0_4_1_ge * r,const rustsecp256k1_v0_4_1_gej * a,size_t len)116 static void rustsecp256k1_v0_4_1_ge_set_all_gej_var(rustsecp256k1_v0_4_1_ge *r, const rustsecp256k1_v0_4_1_gej *a, size_t len) {
117 rustsecp256k1_v0_4_1_fe u;
118 size_t i;
119 size_t last_i = SIZE_MAX;
120
121 for (i = 0; i < len; i++) {
122 if (a[i].infinity) {
123 rustsecp256k1_v0_4_1_ge_set_infinity(&r[i]);
124 } else {
125 /* Use destination's x coordinates as scratch space */
126 if (last_i == SIZE_MAX) {
127 r[i].x = a[i].z;
128 } else {
129 rustsecp256k1_v0_4_1_fe_mul(&r[i].x, &r[last_i].x, &a[i].z);
130 }
131 last_i = i;
132 }
133 }
134 if (last_i == SIZE_MAX) {
135 return;
136 }
137 rustsecp256k1_v0_4_1_fe_inv_var(&u, &r[last_i].x);
138
139 i = last_i;
140 while (i > 0) {
141 i--;
142 if (!a[i].infinity) {
143 rustsecp256k1_v0_4_1_fe_mul(&r[last_i].x, &r[i].x, &u);
144 rustsecp256k1_v0_4_1_fe_mul(&u, &u, &a[last_i].z);
145 last_i = i;
146 }
147 }
148 VERIFY_CHECK(!a[last_i].infinity);
149 r[last_i].x = u;
150
151 for (i = 0; i < len; i++) {
152 if (!a[i].infinity) {
153 rustsecp256k1_v0_4_1_ge_set_gej_zinv(&r[i], &a[i], &r[i].x);
154 }
155 }
156 }
157
rustsecp256k1_v0_4_1_ge_globalz_set_table_gej(size_t len,rustsecp256k1_v0_4_1_ge * r,rustsecp256k1_v0_4_1_fe * globalz,const rustsecp256k1_v0_4_1_gej * a,const rustsecp256k1_v0_4_1_fe * zr)158 static void rustsecp256k1_v0_4_1_ge_globalz_set_table_gej(size_t len, rustsecp256k1_v0_4_1_ge *r, rustsecp256k1_v0_4_1_fe *globalz, const rustsecp256k1_v0_4_1_gej *a, const rustsecp256k1_v0_4_1_fe *zr) {
159 size_t i = len - 1;
160 rustsecp256k1_v0_4_1_fe zs;
161
162 if (len > 0) {
163 /* The z of the final point gives us the "global Z" for the table. */
164 r[i].x = a[i].x;
165 r[i].y = a[i].y;
166 /* Ensure all y values are in weak normal form for fast negation of points */
167 rustsecp256k1_v0_4_1_fe_normalize_weak(&r[i].y);
168 *globalz = a[i].z;
169 r[i].infinity = 0;
170 zs = zr[i];
171
172 /* Work our way backwards, using the z-ratios to scale the x/y values. */
173 while (i > 0) {
174 if (i != len - 1) {
175 rustsecp256k1_v0_4_1_fe_mul(&zs, &zs, &zr[i]);
176 }
177 i--;
178 rustsecp256k1_v0_4_1_ge_set_gej_zinv(&r[i], &a[i], &zs);
179 }
180 }
181 }
182
rustsecp256k1_v0_4_1_gej_set_infinity(rustsecp256k1_v0_4_1_gej * r)183 static void rustsecp256k1_v0_4_1_gej_set_infinity(rustsecp256k1_v0_4_1_gej *r) {
184 r->infinity = 1;
185 rustsecp256k1_v0_4_1_fe_clear(&r->x);
186 rustsecp256k1_v0_4_1_fe_clear(&r->y);
187 rustsecp256k1_v0_4_1_fe_clear(&r->z);
188 }
189
rustsecp256k1_v0_4_1_ge_set_infinity(rustsecp256k1_v0_4_1_ge * r)190 static void rustsecp256k1_v0_4_1_ge_set_infinity(rustsecp256k1_v0_4_1_ge *r) {
191 r->infinity = 1;
192 rustsecp256k1_v0_4_1_fe_clear(&r->x);
193 rustsecp256k1_v0_4_1_fe_clear(&r->y);
194 }
195
rustsecp256k1_v0_4_1_gej_clear(rustsecp256k1_v0_4_1_gej * r)196 static void rustsecp256k1_v0_4_1_gej_clear(rustsecp256k1_v0_4_1_gej *r) {
197 r->infinity = 0;
198 rustsecp256k1_v0_4_1_fe_clear(&r->x);
199 rustsecp256k1_v0_4_1_fe_clear(&r->y);
200 rustsecp256k1_v0_4_1_fe_clear(&r->z);
201 }
202
rustsecp256k1_v0_4_1_ge_clear(rustsecp256k1_v0_4_1_ge * r)203 static void rustsecp256k1_v0_4_1_ge_clear(rustsecp256k1_v0_4_1_ge *r) {
204 r->infinity = 0;
205 rustsecp256k1_v0_4_1_fe_clear(&r->x);
206 rustsecp256k1_v0_4_1_fe_clear(&r->y);
