Annotation of OpenXM_contrib2/asir2018/builtin/ec.c, Revision 1.2
1.1 noro 1: /*
2: * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
3: * All rights reserved.
4: *
5: * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
6: * non-exclusive and royalty-free license to use, copy, modify and
7: * redistribute, solely for non-commercial and non-profit purposes, the
8: * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
9: * conditions of this Agreement. For the avoidance of doubt, you acquire
10: * only a limited right to use the SOFTWARE hereunder, and FLL or any
11: * third party developer retains all rights, including but not limited to
12: * copyrights, in and to the SOFTWARE.
13: *
14: * (1) FLL does not grant you a license in any way for commercial
15: * purposes. You may use the SOFTWARE only for non-commercial and
16: * non-profit purposes only, such as academic, research and internal
17: * business use.
18: * (2) The SOFTWARE is protected by the Copyright Law of Japan and
19: * international copyright treaties. If you make copies of the SOFTWARE,
20: * with or without modification, as permitted hereunder, you shall affix
21: * to all such copies of the SOFTWARE the above copyright notice.
22: * (3) An explicit reference to this SOFTWARE and its copyright owner
23: * shall be made on your publication or presentation in any form of the
24: * results obtained by use of the SOFTWARE.
25: * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
27: * for such modification or the source code of the modified part of the
28: * SOFTWARE.
29: *
30: * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
31: * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
32: * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
33: * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
43: * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
44: * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
45: * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
46: * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
47: *
1.2 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2018/builtin/ec.c,v 1.1 2018/09/19 05:45:05 noro Exp $
1.1 noro 49: */
50: #include "ca.h"
51: #include "parse.h"
52: #include "inline.h"
53:
54: /*
55: * Elliptic curve related functions
56: *
57: * Argument specifications
58: * Point = vector(x,y,z) (projective representation)
59: * ECInfo = vector(a,b,p)
60: * a,b : integer for GF(p), GF2N for GF(2^n)
61: * p : integer for GF(p), polynomial for GF(2^n)
62: *
63: */
64:
65: struct oKeyIndexPair {
66: unsigned int key;
67: int index;
68: };
69:
70: void Psha1();
71: void Psha1_ec();
72: void Pecm_add_ff();
73: void Pecm_chsgn_ff();
74: void Pecm_sub_ff();
75: void Pecm_compute_all_key_homo_ff();
76: void Pnextvect1(),Psort_ktarray(),Pecm_find_match(),Pseparate_vect();
