b0ab12e6 |
1 | /* -*-c-*- |
2 | * |
b0ab12e6 |
3 | * Elliptic curves over prime fields |
4 | * |
5 | * (c) 2001 Straylight/Edgeware |
6 | */ |
7 | |
45c0fd36 |
8 | /*----- Licensing notice --------------------------------------------------* |
b0ab12e6 |
9 | * |
10 | * This file is part of Catacomb. |
11 | * |
12 | * Catacomb is free software; you can redistribute it and/or modify |
13 | * it under the terms of the GNU Library General Public License as |
14 | * published by the Free Software Foundation; either version 2 of the |
15 | * License, or (at your option) any later version. |
45c0fd36 |
16 | * |
b0ab12e6 |
17 | * Catacomb is distributed in the hope that it will be useful, |
18 | * but WITHOUT ANY WARRANTY; without even the implied warranty of |
19 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
20 | * GNU Library General Public License for more details. |
45c0fd36 |
21 | * |
b0ab12e6 |
22 | * You should have received a copy of the GNU Library General Public |
23 | * License along with Catacomb; if not, write to the Free |
24 | * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, |
25 | * MA 02111-1307, USA. |
26 | */ |
27 | |
b0ab12e6 |
28 | /*----- Header files ------------------------------------------------------*/ |
29 | |
41cb1beb |
30 | #include <mLib/sub.h> |
31 | |
b0ab12e6 |
32 | #include "ec.h" |
33 | |
dbfee00a |
34 | /*----- Simple prime curves -----------------------------------------------*/ |
b0ab12e6 |
35 | |
8823192f |
36 | static const ec_ops ec_primeops, ec_primeprojops, ec_primeprojxops; |
41cb1beb |
37 | |
38 | static ec *ecneg(ec_curve *c, ec *d, const ec *p) |
b085fd91 |
39 | { |
40 | EC_COPY(d, p); |
ceb3f0c0 |
41 | if (d->y) |
42 | d->y = F_NEG(c->f, d->y, d->y); |
b085fd91 |
43 | return (d); |
44 | } |
45 | |
8823192f |
46 | static ec *ecfind(ec_curve *c, ec *d, mp *x) |
47 | { |
48 | mp *p, *q; |
8823192f |
49 | field *f = c->f; |
50 | |
51 | q = F_SQR(f, MP_NEW, x); |
52 | p = F_MUL(f, MP_NEW, x, q); |
432c4e18 |
53 | q = F_MUL(f, q, x, c->a); |
8823192f |
54 | p = F_ADD(f, p, p, q); |
432c4e18 |
55 | p = F_ADD(f, p, p, c->b); |
8823192f |
56 | MP_DROP(q); |
57 | p = F_SQRT(f, p, p); |
58 | if (!p) |
59 | return (0); |
60 | EC_DESTROY(d); |
61 | d->x = MP_COPY(x); |
62 | d->y = p; |
63 | d->z = MP_COPY(f->one); |
b085fd91 |
64 | return (d); |
65 | } |
66 | |
67 | static ec *ecdbl(ec_curve *c, ec *d, const ec *a) |
b0ab12e6 |
68 | { |
1ccdb13a |
69 | if (EC_ATINF(a) || F_ZEROP(c->f, a->y)) |
b085fd91 |
70 | EC_SETINF(d); |
b085fd91 |
71 | else { |
72 | field *f = c->f; |
b085fd91 |
73 | mp *lambda; |
74 | mp *dy, *dx; |
75 | |
8823192f |
76 | dx = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */ |
77 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y$% */ |
78 | dx = F_TPL(f, dx, dx); /* %$3 x^2$% */ |
432c4e18 |
79 | dx = F_ADD(f, dx, dx, c->a); /* %$3 x^2 + A$% */ |
8823192f |
80 | dy = F_INV(f, dy, dy); /* %$(2 y)^{-1}$% */ |
81 | lambda = F_MUL(f, MP_NEW, dx, dy); /* %$\lambda = (3 x^2 + A)/(2 y)$% */ |
b085fd91 |
82 | |
8823192f |
83 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
84 | dy = F_DBL(f, dy, a->x); /* %$2 x$% */ |
85 | dx = F_SUB(f, dx, dx, dy); /* %$x' = \lambda^2 - 2 x */ |
86 | dy = F_SUB(f, dy, a->x, dx); /* %$x - x'$% */ |
87 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x - x')$% */ |
88 | dy = F_SUB(f, dy, dy, a->y); /* %$y' = \lambda (x - x') - y$% */ |
b0ab12e6 |
89 | |
b085fd91 |
90 | EC_DESTROY(d); |
91 | d->x = dx; |
92 | d->y = dy; |
93 | d->z = 0; |
94 | MP_DROP(lambda); |
95 | } |
96 | return (d); |
97 | } |
98 | |
8823192f |
99 | static ec *ecprojdbl(ec_curve *c, ec *d, const ec *a) |
100 | { |
1ccdb13a |
101 | if (EC_ATINF(a) || F_ZEROP(c->f, a->y)) |
8823192f |
102 | EC_SETINF(d); |
8823192f |
103 | else { |
104 | field *f = c->f; |
8823192f |
105 | mp *p, *q, *m, *s, *dx, *dy, *dz; |
106 | |
107 | p = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */ |
108 | q = F_SQR(f, MP_NEW, p); /* %$z^4$% */ |
432c4e18 |
109 | p = F_MUL(f, p, q, c->a); /* %$A z^4$% */ |
8823192f |
110 | m = F_SQR(f, MP_NEW, a->x); /* %$x^2$% */ |
111 | m = F_TPL(f, m, m); /* %$3 x^2$% */ |
112 | m = F_ADD(f, m, m, p); /* %$m = 3 x^2 + A z^4$% */ |
113 | |
114 | q = F_DBL(f, q, a->y); /* %$2 y$% */ |
115 | dz = F_MUL(f, MP_NEW, q, a->z); /* %$z' = 2 y z$% */ |
116 | |
117 | p = F_SQR(f, p, q); /* %$4 y^2$% */ |
118 | s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */ |
119 | q = F_SQR(f, q, p); /* %$16 y^4$% */ |
120 | q = F_HLV(f, q, q); /* %$t = 8 y^4$% */ |
121 | |
122 | p = F_DBL(f, p, s); /* %$2 s$% */ |
123 | dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */ |
124 | dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */ |
125 | |
126 | s = F_SUB(f, s, s, dx); /* %$s - x'$% */ |
127 | dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */ |
128 | dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */ |
129 | |
130 | EC_DESTROY(d); |
131 | d->x = dx; |
132 | d->y = dy; |
133 | d->z = dz; |
134 | MP_DROP(m); |
135 | MP_DROP(q); |
136 | MP_DROP(s); |
137 | } |
138 | return (d); |
139 | } |
140 | |
141 | static ec *ecprojxdbl(ec_curve *c, ec *d, const ec *a) |
142 | { |
1ccdb13a |
143 | if (EC_ATINF(a) || F_ZEROP(c->f, a->y)) |
8823192f |
144 | EC_SETINF(d); |
8823192f |
145 | else { |
146 | field *f = c->f; |
147 | mp *p, *q, *m, *s, *dx, *dy, *dz; |
148 | |
149 | m = F_SQR(f, MP_NEW, a->z); /* %$z^2$% */ |