207 }
208
rustsecp256k1_v0_4_1_ge_set_xo_var(rustsecp256k1_v0_4_1_ge * r,const rustsecp256k1_v0_4_1_fe * x,int odd)209 static int rustsecp256k1_v0_4_1_ge_set_xo_var(rustsecp256k1_v0_4_1_ge *r, const rustsecp256k1_v0_4_1_fe *x, int odd) {
210 rustsecp256k1_v0_4_1_fe x2, x3;
211 r->x = *x;
212 rustsecp256k1_v0_4_1_fe_sqr(&x2, x);
213 rustsecp256k1_v0_4_1_fe_mul(&x3, x, &x2);
214 r->infinity = 0;
215 rustsecp256k1_v0_4_1_fe_add(&x3, &rustsecp256k1_v0_4_1_fe_const_b);
216 if (!rustsecp256k1_v0_4_1_fe_sqrt(&r->y, &x3)) {
217 return 0;
218 }
219 rustsecp256k1_v0_4_1_fe_normalize_var(&r->y);
220 if (rustsecp256k1_v0_4_1_fe_is_odd(&r->y) != odd) {
221 rustsecp256k1_v0_4_1_fe_negate(&r->y, &r->y, 1);
222 }
223 return 1;
224
225 }
226
rustsecp256k1_v0_4_1_gej_set_ge(rustsecp256k1_v0_4_1_gej * r,const rustsecp256k1_v0_4_1_ge * a)227 static void rustsecp256k1_v0_4_1_gej_set_ge(rustsecp256k1_v0_4_1_gej *r, const rustsecp256k1_v0_4_1_ge *a) {
228 r->infinity = a->infinity;
229 r->x = a->x;
230 r->y = a->y;
231 rustsecp256k1_v0_4_1_fe_set_int(&r->z, 1);
232 }
233
rustsecp256k1_v0_4_1_gej_eq_x_var(const rustsecp256k1_v0_4_1_fe * x,const rustsecp256k1_v0_4_1_gej * a)234 static int rustsecp256k1_v0_4_1_gej_eq_x_var(const rustsecp256k1_v0_4_1_fe *x, const rustsecp256k1_v0_4_1_gej *a) {
235 rustsecp256k1_v0_4_1_fe r, r2;
236 VERIFY_CHECK(!a->infinity);
237 rustsecp256k1_v0_4_1_fe_sqr(&r, &a->z); rustsecp256k1_v0_4_1_fe_mul(&r, &r, x);
238 r2 = a->x; rustsecp256k1_v0_4_1_fe_normalize_weak(&r2);
239 return rustsecp256k1_v0_4_1_fe_equal_var(&r, &r2);
240 }
241
rustsecp256k1_v0_4_1_gej_neg(rustsecp256k1_v0_4_1_gej * r,const rustsecp256k1_v0_4_1_gej * a)242 static void rustsecp256k1_v0_4_1_gej_neg(rustsecp256k1_v0_4_1_gej *r, const rustsecp256k1_v0_4_1_gej *a) {
243 r->infinity = a->infinity;
244 r->x = a->x;
245 r->y = a->y;
246 r->z = a->z;
247 rustsecp256k1_v0_4_1_fe_normalize_weak(&r->y);
248 rustsecp256k1_v0_4_1_fe_negate(&r->y, &r->y, 1);
249 }
250
rustsecp256k1_v0_4_1_gej_is_infinity(const rustsecp256k1_v0_4_1_gej * a)251 static int rustsecp256k1_v0_4_1_gej_is_infinity(const rustsecp256k1_v0_4_1_gej *a) {
252 return a->infinity;
253 }
254
rustsecp256k1_v0_4_1_ge_is_valid_var(const rustsecp256k1_v0_4_1_ge * a)255 static int rustsecp256k1_v0_4_1_ge_is_valid_var(const rustsecp256k1_v0_4_1_ge *a) {
256 rustsecp256k1_v0_4_1_fe y2, x3;
257 if (a->infinity) {
258 return 0;
259 }
260 /* y^2 = x^3 + 7 */
261 rustsecp256k1_v0_4_1_fe_sqr(&y2, &a->y);
262 rustsecp256k1_v0_4_1_fe_sqr(&x3, &a->x); rustsecp256k1_v0_4_1_fe_mul(&x3, &x3, &a->x);
263 rustsecp256k1_v0_4_1_fe_add(&x3, &rustsecp256k1_v0_4_1_fe_const_b);
264 rustsecp256k1_v0_4_1_fe_normalize_weak(&x3);
265 return rustsecp256k1_v0_4_1_fe_equal_var(&y2, &x3);
266 }
267
rustsecp256k1_v0_4_1_gej_double(rustsecp256k1_v0_4_1_gej * r,const rustsecp256k1_v0_4_1_gej * a)268 static SECP256K1_INLINE void rustsecp256k1_v0_4_1_gej_double(rustsecp256k1_v0_4_1_gej *r, const rustsecp256k1_v0_4_1_gej *a) {
269 /* Operations: 3 mul, 4 sqr, 0 normalize, 12 mul_int/add/negate.
270 *
271 * Note that there is an implementation described at
272 * https://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
273 * which trades a multiply for a square, but in practice this is actually slower,
274 * mainly because it requires more normalizations.