77: void Pecm_set_addcounter();
78: void Pecm_count_order();
79:
80: void ecm_add_ff(VECT,VECT,VECT,VECT *);
81: void ecm_add_gfp(VECT,VECT,VECT,VECT *);
82: void ecm_add_gf2n(VECT,VECT,VECT,VECT *);
83:
84: void ecm_chsgn_ff(VECT,VECT *);
85: void ecm_sub_ff(VECT,VECT,VECT,VECT *);
86:
87: void compute_all_key_homo_gfp(VECT *,int,unsigned int *);
88: void compute_all_key_homo_gf2n(VECT *,int,unsigned int *);
89:
90: unsigned int separate_vect(double *,int);
91: void ecm_find_match(unsigned int *,int,unsigned int *,int,LIST *);
92: int find_match(unsigned int,unsigned int *,int);
93:
94: void sort_ktarray(VECT,VECT,LIST *);
95: int comp_kip(struct oKeyIndexPair *,struct oKeyIndexPair *);
96:
97: int nextvect1(VECT,VECT);
98:
99: unsigned int ecm_count_order_gfp(unsigned int,unsigned int,unsigned int);
100: unsigned int ecm_count_order_gf2n(UP2,GF2N,GF2N);
101:
102: void sha_memory(unsigned char *,unsigned int,unsigned int *);
103:
104: unsigned int ecm_addcounter;
105: extern int current_ff,lm_lazy;
106:
107: struct ftab ec_tab[] = {
108: /* point addition */
109: {"ecm_add_ff",Pecm_add_ff,3},
110:
111: /* point change sign */
112: {"ecm_chsgn_ff",Pecm_chsgn_ff,1},
113:
114: /* point subtraction */
115: {"ecm_sub_ff",Pecm_sub_ff,3},
116:
117: /* key computation for sort and match */
118: {"ecm_compute_all_key_homo_ff",Pecm_compute_all_key_homo_ff,1},
119:
120: /* exhausitve search of rational points */
121: {"ecm_count_order",Pecm_count_order,1},
122:
123: /* common functions */
124: {"nextvect1",Pnextvect1,2},
125: {"sort_ktarray",Psort_ktarray,2},
126: {"separate_vect",Pseparate_vect,1},
127: {"ecm_find_match",Pecm_find_match,2},
128: {"ecm_set_addcounter",Pecm_set_addcounter,-1},
129: {"sha1",Psha1,-2},
130: #if 0
131: {"sha1_free",Psha1_free,1},
132: #endif
133: {0,0,0},
134: };
135:
136: void Psha1(NODE arg,Z *rp)
137: {
138: unsigned char *s;
139: unsigned int digest[5];
140: size_t bl;
141: Z z;
142: mpz_t r;
143:
144: asir_assert(ARG0(arg),O_N,"sha1_free");
145: z = (Z)ARG0(arg);
146: s = (unsigned char *)mpz_export(0,&bl,1,sizeof(unsigned char),1,0,BDY(z));
147: sha_memory(s,bl,digest);
148: mpz_init(r);
149: mpz_import(r,5,1,sizeof(int),0,0,digest);
150: MPZTOZ(r,*rp);
151: }
152:
153: #if 0
154: void Psha1_ec(arg,rp)
155: NODE arg;
156: Q *rp;
157: {
158: #include <fj_crypt.h>
159: SHS_CTX context;
160: unsigned char *s;
161: int i,j,l,bl,n;
162: unsigned int t;
163: N z,r;
164: extern int little_endian;
165:
166: asir_assert(ARG0(arg),O_N,"sha1");
167: z = NM((Q)ARG0(arg));
168: n = PL(z);
169: l = n_bits(z);
170: bl = (l+7)/8;
171: s = (unsigned char *)MALLOC(bl);
172: for ( i = 0, j = bl-1; i < n; i++ ) {
173: t = BD(z)[i];
174: if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