150 | p = F_SUB(f, MP_NEW, a->x, m); /* %$x - z^2$% */ |
151 | q = F_ADD(f, MP_NEW, a->x, m); /* %$x + z^2$% */ |
152 | m = F_MUL(f, m, p, q); /* %$x^2 - z^4$% */ |
153 | m = F_TPL(f, m, m); /* %$m = 3 x^2 - 3 z^4$% */ |
154 | |
155 | q = F_DBL(f, q, a->y); /* %$2 y$% */ |
156 | dz = F_MUL(f, MP_NEW, q, a->z); /* %$z' = 2 y z$% */ |
157 | |
158 | p = F_SQR(f, p, q); /* %$4 y^2$% */ |
159 | s = F_MUL(f, MP_NEW, p, a->x); /* %$s = 4 x y^2$% */ |
160 | q = F_SQR(f, q, p); /* %$16 y^4$% */ |
161 | q = F_HLV(f, q, q); /* %$t = 8 y^4$% */ |
162 | |
163 | p = F_DBL(f, p, s); /* %$2 s$% */ |
164 | dx = F_SQR(f, MP_NEW, m); /* %$m^2$% */ |
165 | dx = F_SUB(f, dx, dx, p); /* %$x' = m^2 - 2 s$% */ |
166 | |
167 | s = F_SUB(f, s, s, dx); /* %$s - x'$% */ |
168 | dy = F_MUL(f, p, m, s); /* %$m (s - x')$% */ |
169 | dy = F_SUB(f, dy, dy, q); /* %$y' = m (s - x') - t$% */ |
170 | |
171 | EC_DESTROY(d); |
172 | d->x = dx; |
173 | d->y = dy; |
174 | d->z = dz; |
175 | MP_DROP(m); |
176 | MP_DROP(q); |
177 | MP_DROP(s); |
178 | } |
179 | return (d); |
180 | } |
181 | |
b085fd91 |
182 | static ec *ecadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
183 | { |
b0ab12e6 |
184 | if (a == b) |
185 | ecdbl(c, d, a); |
186 | else if (EC_ATINF(a)) |
187 | EC_COPY(d, b); |
188 | else if (EC_ATINF(b)) |
189 | EC_COPY(d, a); |
b085fd91 |
190 | else { |
191 | field *f = c->f; |
192 | mp *lambda; |
193 | mp *dy, *dx; |
194 | |
195 | if (!MP_EQ(a->x, b->x)) { |
8823192f |
196 | dy = F_SUB(f, MP_NEW, a->y, b->y); /* %$y_0 - y_1$% */ |
197 | dx = F_SUB(f, MP_NEW, a->x, b->x); /* %$x_0 - x_1$% */ |
198 | dx = F_INV(f, dx, dx); /* %$(x_0 - x_1)^{-1}$% */ |
b085fd91 |
199 | lambda = F_MUL(f, MP_NEW, dy, dx); |
8823192f |
200 | /* %$\lambda = (y_0 - y1)/(x_0 - x_1)$% */ |
201 | } else if (F_ZEROP(c->f, a->y) || !MP_EQ(a->y, b->y)) { |
b0ab12e6 |
202 | EC_SETINF(d); |
b085fd91 |
203 | return (d); |
204 | } else { |
8823192f |
205 | dx = F_SQR(f, MP_NEW, a->x); /* %$x_0^2$% */ |
206 | dx = F_TPL(f, dx, dx); /* %$3 x_0^2$% */ |
432c4e18 |
207 | dx = F_ADD(f, dx, dx, c->a); /* %$3 x_0^2 + A$% */ |
8823192f |
208 | dy = F_DBL(f, MP_NEW, a->y); /* %$2 y_0$% */ |
209 | dy = F_INV(f, dy, dy); /* %$(2 y_0)^{-1}$% */ |
41cb1beb |
210 | lambda = F_MUL(f, MP_NEW, dx, dy); |
8823192f |
211 | /* %$\lambda = (3 x_0^2 + A)/(2 y_0)$% */ |
b085fd91 |
212 | } |
213 | |
8823192f |
214 | dx = F_SQR(f, dx, lambda); /* %$\lambda^2$% */ |
215 | dx = F_SUB(f, dx, dx, a->x); /* %$\lambda^2 - x_0$% */ |
216 | dx = F_SUB(f, dx, dx, b->x); /* %$x' = \lambda^2 - x_0 - x_1$% */ |
217 | dy = F_SUB(f, dy, b->x, dx); /* %$x_1 - x'$% */ |
218 | dy = F_MUL(f, dy, lambda, dy); /* %$\lambda (x_1 - x')$% */ |
ceb3f0c0 |