275 */
276 rustsecp256k1_v0_4_1_fe t1,t2,t3,t4;
277
278 r->infinity = a->infinity;
279
280 rustsecp256k1_v0_4_1_fe_mul(&r->z, &a->z, &a->y);
281 rustsecp256k1_v0_4_1_fe_mul_int(&r->z, 2); /* Z' = 2*Y*Z (2) */
282 rustsecp256k1_v0_4_1_fe_sqr(&t1, &a->x);
283 rustsecp256k1_v0_4_1_fe_mul_int(&t1, 3); /* T1 = 3*X^2 (3) */
284 rustsecp256k1_v0_4_1_fe_sqr(&t2, &t1); /* T2 = 9*X^4 (1) */
285 rustsecp256k1_v0_4_1_fe_sqr(&t3, &a->y);
286 rustsecp256k1_v0_4_1_fe_mul_int(&t3, 2); /* T3 = 2*Y^2 (2) */
287 rustsecp256k1_v0_4_1_fe_sqr(&t4, &t3);
288 rustsecp256k1_v0_4_1_fe_mul_int(&t4, 2); /* T4 = 8*Y^4 (2) */
289 rustsecp256k1_v0_4_1_fe_mul(&t3, &t3, &a->x); /* T3 = 2*X*Y^2 (1) */
290 r->x = t3;
291 rustsecp256k1_v0_4_1_fe_mul_int(&r->x, 4); /* X' = 8*X*Y^2 (4) */
292 rustsecp256k1_v0_4_1_fe_negate(&r->x, &r->x, 4); /* X' = -8*X*Y^2 (5) */
293 rustsecp256k1_v0_4_1_fe_add(&r->x, &t2); /* X' = 9*X^4 - 8*X*Y^2 (6) */
294 rustsecp256k1_v0_4_1_fe_negate(&t2, &t2, 1); /* T2 = -9*X^4 (2) */
295 rustsecp256k1_v0_4_1_fe_mul_int(&t3, 6); /* T3 = 12*X*Y^2 (6) */
296 rustsecp256k1_v0_4_1_fe_add(&t3, &t2); /* T3 = 12*X*Y^2 - 9*X^4 (8) */
297 rustsecp256k1_v0_4_1_fe_mul(&r->y, &t1, &t3); /* Y' = 36*X^3*Y^2 - 27*X^6 (1) */
298 rustsecp256k1_v0_4_1_fe_negate(&t2, &t4, 2); /* T2 = -8*Y^4 (3) */
299 rustsecp256k1_v0_4_1_fe_add(&r->y, &t2); /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */
300 }
301
rustsecp256k1_v0_4_1_gej_double_var(rustsecp256k1_v0_4_1_gej * r,const rustsecp256k1_v0_4_1_gej * a,rustsecp256k1_v0_4_1_fe * rzr)302 static void rustsecp256k1_v0_4_1_gej_double_var(rustsecp256k1_v0_4_1_gej *r, const rustsecp256k1_v0_4_1_gej *a, rustsecp256k1_v0_4_1_fe *rzr) {
303 /** For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
304 * Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
305 * y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
306 *
307 * Having said this, if this function receives a point on a sextic twist, e.g. by
308 * a fault attack, it is possible for y to be 0. This happens for y^2 = x^3 + 6,
309 * since -6 does have a cube root mod p. For this point, this function will not set
310 * the infinity flag even though the point doubles to infinity, and the result
311 * point will be gibberish (z = 0 but infinity = 0).
312 */
313 if (a->infinity) {
314 rustsecp256k1_v0_4_1_gej_set_infinity(r);
315 if (rzr != NULL) {
316 rustsecp256k1_v0_4_1_fe_set_int(rzr, 1);
317 }
318 return;
319 }
320
321 if (rzr != NULL) {
322 *rzr = a->y;
323 rustsecp256k1_v0_4_1_fe_normalize_weak(rzr);
324 rustsecp256k1_v0_4_1_fe_mul_int(rzr, 2);
325 }
326
327 rustsecp256k1_v0_4_1_gej_double(r, a);
328 }
329
rustsecp256k1_v0_4_1_gej_add_var(rustsecp256k1_v0_4_1_gej * r,const rustsecp256k1_v0_4_1_gej * a,const rustsecp256k1_v0_4_1_gej * b,rustsecp256k1_v0_4_1_fe * rzr)330 static void rustsecp256k1_v0_4_1_gej_add_var(rustsecp256k1_v0_4_1_gej *r, const rustsecp256k1_v0_4_1_gej *a, const rustsecp256k1_v0_4_1_gej *b, rustsecp256k1_v0_4_1_fe *rzr) {
331 /* Operations: 12 mul, 4 sqr, 2 normalize, 12 mul_int/add/negate */
332 rustsecp256k1_v0_4_1_fe z22, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
333
334 if (a->infinity) {
335 VERIFY_CHECK(rzr == NULL);
336 *r = *b;
337 return;
338 }
339
340 if (b->infinity) {
341 if (rzr != NULL) {
342 rustsecp256k1_v0_4_1_fe_set_int(rzr, 1);
343 }