175: if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
176: if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
177: if ( j >= 0 ) s[j--] = t;
178: }
179: SHSInit(&context);
180: SHSUpdate(&context,s,bl);
181: SHSFinal(&context);
182: r = NALLOC(5);
183: if ( little_endian )
184: for ( i = 0; i < 5; i++ ) {
185: t = context.digest[4-i];
186: BD(r)[i] = (t>>24)|((t&0xff0000)>>8)|((t&0xff00)<<8)|(t<<24);
187: } else
188: for ( i = 0; i < 5; i++ )
189: BD(r)[i] = context.digest[4-i];
190: for ( i = 4; i >= 0 && !BD(r)[i]; i-- );
191: if ( i < 0 )
192: *rp = 0;
193: else {
194: PL(r) = i+1;
195: NTOQ(r,1,*rp);
196: }
197: }
198: #endif
199:
200: void Pecm_count_order(NODE arg,Z *rp)
201: {
202: Z p;
203: UP2 d;
204: Obj a,b;
205: unsigned int p0,a0,b0,ord;
206: VECT ec;
207: Obj *vb;
208:
209: switch ( current_ff ) {
210: case FF_GFP:
211: getmod_lm(&p);
212: if ( z_bits((Q)p) > 32 )
213: error("ecm_count_order : ground field too large");
1.2 ! noro 214: p0 = ZTOS(p);
1.1 noro 215: ec = (VECT)ARG0(arg);
216: vb = (Obj *)BDY(ec); simp_ff(vb[0],&a); simp_ff(vb[1],&b);
217: a0 = LMTOS((LM)a);
218: b0 = LMTOS((LM)b);
219: ord = ecm_count_order_gfp(p0,a0,b0);
1.2 ! noro 220: UTOZ(ord,*rp);
1.1 noro 221: break;
222: case FF_GF2N:
223: getmod_gf2n(&d);
224: if ( degup2(d) > 10 )
225: error("ecm_count_order : ground field too large");
226: ec = (VECT)ARG0(arg);
227: vb = (Obj *)BDY(ec); simp_ff(vb[0],&a); simp_ff(vb[1],&b);
228: ord = ecm_count_order_gf2n(d,(GF2N)a,(GF2N)b);
1.2 ! noro 229: UTOZ(ord,*rp);
1.1 noro 230: break;
231: default:
232: error("ecm_count_order : current_ff is not set");
233: }
234: }
235:
236: void Pecm_set_addcounter(NODE arg,Z *rp)
237: {
238: if ( arg )
1.2 ! noro 239: ecm_addcounter = ZTOS((Q)ARG0(arg));
! 240: UTOZ(ecm_addcounter,*rp);
1.1 noro 241: }
242:
243: void Pecm_compute_all_key_homo_ff(NODE arg,VECT *rp)
244: {
245: unsigned int *ka;
246: int len,i;
247: VECT *pa;
248: VECT r,v;
249: LIST *vb;
250: USINT *b;
251:
252: v = (VECT)ARG0(arg);
253: len = v->len;
254: vb = (LIST *)v->body;
255: pa = (VECT *)ALLOCA(len*sizeof(VECT));
256: ka = (unsigned int *)ALLOCA(len*sizeof(unsigned int));
257: for ( i = 0; i < len; i++ )
258: pa[i] = (VECT)BDY(NEXT(BDY(vb[i])));
259: switch ( current_ff ) {
260: case FF_GFP:
261: compute_all_key_homo_gfp(pa,len,ka); break;
262: case FF_GF2N:
263: compute_all_key_homo_gf2n(pa,len,ka); break;
264: default:
265: error("ecm_compute_all_key_homo_ff : current_ff is not set");
266: }
267: MKVECT(r,len); *rp = r;
268: b = (USINT *)r->body;
269: for ( i = 0; i < len; i++ )
270: MKUSINT(b[i],ka[i]);
271: }
272:
273: void Psort_ktarray(NODE arg,LIST *rp)
274: {
275: sort_ktarray((VECT)ARG0(arg),(VECT)ARG1(arg),rp);
276: }
277:
278: void Pecm_add_ff(NODE arg,VECT *rp)
279: {
280: ecm_add_ff(ARG0(arg),ARG1(arg),ARG2(arg),rp);
281: }