219 | dy = F_SUB(f, dy, dy, b->y); /* %$y' = \lambda (x_1 - x') - y_1$% */ |
b0ab12e6 |
220 | |
b085fd91 |
221 | EC_DESTROY(d); |
222 | d->x = dx; |
223 | d->y = dy; |
224 | d->z = 0; |
225 | MP_DROP(lambda); |
b0ab12e6 |
226 | } |
b085fd91 |
227 | return (d); |
b0ab12e6 |
228 | } |
229 | |
8823192f |
230 | static ec *ecprojadd(ec_curve *c, ec *d, const ec *a, const ec *b) |
231 | { |
232 | if (a == b) |
233 | c->ops->dbl(c, d, a); |
234 | else if (EC_ATINF(a)) |
235 | EC_COPY(d, b); |
236 | else if (EC_ATINF(b)) |
237 | EC_COPY(d, a); |
238 | else { |
239 | field *f = c->f; |
391faf42 |
240 | mp *p, *q, *r, *w, *u, *uu, *s, *ss, *dx, *dy, *dz; |
8823192f |
241 | |
242 | q = F_SQR(f, MP_NEW, a->z); /* %$z_0^2$% */ |
243 | u = F_MUL(f, MP_NEW, q, b->x); /* %$u = x_1 z_0^2$% */ |
244 | p = F_MUL(f, MP_NEW, q, b->y); /* %$y_1 z_0^2$% */ |
245 | s = F_MUL(f, q, p, a->z); /* %$s = y_1 z_0^3$% */ |
246 | |
391faf42 |
247 | q = F_SQR(f, MP_NEW, b->z); /* %$z_1^2$% */ |
248 | uu = F_MUL(f, MP_NEW, q, a->x); /* %$uu = x_0 z_1^2$%*/ |
249 | p = F_MUL(f, p, q, a->y); /* %$y_0 z_1^2$% */ |
250 | ss = F_MUL(f, q, p, b->z); /* %$ss = y_0 z_1^3$% */ |
251 | |
252 | w = F_SUB(f, p, uu, u); /* %$w = uu - u$% */ |
253 | r = F_SUB(f, MP_NEW, ss, s); /* %$r = ss - s$% */ |
8823192f |
254 | if (F_ZEROP(f, w)) { |
ceb3f0c0 |
255 | MP_DROP(w); |
256 | MP_DROP(u); |
257 | MP_DROP(s); |
391faf42 |
258 | MP_DROP(uu); |
259 | MP_DROP(ss); |
8823192f |
260 | if (F_ZEROP(f, r)) { |
8823192f |
261 | MP_DROP(r); |
8823192f |
262 | return (c->ops->dbl(c, d, a)); |
263 | } else { |
8823192f |
264 | MP_DROP(r); |
8823192f |
265 | EC_SETINF(d); |
266 | return (d); |
267 | } |
268 | } |
391faf42 |
269 | u = F_ADD(f, u, u, uu); /* %$t = uu + u$% */ |
270 | s = F_ADD(f, s, s, ss); /* %$m = ss + r$% */ |
8823192f |
271 | |
391faf42 |
272 | uu = F_MUL(f, uu, a->z, w); /* %$z_0 w$% */ |
273 | dz = F_MUL(f, ss, uu, b->z); /* %$z' = z_0 z_1 w$% */ |
8823192f |
274 | |
391faf42 |
275 | p = F_SQR(f, uu, w); /* %$w^2$% */ |
8823192f |
276 | q = F_MUL(f, MP_NEW, p, u); /* %$t w^2$% */ |
277 | u = F_MUL(f, u, p, w); /* %$w^3$% */ |
278 | p = F_MUL(f, p, u, s); /* %$m w^3$% */ |
45c0fd36 |
279 | |
8823192f |
280 | dx = F_SQR(f, u, r); /* %$r^2$% */ |
281 | dx = F_SUB(f, dx, dx, q); /* %$x' = r^2 - t w^2$% */ |
282 | |
283 | s = F_DBL(f, s, dx); /* %$2 x'$% */ |
284 | q = F_SUB(f, q, q, s); /* %$v = t w^2 - 2 x'$% */ |
285 | dy = F_MUL(f, s, q, r); /* %$v r$% */ |
286 | dy = F_SUB(f, dy, dy, p); /* %$v r - m w^3$% */ |
287 | dy = F_HLV(f, dy, dy); /* %$y' = (v r - m w^3)/2$% */ |
288 | |
289 | EC_DESTROY(d); |
290 | d->x = dx; |
291 | d->y = dy; |
292 | d->z = dz; |
293 | MP_DROP(p); |
294 | MP_DROP(q); |