344 *r = *a;
345 return;
346 }
347
348 r->infinity = 0;
349 rustsecp256k1_v0_4_1_fe_sqr(&z22, &b->z);
350 rustsecp256k1_v0_4_1_fe_sqr(&z12, &a->z);
351 rustsecp256k1_v0_4_1_fe_mul(&u1, &a->x, &z22);
352 rustsecp256k1_v0_4_1_fe_mul(&u2, &b->x, &z12);
353 rustsecp256k1_v0_4_1_fe_mul(&s1, &a->y, &z22); rustsecp256k1_v0_4_1_fe_mul(&s1, &s1, &b->z);
354 rustsecp256k1_v0_4_1_fe_mul(&s2, &b->y, &z12); rustsecp256k1_v0_4_1_fe_mul(&s2, &s2, &a->z);
355 rustsecp256k1_v0_4_1_fe_negate(&h, &u1, 1); rustsecp256k1_v0_4_1_fe_add(&h, &u2);
356 rustsecp256k1_v0_4_1_fe_negate(&i, &s1, 1); rustsecp256k1_v0_4_1_fe_add(&i, &s2);
357 if (rustsecp256k1_v0_4_1_fe_normalizes_to_zero_var(&h)) {
358 if (rustsecp256k1_v0_4_1_fe_normalizes_to_zero_var(&i)) {
359 rustsecp256k1_v0_4_1_gej_double_var(r, a, rzr);
360 } else {
361 if (rzr != NULL) {
362 rustsecp256k1_v0_4_1_fe_set_int(rzr, 0);
363 }
364 rustsecp256k1_v0_4_1_gej_set_infinity(r);
365 }
366 return;
367 }
368 rustsecp256k1_v0_4_1_fe_sqr(&i2, &i);
369 rustsecp256k1_v0_4_1_fe_sqr(&h2, &h);
370 rustsecp256k1_v0_4_1_fe_mul(&h3, &h, &h2);
371 rustsecp256k1_v0_4_1_fe_mul(&h, &h, &b->z);
372 if (rzr != NULL) {
373 *rzr = h;
374 }
375 rustsecp256k1_v0_4_1_fe_mul(&r->z, &a->z, &h);
376 rustsecp256k1_v0_4_1_fe_mul(&t, &u1, &h2);
377 r->x = t; rustsecp256k1_v0_4_1_fe_mul_int(&r->x, 2); rustsecp256k1_v0_4_1_fe_add(&r->x, &h3); rustsecp256k1_v0_4_1_fe_negate(&r->x, &r->x, 3); rustsecp256k1_v0_4_1_fe_add(&r->x, &i2);
378 rustsecp256k1_v0_4_1_fe_negate(&r->y, &r->x, 5); rustsecp256k1_v0_4_1_fe_add(&r->y, &t); rustsecp256k1_v0_4_1_fe_mul(&r->y, &r->y, &i);
379 rustsecp256k1_v0_4_1_fe_mul(&h3, &h3, &s1); rustsecp256k1_v0_4_1_fe_negate(&h3, &h3, 1);
380 rustsecp256k1_v0_4_1_fe_add(&r->y, &h3);
381 }
382
rustsecp256k1_v0_4_1_gej_add_ge_var(rustsecp256k1_v0_4_1_gej * r,const rustsecp256k1_v0_4_1_gej * a,const rustsecp256k1_v0_4_1_ge * b,rustsecp256k1_v0_4_1_fe * rzr)383 static void rustsecp256k1_v0_4_1_gej_add_ge_var(rustsecp256k1_v0_4_1_gej *r, const rustsecp256k1_v0_4_1_gej *a, const rustsecp256k1_v0_4_1_ge *b, rustsecp256k1_v0_4_1_fe *rzr) {
384 /* 8 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
385 rustsecp256k1_v0_4_1_fe z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
386 if (a->infinity) {
387 VERIFY_CHECK(rzr == NULL);
388 rustsecp256k1_v0_4_1_gej_set_ge(r, b);
389 return;
390 }
391 if (b->infinity) {
392 if (rzr != NULL) {
393 rustsecp256k1_v0_4_1_fe_set_int(rzr, 1);
394 }
395 *r = *a;
396 return;
397 }
398 r->infinity = 0;
399
400 rustsecp256k1_v0_4_1_fe_sqr(&z12, &a->z);
401 u1 = a->x; rustsecp256k1_v0_4_1_fe_normalize_weak(&u1);
402 rustsecp256k1_v0_4_1_fe_mul(&u2, &b->x, &z12);
403 s1 = a->y; rustsecp256k1_v0_4_1_fe_normalize_weak(&s1);
404 rustsecp256k1_v0_4_1_fe_mul(&s2, &b->y, &z12); rustsecp256k1_v0_4_1_fe_mul(&s2, &s2, &a->z);
405 rustsecp256k1_v0_4_1_fe_negate(&h, &u1, 1); rustsecp256k1_v0_4_1_fe_add(&h, &u2);
406 rustsecp256k1_v0_4_1_fe_negate(&i, &s1, 1); rustsecp256k1_v0_4_1_fe_add(&i, &s2);
407 if (rustsecp256k1_v0_4_1_fe_normalizes_to_zero_var(&h)) {
408 if (rustsecp256k1_v0_4_1_fe_normalizes_to_zero_var(&i)) {
409 rustsecp256k1_v0_4_1_gej_double_var(r, a, rzr);
410 } else {
411 if (rzr != NULL) {
412 rustsecp256k1_v0_4_1_fe_set_int(rzr, 0);
413 }
414 rustsecp256k1_v0_4_1_gej_set_infinity(r);
415 }
416 return;
417 }