282:
283: void Pecm_sub_ff(NODE arg,VECT *rp)
284: {
285: ecm_sub_ff(ARG0(arg),ARG1(arg),ARG2(arg),rp);
286: }
287:
288: void Pecm_chsgn_ff(NODE arg,VECT *rp)
289: {
290: ecm_chsgn_ff(ARG0(arg),rp);
291: }
292:
293: void Pnextvect1(NODE arg,Z *rp)
294: {
295: int index;
296:
297: index = nextvect1(ARG0(arg),ARG1(arg));
1.2 ! noro 298: STOZ(index,*rp);
1.1 noro 299: }
300:
301: /* XXX at least n < 32 must hold. What is the strict restriction for n ? */
302:
303: void Pseparate_vect(NODE arg,LIST *rp)
304: {
305: VECT v;
306: int n,i;
307: Z *b;
308: double *w;
309: unsigned int s;
310: NODE ns,nc,t,t1;
311: Z iq;
312: LIST ls,lc;
313:
314: v = (VECT)ARG0(arg);
315: n = v->len; b = (Z *)v->body;
316: w = (double *)ALLOCA(n*sizeof(double));
317: for ( i = 0; i < n; i++ )
1.2 ! noro 318: w[i] = (double)ZTOS(b[i]);
1.1 noro 319: s = separate_vect(w,n);
320: ns = nc = 0;
321: for ( i = n-1; i >= 0; i-- )
322: if ( s & (1<<i) ) {
1.2 ! noro 323: STOZ(i,iq); MKNODE(t,iq,ns); ns = t;
1.1 noro 324: } else {
1.2 ! noro 325: STOZ(i,iq); MKNODE(t,iq,nc); nc = t;
1.1 noro 326: }
327: MKLIST(ls,ns); MKLIST(lc,nc);
328: MKNODE(t,lc,0); MKNODE(t1,ls,t);
329: MKLIST(*rp,t1);
330: }
331:
332: void Pecm_find_match(NODE arg,LIST *rp)
333: {
334: VECT g,b;
335: int ng,nb,i;
336: USINT *p;
337: unsigned int *kg,*kb;
338:
339: g = (VECT)ARG0(arg); ng = g->len;
340: kg = (unsigned int *)ALLOCA(ng*sizeof(unsigned int));
341: for ( i = 0, p = (USINT *)g->body; i < ng; i++ )
342: kg[i] = p[i]?BDY(p[i]):0;
343: b = (VECT)ARG1(arg); nb = b->len;
344: kb = (unsigned int *)ALLOCA(nb*sizeof(unsigned int));
345: for ( i = 0, p = (USINT *)b->body; i < nb; i++ )
346: kb[i] = p[i]?BDY(p[i]):0;
347: ecm_find_match(kg,ng,kb,nb,rp);
348: }
349:
350: void ecm_add_ff(VECT p1,VECT p2,VECT ec,VECT *pr)
351: {
352: if ( !p1 )
353: *pr = p2;
354: else if ( !p2 )
355: *pr = p1;
356: else {
357: switch ( current_ff ) {
358: case FF_GFP:
359: ecm_add_gfp(p1,p2,ec,pr); break;
360: case FF_GF2N:
361: ecm_add_gf2n(p1,p2,ec,pr); break;
362: default:
363: error("ecm_add_ff : current_ff is not set");
364: }
365: }
366: }
367:
368: /* ec = [AX,BC] */
369:
370: void ecm_add_gf2n(VECT p1,VECT p2,VECT ec,VECT *rp)
371: {
372: GF2N ax,bc,a0,a1,a2,b0,b1,b2;
373: GF2N a2b0,a0b2,a2b1,a1b2,a02,a04,a22,a24,a0a2,a0a22,a1a2;
374: GF2N t,s,u,r0,r1,r00,r01,r02,r002,r003,r02q;
375: VECT r;
376: GF2N *vb,*rb;
377:
378: ecm_addcounter++;
379: /* addition with O */
380: if ( !p1 ) {
381: *rp = p2;
382: return;
383: }
384: if ( !p2 ) {
385: *rp = p1;
386: return;
387: }
388: vb = (GF2N *)BDY(ec); ax = vb[0]; bc = vb[1];
389: vb = (GF2N *)BDY(p1); a0 = vb[0]; a1 = vb[1]; a2 = vb[2];
390: vb = (GF2N *)BDY(p2); b0 = vb[0]; b1 = vb[1]; b2 = vb[2];
391:
392: mulgf2n(a2,b0,&a2b0); mulgf2n(a0,b2,&a0b2);
393: if ( !cmpgf2n(a2b0,a0b2) ) {