295 | MP_DROP(r); |
296 | MP_DROP(w); |
297 | } |
298 | return (d); |
299 | } |
300 | |
301 | static int eccheck(ec_curve *c, const ec *p) |
302 | { |
8823192f |
303 | field *f = c->f; |
34e4f738 |
304 | mp *l, *x, *r; |
8823192f |
305 | int rc; |
34e4f738 |
306 | if (EC_ATINF(p)) return (0); |
307 | l = F_SQR(f, MP_NEW, p->y); |
308 | x = F_SQR(f, MP_NEW, p->x); |
309 | r = F_MUL(f, MP_NEW, x, p->x); |
432c4e18 |
310 | x = F_MUL(f, x, c->a, p->x); |
8823192f |
311 | r = F_ADD(f, r, r, x); |
432c4e18 |
312 | r = F_ADD(f, r, r, c->b); |
8823192f |
313 | rc = MP_EQ(l, r) ? 0 : -1; |
314 | mp_drop(l); |
315 | mp_drop(x); |
316 | mp_drop(r); |
317 | return (rc); |
318 | } |
319 | |
320 | static int ecprojcheck(ec_curve *c, const ec *p) |
321 | { |
322 | ec t = EC_INIT; |
323 | int rc; |
45c0fd36 |
324 | |
8823192f |
325 | c->ops->fix(c, &t, p); |
326 | rc = eccheck(c, &t); |
327 | EC_DESTROY(&t); |
328 | return (rc); |
329 | } |
330 | |
41cb1beb |
331 | static void ecdestroy(ec_curve *c) |
332 | { |
432c4e18 |
333 | MP_DROP(c->a); |
334 | MP_DROP(c->b); |
335 | DESTROY(c); |
41cb1beb |
336 | } |
337 | |
338 | /* --- @ec_prime@, @ec_primeproj@ --- * |
339 | * |
dbfee00a |
340 | * Arguments: @field *f@ = the underlying field for this elliptic curve |
41cb1beb |
341 | * @mp *a, *b@ = the coefficients for this curve |
342 | * |
02d7884d |
343 | * Returns: A pointer to the curve, or null. |
41cb1beb |
344 | * |
345 | * Use: Creates a curve structure for an elliptic curve defined over |
346 | * a prime field. The @primeproj@ variant uses projective |
347 | * coordinates, which can be a win. |
348 | */ |
349 | |
350 | extern ec_curve *ec_prime(field *f, mp *a, mp *b) |
351 | { |
432c4e18 |
352 | ec_curve *c = CREATE(ec_curve); |
353 | c->ops = &ec_primeops; |
354 | c->f = f; |
355 | c->a = F_IN(f, MP_NEW, a); |
356 | c->b = F_IN(f, MP_NEW, b); |
357 | return (c); |
41cb1beb |
358 | } |
359 | |
8823192f |
360 | extern ec_curve *ec_primeproj(field *f, mp *a, mp *b) |
361 | { |
432c4e18 |
362 | ec_curve *c = CREATE(ec_curve); |
8823192f |
363 | mp *ax; |
364 | |
365 | ax = mp_add(MP_NEW, a, MP_THREE); |
366 | ax = F_IN(f, ax, ax); |
367 | if (F_ZEROP(f, ax)) |
432c4e18 |
368 | c->ops = &ec_primeprojxops; |
8823192f |
369 | else |
432c4e18 |
370 | c->ops = &ec_primeprojops; |
8823192f |
371 | MP_DROP(ax); |
432c4e18 |
372 | c->f = f; |
373 | c->a = F_IN(f, MP_NEW, a); |
374 | c->b = F_IN(f, MP_NEW, b); |
375 | return (c); |
41cb1beb |
376 | } |
377 | |
378 | static const ec_ops ec_primeops = { |
f94b972d |
379 | "prime", |
34e4f738 |
380 | ecdestroy, ec_stdsamep, ec_idin, ec_idout, ec_idfix, |
bc985cef |
381 | ecfind, ecneg, ecadd, ec_stdsub, ecdbl, eccheck |
8823192f |