418 rustsecp256k1_v0_4_1_fe_sqr(&i2, &i);
419 rustsecp256k1_v0_4_1_fe_sqr(&h2, &h);
420 rustsecp256k1_v0_4_1_fe_mul(&h3, &h, &h2);
421 if (rzr != NULL) {
422 *rzr = h;
423 }
424 rustsecp256k1_v0_4_1_fe_mul(&r->z, &a->z, &h);
425 rustsecp256k1_v0_4_1_fe_mul(&t, &u1, &h2);
426 r->x = t; rustsecp256k1_v0_4_1_fe_mul_int(&r->x, 2); rustsecp256k1_v0_4_1_fe_add(&r->x, &h3); rustsecp256k1_v0_4_1_fe_negate(&r->x, &r->x, 3); rustsecp256k1_v0_4_1_fe_add(&r->x, &i2);
427 rustsecp256k1_v0_4_1_fe_negate(&r->y, &r->x, 5); rustsecp256k1_v0_4_1_fe_add(&r->y, &t); rustsecp256k1_v0_4_1_fe_mul(&r->y, &r->y, &i);
428 rustsecp256k1_v0_4_1_fe_mul(&h3, &h3, &s1); rustsecp256k1_v0_4_1_fe_negate(&h3, &h3, 1);
429 rustsecp256k1_v0_4_1_fe_add(&r->y, &h3);
430 }
431
rustsecp256k1_v0_4_1_gej_add_zinv_var(rustsecp256k1_v0_4_1_gej * r,const rustsecp256k1_v0_4_1_gej * a,const rustsecp256k1_v0_4_1_ge * b,const rustsecp256k1_v0_4_1_fe * bzinv)432 static void rustsecp256k1_v0_4_1_gej_add_zinv_var(rustsecp256k1_v0_4_1_gej *r, const rustsecp256k1_v0_4_1_gej *a, const rustsecp256k1_v0_4_1_ge *b, const rustsecp256k1_v0_4_1_fe *bzinv) {
433 /* 9 mul, 3 sqr, 4 normalize, 12 mul_int/add/negate */
434 rustsecp256k1_v0_4_1_fe az, z12, u1, u2, s1, s2, h, i, i2, h2, h3, t;
435
436 if (b->infinity) {
437 *r = *a;
438 return;
439 }
440 if (a->infinity) {
441 rustsecp256k1_v0_4_1_fe bzinv2, bzinv3;
442 r->infinity = b->infinity;
443 rustsecp256k1_v0_4_1_fe_sqr(&bzinv2, bzinv);
444 rustsecp256k1_v0_4_1_fe_mul(&bzinv3, &bzinv2, bzinv);
445 rustsecp256k1_v0_4_1_fe_mul(&r->x, &b->x, &bzinv2);
446 rustsecp256k1_v0_4_1_fe_mul(&r->y, &b->y, &bzinv3);
447 rustsecp256k1_v0_4_1_fe_set_int(&r->z, 1);
448 return;
449 }
450 r->infinity = 0;
451
452 /** We need to calculate (rx,ry,rz) = (ax,ay,az) + (bx,by,1/bzinv). Due to
453 * secp256k1's isomorphism we can multiply the Z coordinates on both sides
454 * by bzinv, and get: (rx,ry,rz*bzinv) = (ax,ay,az*bzinv) + (bx,by,1).
455 * This means that (rx,ry,rz) can be calculated as
456 * (ax,ay,az*bzinv) + (bx,by,1), when not applying the bzinv factor to rz.
457 * The variable az below holds the modified Z coordinate for a, which is used
458 * for the computation of rx and ry, but not for rz.
459 */
460 rustsecp256k1_v0_4_1_fe_mul(&az, &a->z, bzinv);
461
462 rustsecp256k1_v0_4_1_fe_sqr(&z12, &az);
463 u1 = a->x; rustsecp256k1_v0_4_1_fe_normalize_weak(&u1);
464 rustsecp256k1_v0_4_1_fe_mul(&u2, &b->x, &z12);
465 s1 = a->y; rustsecp256k1_v0_4_1_fe_normalize_weak(&s1);
466 rustsecp256k1_v0_4_1_fe_mul(&s2, &b->y, &z12); rustsecp256k1_v0_4_1_fe_mul(&s2, &s2, &az);
467 rustsecp256k1_v0_4_1_fe_negate(&h, &u1, 1); rustsecp256k1_v0_4_1_fe_add(&h, &u2);
468 rustsecp256k1_v0_4_1_fe_negate(&i, &s1, 1); rustsecp256k1_v0_4_1_fe_add(&i, &s2);
469 if (rustsecp256k1_v0_4_1_fe_normalizes_to_zero_var(&h)) {
470 if (rustsecp256k1_v0_4_1_fe_normalizes_to_zero_var(&i)) {
471 rustsecp256k1_v0_4_1_gej_double_var(r, a, NULL);
472 } else {
473 rustsecp256k1_v0_4_1_gej_set_infinity(r);
474 }
475 return;
476 }
477 rustsecp256k1_v0_4_1_fe_sqr(&i2, &i);
478 rustsecp256k1_v0_4_1_fe_sqr(&h2, &h);
479 rustsecp256k1_v0_4_1_fe_mul(&h3, &h, &h2);
480 r->z = a->z; rustsecp256k1_v0_4_1_fe_mul(&r->z, &r->z, &h);
481 rustsecp256k1_v0_4_1_fe_mul(&t, &u1, &h2);