394: mulgf2n(a2,b1,&a2b1);
395: mulgf2n(a1,b2,&a1b2);
396: if ( !cmpgf2n(a2b1,a1b2) ) {
397: if ( !a0 )
398: *rp = 0;
399: else {
400: squaregf2n(a0,&a02); squaregf2n(a02,&a04);
401: squaregf2n(a2,&a22); squaregf2n(a22,&a24);
402: mulgf2n(a0,a2,&a0a2); squaregf2n(a0a2,&a0a22);
403: mulgf2n(bc,a24,&t); addgf2n(a04,t,&r0);
404: mulgf2n(a04,a0a2,&t); mulgf2n(a1,a2,&a1a2);
405: addgf2n(a02,a1a2,&s); addgf2n(s,a0a2,&u);
406: mulgf2n(u,r0,&s); addgf2n(t,s,&r1);
407:
408: MKVECT(r,3); rb = (GF2N *)r->body;
409: mulgf2n(r0,a0a2,&rb[0]); rb[1] = r1; mulgf2n(a0a22,a0a2,&rb[2]);
410: *rp = r;
411: }
412: } else
413: *rp = 0;
414: } else {
415: mulgf2n(a1,b2,&a1b2); addgf2n(a0b2,a2b0,&r00);
416: mulgf2n(a2,b1,&t); addgf2n(a1b2,t,&r01); mulgf2n(a2,b2,&r02);
417: squaregf2n(r00,&r002); mulgf2n(r002,r00,&r003);
418:
419: addgf2n(r00,r01,&t); mulgf2n(t,r01,&s); mulgf2n(s,r02,&t);
420: if ( ax ) {
421: mulgf2n(r02,ax,&r02q);
422: addgf2n(t,r003,&s); mulgf2n(r02q,r002,&t); addgf2n(s,t,&r0);
423: } else
424: addgf2n(t,r003,&r0);
425:
426: mulgf2n(a0b2,r002,&t); addgf2n(t,r0,&s); mulgf2n(r01,s,&t);
427: mulgf2n(r002,a1b2,&s); addgf2n(r0,s,&u); mulgf2n(r00,u,&s);
428: addgf2n(t,s,&r1);
429:
430: MKVECT(r,3); rb = (GF2N *)r->body;
431: mulgf2n(r0,r00,&rb[0]); rb[1] = r1; mulgf2n(r003,r02,&rb[2]);
432: *rp = r;
433: }
434: }
435:
436: extern LM THREE_LM,FOUR_LM,EIGHT_LM;
437:
438: /* 0 < p < 2^16, 0 <= a,b < p */
439:
440: unsigned int ecm_count_order_gfp(unsigned int p,unsigned int a,unsigned int b)
441: {
442: unsigned int x,rhs,ord,t;
443:
444: for ( x = 0, ord = 1; x < p; x++ ) {
445: DMAR(x,x,a,p,t) /* t = x^2+a mod p */
446: DMAR(t,x,b,p,rhs) /* rhs = x*(x^2+a)+b mod p */
447: if ( !rhs )
448: ord++;
449: else if ( small_jacobi(rhs,p)==1 )
450: ord+=2;
451: }
452: return ord;
453: }
454:
455: unsigned int ecm_count_order_gf2n(UP2 d,GF2N a,GF2N b)
456: {
457: error("ecm_count_order_gf2n : not implemented yet");
458: /* NOTREACHED */
459: return 0;
460: }
461:
462: /* ec = [AX,BC] */
463:
464: void ecm_add_gfp(VECT p1,VECT p2,VECT ec,VECT *pr)
465: {
466: LM aa,bb,x1,y1,z1,x2,y2,z2,x1z2,v1,y1z2,u1,u2,v2,v3,z1z2;
467: LM v2x1z2,a1,x3,y3,z3,w1,s1,s2,s3,s1y1,b1,h1;
468: LM t,s,u;
469: LM *vb;
470: VECT r;
471:
472: ecm_addcounter++;
473: /* addition with O */
474: if( !p1 ) {
475: *pr = p2;
476: return;
477: }
478: if( !p2 ) {
479: *pr = p1;
480: return;
481: }
482:
483: /* set parameters */
484:
485: /* aa = ec[0]; bb = ec[1]; */
486: vb = (LM *)BDY(ec); aa = vb[0]; bb = vb[1];
487:
488: /* x1 = p1[0]; y1 = p1[1]; z1 = p1[2]; */
489: vb = (LM *)BDY(p1); x1 = vb[0]; y1 = vb[1]; z1 = vb[2];
490:
491: /* x2 = p2[0]; y2 = p2[1]; z2 = p2[2]; */
492: vb = (LM *)BDY(p2); x2 = vb[0]; y2 = vb[1]; z2 = vb[2];
493:
494: /* addition */
495:
496: /* x1z2 = (x1*z2) %p; */
497: mullm(x1,z2,&x1z2);