382 | }; |
383 | |
384 | static const ec_ops ec_primeprojops = { |
f94b972d |
385 | "primeproj", |
34e4f738 |
386 | ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix, |
bc985cef |
387 | ecfind, ecneg, ecprojadd, ec_stdsub, ecprojdbl, ecprojcheck |
8823192f |
388 | }; |
389 | |
390 | static const ec_ops ec_primeprojxops = { |
f94b972d |
391 | "primeproj", |
34e4f738 |
392 | ecdestroy, ec_stdsamep, ec_projin, ec_projout, ec_projfix, |
bc985cef |
393 | ecfind, ecneg, ecprojadd, ec_stdsub, ecprojxdbl, ecprojcheck |
41cb1beb |
394 | }; |
395 | |
396 | /*----- Test rig ----------------------------------------------------------*/ |
397 | |
398 | #ifdef TEST_RIG |
399 | |
400 | #define MP(x) mp_readstring(MP_NEW, #x, 0, 0) |
401 | |
ceb3f0c0 |
402 | int main(int argc, char *argv[]) |
41cb1beb |
403 | { |
404 | field *f; |
405 | ec_curve *c; |
406 | ec g = EC_INIT, d = EC_INIT; |
407 | mp *p, *a, *b, *r; |
ceb3f0c0 |
408 | int i, n = argc == 1 ? 1 : atoi(argv[1]); |
41cb1beb |
409 | |
dbfee00a |
410 | printf("ec-prime: "); |
411 | fflush(stdout); |
41cb1beb |
412 | a = MP(-3); |
432c4e18 |
413 | b = MP(0xb3312fa7e23ee7e4988e056be3f82d19181d9c6efe8141120314088f5013875ac656398d8a2ed19d2a85c8edd3ec2aef); |
414 | p = MP(39402006196394479212279040100143613805079739270465446667948293404245721771496870329047266088258938001861606973112319); |
415 | r = MP(39402006196394479212279040100143613805079739270465446667946905279627659399113263569398956308152294913554433653942642); |
41cb1beb |
416 | |
f46efa79 |
417 | f = field_niceprime(p); |
ceb3f0c0 |
418 | c = ec_primeproj(f, a, b); |
45c0fd36 |
419 | |
432c4e18 |
420 | g.x = MP(0xaa87ca22be8b05378eb1c71ef320ad746e1d3b628ba79b9859f741e082542a385502f25dbf55296c3a545e3872760ab7); |
421 | g.y = MP(0x3617de4a96262c6f5d9e98bf9292dc29f8f41dbd289a147ce9da3113b5f0b8c00a60b1ce1d7e819d7a431d7c90ea0e5f); |
41cb1beb |
422 | |
45c0fd36 |
423 | for (i = 0; i < n; i++) { |
ceb3f0c0 |
424 | ec_mul(c, &d, &g, r); |
425 | if (EC_ATINF(&d)) { |
426 | fprintf(stderr, "zero too early\n"); |
427 | return (1); |
428 | } |
429 | ec_add(c, &d, &d, &g); |
430 | if (!EC_ATINF(&d)) { |
431 | fprintf(stderr, "didn't reach zero\n"); |
432 | MP_EPRINT("d.x", d.x); |
433 | MP_EPRINT("d.y", d.y); |
434 | return (1); |
435 | } |
436 | ec_destroy(&d); |
dbfee00a |
437 | } |
41cb1beb |
438 | ec_destroy(&g); |
439 | ec_destroycurve(c); |
440 | F_DESTROY(f); |
dbfee00a |
441 | MP_DROP(p); MP_DROP(a); MP_DROP(b); MP_DROP(r); |
442 | assert(!mparena_count(&mparena_global)); |
443 | printf("ok\n"); |
41cb1beb |
444 | return (0); |
445 | } |
446 | |
447 | #endif |
448 | |
b0ab12e6 |
449 | /*----- That's all, folks -------------------------------------------------*/ |