482 r->x = t; rustsecp256k1_v0_4_1_fe_mul_int(&r->x, 2); rustsecp256k1_v0_4_1_fe_add(&r->x, &h3); rustsecp256k1_v0_4_1_fe_negate(&r->x, &r->x, 3); rustsecp256k1_v0_4_1_fe_add(&r->x, &i2);
483 rustsecp256k1_v0_4_1_fe_negate(&r->y, &r->x, 5); rustsecp256k1_v0_4_1_fe_add(&r->y, &t); rustsecp256k1_v0_4_1_fe_mul(&r->y, &r->y, &i);
484 rustsecp256k1_v0_4_1_fe_mul(&h3, &h3, &s1); rustsecp256k1_v0_4_1_fe_negate(&h3, &h3, 1);
485 rustsecp256k1_v0_4_1_fe_add(&r->y, &h3);
486 }
487
488
rustsecp256k1_v0_4_1_gej_add_ge(rustsecp256k1_v0_4_1_gej * r,const rustsecp256k1_v0_4_1_gej * a,const rustsecp256k1_v0_4_1_ge * b)489 static void rustsecp256k1_v0_4_1_gej_add_ge(rustsecp256k1_v0_4_1_gej *r, const rustsecp256k1_v0_4_1_gej *a, const rustsecp256k1_v0_4_1_ge *b) {
490 /* Operations: 7 mul, 5 sqr, 4 normalize, 21 mul_int/add/negate/cmov */
491 static const rustsecp256k1_v0_4_1_fe fe_1 = SECP256K1_FE_CONST(0, 0, 0, 0, 0, 0, 0, 1);
492 rustsecp256k1_v0_4_1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr;
493 rustsecp256k1_v0_4_1_fe m_alt, rr_alt;
494 int infinity, degenerate;
495 VERIFY_CHECK(!b->infinity);
496 VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
497
498 /** In:
499 * Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks.
500 * In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002.
501 * we find as solution for a unified addition/doubling formula:
502 * lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation.
503 * x3 = lambda^2 - (x1 + x2)
504 * 2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2).
505 *
506 * Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives:
507 * U1 = X1*Z2^2, U2 = X2*Z1^2
508 * S1 = Y1*Z2^3, S2 = Y2*Z1^3
509 * Z = Z1*Z2
510 * T = U1+U2
511 * M = S1+S2
512 * Q = T*M^2
513 * R = T^2-U1*U2
514 * X3 = 4*(R^2-Q)
515 * Y3 = 4*(R*(3*Q-2*R^2)-M^4)
516 * Z3 = 2*M*Z
517 * (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
518 *
519 * This formula has the benefit of being the same for both addition
520 * of distinct points and doubling. However, it breaks down in the
521 * case that either point is infinity, or that y1 = -y2. We handle
522 * these cases in the following ways:
523 *
524 * - If b is infinity we simply bail by means of a VERIFY_CHECK.
525 *
526 * - If a is infinity, we detect this, and at the end of the
527 * computation replace the result (which will be meaningless,
528 * but we compute to be constant-time) with b.x : b.y : 1.
529 *
530 * - If a = -b, we have y1 = -y2, which is a degenerate case.
531 * But here the answer is infinity, so we simply set the
532 * infinity flag of the result, overriding the computed values
533 * without even needing to cmov.
534 *
535 * - If y1 = -y2 but x1 != x2, which does occur thanks to certain
536 * properties of our curve (specifically, 1 has nontrivial cube
537 * roots in our field, and the curve equation has no x coefficient)
538 * then the answer is not infinity but also not given by the above
539 * equation. In this case, we cmov in place an alternate expression
540 * for lambda. Specifically (y1 - y2)/(x1 - x2). Where both these
541 * expressions for lambda are defined, they are equal, and can be
542 * obtained from each other by multiplication by (y1 + y2)/(y1 + y2)
543 * then substitution of x^3 + 7 for y^2 (using the curve equation).
544 * For all pairs of nonzero points (a, b) at least one is defined,
545 * so this covers everything.
