Annotation of OpenXM_contrib2/asir2000/builtin/ec.c, Revision 1.6
1.3 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
1.4 noro 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.3 noro 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: *
1.6 ! noro 48: * $OpenXM: OpenXM_contrib2/asir2000/builtin/ec.c,v 1.5 2001/10/09 01:36:05 noro Exp $
1.3 noro 49: */
1.1 noro 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 {
1.6 ! noro 66: unsigned int key;
! 67: int index;
1.1 noro 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 */
1.6 ! noro 109: {"ecm_add_ff",Pecm_add_ff,3},
1.1 noro 110:
111: /* point change sign */
1.6 ! noro 112: {"ecm_chsgn_ff",Pecm_chsgn_ff,1},
1.1 noro 113:
114: /* point subtraction */
1.6 ! noro 115: {"ecm_sub_ff",Pecm_sub_ff,3},
1.1 noro 116:
117: /* key computation for sort and match */
1.6 ! noro 118: {"ecm_compute_all_key_homo_ff",Pecm_compute_all_key_homo_ff,1},
1.1 noro 119:
120: /* exhausitve search of rational points */
1.6 ! noro 121: {"ecm_count_order",Pecm_count_order,1},
1.1 noro 122:
123: /* common functions */
1.6 ! noro 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},
1.1 noro 130: #if 0
1.6 ! noro 131: {"sha1_free",Psha1_free,1},
1.1 noro 132: #endif
1.6 ! noro 133: {0,0,0},
1.1 noro 134: };
135:
136: void Psha1(arg,rp)
137: NODE arg;
138: Q *rp;
139: {
1.6 ! noro 140: unsigned char *s;
! 141: unsigned int digest[5];
! 142: int i,j,l,bl,n;
! 143: unsigned int t;
! 144: N z,r;
! 145:
! 146: asir_assert(ARG0(arg),O_N,"sha1_free");
! 147: z = NM((Q)ARG0(arg));
! 148: n = PL(z);
! 149: l = n_bits(z);
! 150: if ( argc(arg) == 2 )
! 151: bl = QTOS((Q)ARG1(arg));
! 152: else
! 153: bl = (l+7)/8;
! 154: s = (unsigned char *)MALLOC(bl);
! 155: for ( i = 0, j = bl-1; i < n; i++ ) {
! 156: t = BD(z)[i];
! 157: if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
! 158: if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
! 159: if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
! 160: if ( j >= 0 ) s[j--] = t;
! 161: }
! 162: sha_memory(s,bl,digest);
! 163: r = NALLOC(5);
! 164: for ( i = 0; i < 5; i++ )
! 165: BD(r)[i] = digest[4-i];
! 166: for ( i = 4; i >= 0 && !BD(r)[i]; i-- );
! 167: if ( i < 0 )
! 168: *rp = 0;
! 169: else {
! 170: PL(r) = i+1;
! 171: NTOQ(r,1,*rp);
! 172: }
1.1 noro 173: }
174:
175: #if 0
176: void Psha1_ec(arg,rp)
177: NODE arg;
178: Q *rp;
179: {
180: #include <fj_crypt.h>
1.6 ! noro 181: SHS_CTX context;
! 182: unsigned char *s;
! 183: int i,j,l,bl,n;
! 184: unsigned int t;
! 185: N z,r;
! 186: extern int little_endian;
! 187:
! 188: asir_assert(ARG0(arg),O_N,"sha1");
! 189: z = NM((Q)ARG0(arg));
! 190: n = PL(z);
! 191: l = n_bits(z);
! 192: bl = (l+7)/8;
! 193: s = (unsigned char *)MALLOC(bl);
! 194: for ( i = 0, j = bl-1; i < n; i++ ) {
! 195: t = BD(z)[i];