498:
499: /* v1 = (x2*z1-x1z2) %p; */
500: lm_lazy = 1;
501: mullm(x2,z1,&t); sublm(t,x1z2,&s);
502: lm_lazy = 0; simplm(s,&v1);
503:
504: /* y1z2 = (y1*z2) %p; */
505: mullm(y1,z2,&y1z2);
506:
507: /* u1 = (y2*z1-y1z2) %p; */
508: lm_lazy = 1;
509: mullm(y2,z1,&t); sublm(t,y1z2,&s);
510: lm_lazy = 0; simplm(s,&u1);
511:
512: if( v1 != 0 ) {
513: /* u2 = (u1*u1) %p; */
514: mullm(u1,u1,&u2);
515:
516: /* v2 = (v1*v1) %p; */
517: mullm(v1,v1,&v2);
518:
519: /* v3 = (v1*v2) %p; */
520: mullm(v1,v2,&v3);
521:
522: /* z1z2 = (z1*z2) %p; */
523: mullm(z1,z2,&z1z2);
524:
525: /* v2x1z2 = (v2*x1z2) %p; */
526: mullm(v2,x1z2,&v2x1z2);
527:
528: /* a1 = (u2*z1z2-v3-2*v2x1z2) %p; */
529: lm_lazy = 1;
530: mullm(u2,z1z2,&t); addlm(v2x1z2,v2x1z2,&s);
531: addlm(v3,s,&u); sublm(t,u,&s);
532: lm_lazy = 0; simplm(s,&a1);
533:
534: /* x3 = ( v1 * a1 ) %p; */
535: mullm(v1,a1,&x3);
536:
537: /* y3 = ( u1 * ( v2x1z2 - a1 ) - v3 * y1z2 ) %p; */
538: lm_lazy = 1;
539: sublm(v2x1z2,a1,&t); mullm(u1,t,&s); mullm(v3,y1z2,&u); sublm(s,u,&t);
540: lm_lazy = 0; simplm(t,&y3);
541:
542: /* z3 = ( v3 * z1z2 ) %p; */
543: mullm(v3,z1z2,&z3);
544: } else if( u1 == 0 ) {
545: /* w1 = (aa*z1*z1+3*x1*x1) %p; */
546: lm_lazy = 1;
547: mullm(z1,z1,&t); mullm(aa,t,&s);
548: mullm(x1,x1,&t); mullm(THREE_LM,t,&u); addlm(s,u,&t);
549: lm_lazy = 0; simplm(t,&w1);
550:
551: /* s1 = (y1*z1) %p; */
552: mullm(y1,z1,&s1);
553:
554: /* s2 = (s1*s1) %p; */
555: mullm(s1,s1,&s2);
556:
557: /* s3 = (s1*s2) %p; */
558: mullm(s1,s2,&s3);
559:
560: /* s1y1 = (s1*y1) %p; */
561: mullm(s1,y1,&s1y1);
562:
563: /* b1 = (s1y1*x1) %p; */
564: mullm(s1y1,x1,&b1);
565:
566: /* h1 = (w1*w1-8*b1) %p; */
567: lm_lazy = 1;
568: mullm(w1,w1,&t); mullm(EIGHT_LM,b1,&s); sublm(t,s,&u);
569: lm_lazy = 0; simplm(u,&h1);
570:
571: /* x3 = ( 2 * h1 * s1 ) %p; */
572: lm_lazy = 1;
573: mullm(h1,s1,&t); addlm(t,t,&s);
574: lm_lazy = 0; simplm(s,&x3);
575:
576: /* y3 = ( w1 * ( 4 * b1 - h1 ) - 8 * s1y1 * s1y1 ) %p; */
577: lm_lazy = 1;
578: mullm(FOUR_LM,b1,&t); sublm(t,h1,&s); mullm(w1,s,&u);
579: mullm(s1y1,s1y1,&t); mullm(EIGHT_LM,t,&s); sublm(u,s,&t);
580: lm_lazy = 0; simplm(t,&y3);
581:
582: /* z3 = ( 8 * s3 ) %p; */
583: mullm(EIGHT_LM,s3,&z3);
584: } else {
585: *pr = 0;
586: return;
587: }
588: if ( !z3 )
589: *pr = 0;
590: else {
591: MKVECT(r,3); *pr = r;
592: vb = (LM *)BDY(r); vb[0] = x3; vb[1] = y3; vb[2] = z3;
593: }
594: }
595:
596: void ecm_chsgn_ff(VECT p,VECT *pr)
597: {
598: Obj x,y,z;
599: LM tl;
600: GF2N tg;
601: Obj *vb;
602: VECT r;
603:
604: if( !p ) {
605: *pr = 0;
606: return;
607: }
608:
609: /* x = p[0]; y = p[1]; z = p[2]; */
610: vb = (Obj *)BDY(p); x = vb[0]; y = vb[1]; z = vb[2];
611: switch ( current_ff ) {
612: case FF_GFP:
613: if ( !y )
614: *pr = p;
615: else {
616: chsgnlm((LM)y,&tl);