546 */
547
548 rustsecp256k1_v0_4_1_fe_sqr(&zz, &a->z); /* z = Z1^2 */
549 u1 = a->x; rustsecp256k1_v0_4_1_fe_normalize_weak(&u1); /* u1 = U1 = X1*Z2^2 (1) */
550 rustsecp256k1_v0_4_1_fe_mul(&u2, &b->x, &zz); /* u2 = U2 = X2*Z1^2 (1) */
551 s1 = a->y; rustsecp256k1_v0_4_1_fe_normalize_weak(&s1); /* s1 = S1 = Y1*Z2^3 (1) */
552 rustsecp256k1_v0_4_1_fe_mul(&s2, &b->y, &zz); /* s2 = Y2*Z1^2 (1) */
553 rustsecp256k1_v0_4_1_fe_mul(&s2, &s2, &a->z); /* s2 = S2 = Y2*Z1^3 (1) */
554 t = u1; rustsecp256k1_v0_4_1_fe_add(&t, &u2); /* t = T = U1+U2 (2) */
555 m = s1; rustsecp256k1_v0_4_1_fe_add(&m, &s2); /* m = M = S1+S2 (2) */
556 rustsecp256k1_v0_4_1_fe_sqr(&rr, &t); /* rr = T^2 (1) */
557 rustsecp256k1_v0_4_1_fe_negate(&m_alt, &u2, 1); /* Malt = -X2*Z1^2 */
558 rustsecp256k1_v0_4_1_fe_mul(&tt, &u1, &m_alt); /* tt = -U1*U2 (2) */
559 rustsecp256k1_v0_4_1_fe_add(&rr, &tt); /* rr = R = T^2-U1*U2 (3) */
560 /** If lambda = R/M = 0/0 we have a problem (except in the "trivial"
561 * case that Z = z1z2 = 0, and this is special-cased later on). */
562 degenerate = rustsecp256k1_v0_4_1_fe_normalizes_to_zero(&m) &
563 rustsecp256k1_v0_4_1_fe_normalizes_to_zero(&rr);
564 /* This only occurs when y1 == -y2 and x1^3 == x2^3, but x1 != x2.
565 * This means either x1 == beta*x2 or beta*x1 == x2, where beta is
566 * a nontrivial cube root of one. In either case, an alternate
567 * non-indeterminate expression for lambda is (y1 - y2)/(x1 - x2),
568 * so we set R/M equal to this. */
569 rr_alt = s1;
570 rustsecp256k1_v0_4_1_fe_mul_int(&rr_alt, 2); /* rr = Y1*Z2^3 - Y2*Z1^3 (2) */
571 rustsecp256k1_v0_4_1_fe_add(&m_alt, &u1); /* Malt = X1*Z2^2 - X2*Z1^2 */
572
573 rustsecp256k1_v0_4_1_fe_cmov(&rr_alt, &rr, !degenerate);
574 rustsecp256k1_v0_4_1_fe_cmov(&m_alt, &m, !degenerate);
575 /* Now Ralt / Malt = lambda and is guaranteed not to be 0/0.
576 * From here on out Ralt and Malt represent the numerator
577 * and denominator of lambda; R and M represent the explicit
578 * expressions x1^2 + x2^2 + x1x2 and y1 + y2. */
579 rustsecp256k1_v0_4_1_fe_sqr(&n, &m_alt); /* n = Malt^2 (1) */
580 rustsecp256k1_v0_4_1_fe_mul(&q, &n, &t); /* q = Q = T*Malt^2 (1) */
581 /* These two lines use the observation that either M == Malt or M == 0,
582 * so M^3 * Malt is either Malt^4 (which is computed by squaring), or
583 * zero (which is "computed" by cmov). So the cost is one squaring
584 * versus two multiplications. */
585 rustsecp256k1_v0_4_1_fe_sqr(&n, &n);
586 rustsecp256k1_v0_4_1_fe_cmov(&n, &m, degenerate); /* n = M^3 * Malt (2) */
587 rustsecp256k1_v0_4_1_fe_sqr(&t, &rr_alt); /* t = Ralt^2 (1) */
588 rustsecp256k1_v0_4_1_fe_mul(&r->z, &a->z, &m_alt); /* r->z = Malt*Z (1) */
589 infinity = rustsecp256k1_v0_4_1_fe_normalizes_to_zero(&r->z) & ~a->infinity;
590 rustsecp256k1_v0_4_1_fe_mul_int(&r->z, 2); /* r->z = Z3 = 2*Malt*Z (2) */
591 rustsecp256k1_v0_4_1_fe_negate(&q, &q, 1); /* q = -Q (2) */
592 rustsecp256k1_v0_4_1_fe_add(&t, &q); /* t = Ralt^2-Q (3) */
593 rustsecp256k1_v0_4_1_fe_normalize_weak(&t);
594 r->x = t; /* r->x = Ralt^2-Q (1) */
595 rustsecp256k1_v0_4_1_fe_mul_int(&t, 2); /* t = 2*x3 (2) */
596 rustsecp256k1_v0_4_1_fe_add(&t, &q); /* t = 2*x3 - Q: (4) */
597 rustsecp256k1_v0_4_1_fe_mul(&t, &t, &rr_alt); /* t = Ralt*(2*x3 - Q) (1) */
598 rustsecp256k1_v0_4_1_fe_add(&t, &n); /* t = Ralt*(2*x3 - Q) + M^3*Malt (3) */
599 rustsecp256k1_v0_4_1_fe_negate(&r->y, &t, 3); /* r->y = Ralt*(Q - 2x3) - M^3*Malt (4) */
600 rustsecp256k1_v0_4_1_fe_normalize_weak(&r->y);
601 rustsecp256k1_v0_4_1_fe_mul_int(&r->x, 4); /* r->x = X3 = 4*(Ralt^2-Q) */
602 rustsecp256k1_v0_4_1_fe_mul_int(&r->y, 4); /* r->y = Y3 = 4*Ralt*(Q - 2x3) - 4*M^3*Malt (4) */