! 196: if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
! 197: if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
! 198: if ( j >= 0 ) s[j--] = t&0xff; t>>=8;
! 199: if ( j >= 0 ) s[j--] = t;
! 200: }
! 201: SHSInit(&context);
! 202: SHSUpdate(&context,s,bl);
! 203: SHSFinal(&context);
! 204: r = NALLOC(5);
! 205: if ( little_endian )
! 206: for ( i = 0; i < 5; i++ ) {
! 207: t = context.digest[4-i];
! 208: BD(r)[i] = (t>>24)|((t&0xff0000)>>8)|((t&0xff00)<<8)|(t<<24);
! 209: } else
! 210: for ( i = 0; i < 5; i++ )
! 211: BD(r)[i] = context.digest[4-i];
! 212: for ( i = 4; i >= 0 && !BD(r)[i]; i-- );
! 213: if ( i < 0 )
! 214: *rp = 0;
! 215: else {
! 216: PL(r) = i+1;
! 217: NTOQ(r,1,*rp);
! 218: }
1.1 noro 219: }
220: #endif
221:
222: void Pecm_count_order(arg,rp)
223: NODE arg;
224: Q *rp;
225: {
1.6 ! noro 226: N p;
! 227: UP2 d;
! 228: Obj a,b;
! 229: unsigned int p0,a0,b0,ord;
! 230: VECT ec;
! 231: Obj *vb;
! 232:
! 233: switch ( current_ff ) {
! 234: case FF_GFP:
! 235: getmod_lm(&p);
! 236: if ( n_bits(p) > 32 )
! 237: error("ecm_count_order : ground field too large");
! 238: p0 = BD(p)[0];
! 239: ec = (VECT)ARG0(arg);
! 240: vb = (Obj *)BDY(ec); simp_ff(vb[0],&a); simp_ff(vb[1],&b);
! 241: a0 = a?BD(BDY((LM)a))[0]:0;
! 242: b0 = b?BD(BDY((LM)b))[0]:0;
! 243: ord = ecm_count_order_gfp(p0,a0,b0);
! 244: UTOQ(ord,*rp);
! 245: break;
! 246: case FF_GF2N:
! 247: getmod_gf2n(&d);
! 248: if ( degup2(d) > 10 )
! 249: error("ecm_count_order : ground field too large");
! 250: ec = (VECT)ARG0(arg);
! 251: vb = (Obj *)BDY(ec); simp_ff(vb[0],&a); simp_ff(vb[1],&b);
! 252: ord = ecm_count_order_gf2n(d,(GF2N)a,(GF2N)b);
! 253: UTOQ(ord,*rp);
! 254: break;
! 255: default:
! 256: error("ecm_count_order : current_ff is not set");
! 257: }
1.1 noro 258: }
259:
260: void Pecm_set_addcounter(arg,rp)
261: NODE arg;
262: Q *rp;
263: {
1.6 ! noro 264: if ( arg )
! 265: ecm_addcounter = QTOS((Q)ARG0(arg));
! 266: UTOQ(ecm_addcounter,*rp);
1.1 noro 267: }
268:
269: void Pecm_compute_all_key_homo_ff(arg,rp)
270: NODE arg;
271: VECT *rp;
272: {
1.6 ! noro 273: unsigned int *ka;
! 274: int len,i;
! 275: VECT *pa;
! 276: VECT r,v;
! 277: LIST *vb;
! 278: USINT *b;
! 279:
! 280: v = (VECT)ARG0(arg);
! 281: len = v->len;
! 282: vb = (LIST *)v->body;
! 283: pa = (VECT *)ALLOCA(len*sizeof(VECT));
! 284: ka = (unsigned int *)ALLOCA(len*sizeof(unsigned int));
! 285: for ( i = 0; i < len; i++ )
! 286: pa[i] = (VECT)BDY(NEXT(BDY(vb[i])));
! 287: switch ( current_ff ) {
! 288: case FF_GFP:
! 289: compute_all_key_homo_gfp(pa,len,ka); break;
! 290: case FF_GF2N:
! 291: compute_all_key_homo_gf2n(pa,len,ka); break;
! 292: default:
! 293: error("ecm_compute_all_key_homo_ff : current_ff is not set");
! 294: }
! 295: MKVECT(r,len); *rp = r;
! 296: b = (USINT *)r->body;
! 297: for ( i = 0; i < len; i++ )
! 298: MKUSINT(b[i],ka[i]);