617: MKVECT(r,3); *pr = r;
618: vb = (Obj *)BDY(r); vb[0] = x; vb[1] = (Obj)tl; vb[2] = z;
619: }
620: break;
621: case FF_GF2N:
622: addgf2n((GF2N)x,(GF2N)y,&tg);
623: MKVECT(r,3); *pr = r;
624: vb = (Obj *)BDY(r); vb[0] = x; vb[1] = (Obj)tg; vb[2] = z;
625: break;
626: default:
627: error("ecm_chsgn_ff : current_ff is not set");
628: }
629: }
630:
631: void ecm_sub_ff(VECT p1,VECT p2,VECT ec,VECT *pr)
632: {
633: VECT mp2;
634:
635: ecm_chsgn_ff(p2,&mp2);
636: ecm_add_ff(p1,mp2,ec,pr);
637: }
638:
639: /* tplist = [[t,p],...]; t:interger, p=[p0,p1]:point (vector) */
640:
641: int comp_kip(struct oKeyIndexPair *a,struct oKeyIndexPair *b)
642: {
643: unsigned int ka,kb;
644:
645: ka = a->key; kb = b->key;
646: if ( ka > kb )
647: return 1;
648: else if ( ka < kb )
649: return -1;
650: else
651: return 0;
652: }
653:
654: #define EC_GET_XZ(p,x,z) \
655: if ( !(p) ) {\
656: (x)=0; (z)=(LM)ONE;\
657: } else { \
658: LM *vb;\
659: vb = (LM *)BDY((VECT)(p));\
660: (x) = vb[0]; (z) = vb[2];\
661: }
662:
663: #define EC_GET_XZ_GF2N(p,x,z) \
664: if ( !(p) ) {\
665: (x)=0; (z)=(GF2N)ONE;\
666: } else { \
667: GF2N *vb;\
668: vb = (GF2N *)BDY((VECT)(p));\
669: (x) = vb[0]; (z) = vb[2];\
670: }
671:
672: void compute_all_key_homo_gfp(VECT *pa,int len,unsigned int *ka)
673: {
674: LM *b,*x,*z;
675: int i;
676: LM t,s,m;
677:
678: b = (LM *)ALLOCA((len+1)*sizeof(LM));
679: x = (LM *)ALLOCA(len*sizeof(LM));
680: z = (LM *)ALLOCA(len*sizeof(LM));
681: b[0] = ONELM;
682: for ( i = 1; i <= len; i++ ) {
683: EC_GET_XZ(pa[i-1],x[i-1],z[i-1]);
684: mullm(b[i-1],z[i-1],&b[i]);
685: }
686: /* b[0] = 1 */
687: divlm(b[0],b[len],&m);
688: for ( i = len-1; i >= 0; i-- ) {
689: mullm(m,b[i],&s); mullm(s,x[i],&t); s = t;
690: ka[i] = LMTOS(s); ka[i] |= 0x80000000;
691: mullm(m,z[i],&s); m = s;
692: }
693: }
694:
695: void compute_all_key_homo_gf2n(VECT *pa,int len,unsigned int *ka)
696: {
697: GF2N *b,*x,*z;
698: int i;
699: GF2N t,s,m;
700:
701: b = (GF2N *)ALLOCA((len+1)*sizeof(Q));
702: x = (GF2N *)ALLOCA(len*sizeof(Q));
703: z = (GF2N *)ALLOCA(len*sizeof(Q));
704: MKGF2N(ONEUP2,b[0]);
705: for ( i = 1; i <= len; i++ ) {
706: EC_GET_XZ_GF2N(pa[i-1],x[i-1],z[i-1]);
707: mulgf2n(b[i-1],z[i-1],&b[i]);
708: }
709: invgf2n(b[len],&m);
710: for ( i = len-1; i >= 0; i-- ) {
711: mulgf2n(m,b[i],&s); mulgf2n(s,x[i],&t); s = t;
712: ka[i] = s ? s->body->b[0] : 0; ka[i] |= 0x80000000;
713: mulgf2n(m,z[i],&s); m = s;
714: }
715: }
716:
717: unsigned int separate_vect(double *v,int n)
718: {
719: unsigned int max = 1<<n;
720: unsigned int i,j,i0;
721: double all,a,total,m;
722:
723: for ( i = 0, all = 1; i < (unsigned int)n; i++ )
724: all *= v[i];
725:
726: for ( i = 0, m = 0; i < max; i++ ) {
727: for ( a = 1, j = 0; j < (unsigned int)n; j++ )
728: if ( i & (1<<j) )
729: a *= v[j];