603
604 /** In case a->infinity == 1, replace r with (b->x, b->y, 1). */
605 rustsecp256k1_v0_4_1_fe_cmov(&r->x, &b->x, a->infinity);
606 rustsecp256k1_v0_4_1_fe_cmov(&r->y, &b->y, a->infinity);
607 rustsecp256k1_v0_4_1_fe_cmov(&r->z, &fe_1, a->infinity);
608 r->infinity = infinity;
609 }
610
rustsecp256k1_v0_4_1_gej_rescale(rustsecp256k1_v0_4_1_gej * r,const rustsecp256k1_v0_4_1_fe * s)611 static void rustsecp256k1_v0_4_1_gej_rescale(rustsecp256k1_v0_4_1_gej *r, const rustsecp256k1_v0_4_1_fe *s) {
612 /* Operations: 4 mul, 1 sqr */
613 rustsecp256k1_v0_4_1_fe zz;
614 VERIFY_CHECK(!rustsecp256k1_v0_4_1_fe_is_zero(s));
615 rustsecp256k1_v0_4_1_fe_sqr(&zz, s);
616 rustsecp256k1_v0_4_1_fe_mul(&r->x, &r->x, &zz); /* r->x *= s^2 */
617 rustsecp256k1_v0_4_1_fe_mul(&r->y, &r->y, &zz);
618 rustsecp256k1_v0_4_1_fe_mul(&r->y, &r->y, s); /* r->y *= s^3 */
619 rustsecp256k1_v0_4_1_fe_mul(&r->z, &r->z, s); /* r->z *= s */
620 }
621
rustsecp256k1_v0_4_1_ge_to_storage(rustsecp256k1_v0_4_1_ge_storage * r,const rustsecp256k1_v0_4_1_ge * a)622 static void rustsecp256k1_v0_4_1_ge_to_storage(rustsecp256k1_v0_4_1_ge_storage *r, const rustsecp256k1_v0_4_1_ge *a) {
623 rustsecp256k1_v0_4_1_fe x, y;
624 VERIFY_CHECK(!a->infinity);
625 x = a->x;
626 rustsecp256k1_v0_4_1_fe_normalize(&x);
627 y = a->y;
628 rustsecp256k1_v0_4_1_fe_normalize(&y);
629 rustsecp256k1_v0_4_1_fe_to_storage(&r->x, &x);
630 rustsecp256k1_v0_4_1_fe_to_storage(&r->y, &y);
631 }
632
rustsecp256k1_v0_4_1_ge_from_storage(rustsecp256k1_v0_4_1_ge * r,const rustsecp256k1_v0_4_1_ge_storage * a)633 static void rustsecp256k1_v0_4_1_ge_from_storage(rustsecp256k1_v0_4_1_ge *r, const rustsecp256k1_v0_4_1_ge_storage *a) {
634 rustsecp256k1_v0_4_1_fe_from_storage(&r->x, &a->x);
635 rustsecp256k1_v0_4_1_fe_from_storage(&r->y, &a->y);
636 r->infinity = 0;
637 }
638
rustsecp256k1_v0_4_1_ge_storage_cmov(rustsecp256k1_v0_4_1_ge_storage * r,const rustsecp256k1_v0_4_1_ge_storage * a,int flag)639 static SECP256K1_INLINE void rustsecp256k1_v0_4_1_ge_storage_cmov(rustsecp256k1_v0_4_1_ge_storage *r, const rustsecp256k1_v0_4_1_ge_storage *a, int flag) {
640 rustsecp256k1_v0_4_1_fe_storage_cmov(&r->x, &a->x, flag);
641 rustsecp256k1_v0_4_1_fe_storage_cmov(&r->y, &a->y, flag);
642 }
643
rustsecp256k1_v0_4_1_ge_mul_lambda(rustsecp256k1_v0_4_1_ge * r,const rustsecp256k1_v0_4_1_ge * a)644 static void rustsecp256k1_v0_4_1_ge_mul_lambda(rustsecp256k1_v0_4_1_ge *r, const rustsecp256k1_v0_4_1_ge *a) {
645 static const rustsecp256k1_v0_4_1_fe beta = SECP256K1_FE_CONST(
646 0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
647 0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
648 );
649 *r = *a;
650 rustsecp256k1_v0_4_1_fe_mul(&r->x, &r->x, &beta);
651 }
652
rustsecp256k1_v0_4_1_ge_is_in_correct_subgroup(const rustsecp256k1_v0_4_1_ge * ge)653 static int rustsecp256k1_v0_4_1_ge_is_in_correct_subgroup(const rustsecp256k1_v0_4_1_ge* ge) {
654 #ifdef EXHAUSTIVE_TEST_ORDER
655 rustsecp256k1_v0_4_1_gej out;
656 int i;
657
658 /* A very simple EC multiplication ladder that avoids a dependency on ecmult. */
659 rustsecp256k1_v0_4_1_gej_set_infinity(&out);
660 for (i = 0; i < 32; ++i) {
661 rustsecp256k1_v0_4_1_gej_double_var(&out, &out, NULL);
662 if ((((uint32_t)EXHAUSTIVE_TEST_ORDER) >> (31 - i)) & 1) {
663 rustsecp256k1_v0_4_1_gej_add_ge_var(&out, &out, ge, NULL);
664 }
665 }
666 return rustsecp256k1_v0_4_1_gej_is_infinity(&out);
667 #else
668 (void)ge;
669 /* The real secp256k1 group has cofactor 1, so the subgroup is the entire curve. */
670 return 1;
671 #endif
672 }
673
674 #endif /* SECP256K1_GROUP_IMPL_H */
675