730: total = a+(all/a)*2;
731: if ( !m || total < m ) {
732: m = total;
733: i0 = i;
734: }
735: }
736: return i0;
737: }
738:
739: void ecm_find_match(unsigned int *g,int ng,unsigned int *b,int nb,LIST *r)
740: {
741: int i,j;
742: Z iq,jq;
743: NODE n0,n1,c0,c;
744: LIST l;
745:
746: for ( i = 0, c0 = 0; i < ng; i++ ) {
747: j = find_match(g[i],b,nb);
748: if ( j >= 0 ) {
1.2 ! noro 749: STOZ(i,iq); STOZ(j,jq);
1.1 noro 750: MKNODE(n1,jq,0); MKNODE(n0,iq,n1); MKLIST(l,n0);
751: NEXTNODE(c0,c);
752: BDY(c) = (pointer)l;
753: }
754: }
755: if ( c0 )
756: NEXT(c) = 0;
757: MKLIST(*r,c0);
758: }
759:
760: int find_match(unsigned int k,unsigned int *key,int n)
761: {
762: int s,e,m;
763:
764: for ( s = 0, e = n; (e-s) > 1; ) {
765: m = (s+e)/2;
766: if ( k==key[m] )
767: return m;
768: else if ( k > key[m] )
769: s = m;
770: else
771: e = m;
772: }
773: if ( k == key[s] )
774: return s;
775: else
776: return -1;
777: }
778:
779: int nextvect1(VECT vect,VECT bound)
780: {
781: int size,i,a;
782: Z *vb,*bb;
783:
784: size = vect->len;
785: vb = (Z *)vect->body;
786: bb = (Z *)bound->body;
787: for ( i = size-1; i >= 0; i-- )
1.2 ! noro 788: if ( (a=ZTOS(vb[i])) < ZTOS(bb[i]) ) {
! 789: a++; STOZ(a,vb[i]);
1.1 noro 790: break;
791: } else
792: vb[i] = 0;
793: return i;
794: }
795:
796: void sort_ktarray(VECT karray,VECT tarray,LIST *rp)
797: {
798: NODE r,r1;
799: int i,i0,k,len,same,tsame;
800: struct oKeyIndexPair *kip;
801: VECT key,value,v;
802: Q *tb,*samebuf;
803: USINT *kb;
804: Obj *svb;
805: USINT *skb;
806:
807: len = karray->len;
808: kb = (USINT *)karray->body;
809:
810: kip = (struct oKeyIndexPair *)ALLOCA(len*sizeof(struct oKeyIndexPair));
811: for ( i = 0; i < len; i++ ) {
812: kip[i].key = BDY(kb[i]); kip[i].index = i;
813: }
814: qsort((void *)kip,len,sizeof(struct oKeyIndexPair),
815: (int (*)(const void *,const void *))comp_kip);
816:
817: for ( same = tsame = i = i0 = 0, k = 1; i < len; i++, tsame++ )
818: if ( kip[i0].key != kip[i].key ) {
819: i0 = i; k++;
820: same = MAX(tsame,same);
821: tsame = 0;
822: }
823: same = MAX(tsame,same);
824: samebuf = (Q *)ALLOCA(same*sizeof(Q));
825:
826: MKVECT(key,k); skb = (USINT *)BDY(key);
827: MKVECT(value,k); svb = (Obj *)BDY(value);
828:
829: tb = (Q *)tarray->body;
830: for ( same = i = i0 = k = 0; i <= len; i++ ) {
831: if ( i == len || kip[i0].key != kip[i].key ) {
832: skb[k] = kb[kip[i0].index];
833: if ( same > 1 ) {
834: MKVECT(v,same);
835: bcopy((char *)samebuf,(char *)v->body,same*sizeof(Q));
836: svb[k] = (Obj)v;
837: } else
838: svb[k] = (Obj)samebuf[0];
839: i0 = i;
840: k++;
841: same = 0;
842: if ( i == len )
843: break;
844: }
845: samebuf[same++] = tb[kip[i].index];
846: }
847: MKNODE(r1,value,0); MKNODE(r,key,r1); MKLIST(*rp,r);
848: }
849:
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