1.1 noro 299: }
300:
301: void Psort_ktarray(arg,rp)
302: NODE arg;
303: LIST *rp;
304: {
1.6 ! noro 305: sort_ktarray((VECT)ARG0(arg),(VECT)ARG1(arg),rp);
1.1 noro 306: }
307:
308: void Pecm_add_ff(arg,rp)
309: NODE arg;
310: VECT *rp;
311: {
1.6 ! noro 312: ecm_add_ff(ARG0(arg),ARG1(arg),ARG2(arg),rp);
1.1 noro 313: }
314:
315: void Pecm_sub_ff(arg,rp)
316: NODE arg;
317: VECT *rp;
318: {
1.6 ! noro 319: ecm_sub_ff(ARG0(arg),ARG1(arg),ARG2(arg),rp);
1.1 noro 320: }
321:
322: void Pecm_chsgn_ff(arg,rp)
323: NODE arg;
324: VECT *rp;
325: {
1.6 ! noro 326: ecm_chsgn_ff(ARG0(arg),rp);
1.1 noro 327: }
328:
329: void Pnextvect1(arg,rp)
330: NODE arg;
331: Q *rp;
332: {
1.6 ! noro 333: int index;
1.1 noro 334:
1.6 ! noro 335: index = nextvect1(ARG0(arg),ARG1(arg));
! 336: STOQ(index,*rp);
1.1 noro 337: }
338:
339: /* XXX at least n < 32 must hold. What is the strict restriction for n ? */
340:
341: void Pseparate_vect(arg,rp)
342: NODE arg;
343: LIST *rp;
344: {
1.6 ! noro 345: VECT v;
! 346: int n,i;
! 347: Q *b;
! 348: double *w;
! 349: unsigned int s;
! 350: NODE ns,nc,t,t1;
! 351: Q iq;
! 352: LIST ls,lc;
! 353:
! 354: v = (VECT)ARG0(arg);
! 355: n = v->len; b = (Q *)v->body;
! 356: w = (double *)ALLOCA(n*sizeof(double));
! 357: for ( i = 0; i < n; i++ )
! 358: w[i] = (double)QTOS(b[i]);
! 359: s = separate_vect(w,n);
! 360: ns = nc = 0;
! 361: for ( i = n-1; i >= 0; i-- )
! 362: if ( s & (1<<i) ) {
! 363: STOQ(i,iq); MKNODE(t,iq,ns); ns = t;
! 364: } else {
! 365: STOQ(i,iq); MKNODE(t,iq,nc); nc = t;
! 366: }
! 367: MKLIST(ls,ns); MKLIST(lc,nc);
! 368: MKNODE(t,lc,0); MKNODE(t1,ls,t);
! 369: MKLIST(*rp,t1);
1.1 noro 370: }
371:
372: void Pecm_find_match(arg,rp)
373: NODE arg;
374: LIST *rp;
375: {
1.6 ! noro 376: VECT g,b;
! 377: int ng,nb,i;
! 378: USINT *p;
! 379: unsigned int *kg,*kb;
! 380:
! 381: g = (VECT)ARG0(arg); ng = g->len;
! 382: kg = (unsigned int *)ALLOCA(ng*sizeof(unsigned int));
! 383: for ( i = 0, p = (USINT *)g->body; i < ng; i++ )
! 384: kg[i] = p[i]?BDY(p[i]):0;
! 385: b = (VECT)ARG1(arg); nb = b->len;
! 386: kb = (unsigned int *)ALLOCA(nb*sizeof(unsigned int));
! 387: for ( i = 0, p = (USINT *)b->body; i < nb; i++ )
! 388: kb[i] = p[i]?BDY(p[i]):0;
! 389: ecm_find_match(kg,ng,kb,nb,rp);
1.1 noro 390: }
391:
392: void ecm_add_ff(p1,p2,ec,pr)
393: VECT p1,p2,ec;
394: VECT *pr;
395: {
1.6 ! noro 396: if ( !p1 )
! 397: *pr = p2;
! 398: else if ( !p2 )
! 399: *pr = p1;
! 400: else {
! 401: switch ( current_ff ) {
! 402: case FF_GFP:
! 403: ecm_add_gfp(p1,p2,ec,pr); break;
! 404: case FF_GF2N:
! 405: ecm_add_gf2n(p1,p2,ec,pr); break;
! 406: default:
! 407: error("ecm_add_ff : current_ff is not set");
! 408: }
! 409: }
1.1 noro 410: }
411:
412: /* ec = [AX,BC] */
413:
414: void ecm_add_gf2n(p1,p2,ec,rp)
415: VECT p1,p2,ec;
416: VECT *rp;
417: {
1.6 ! noro 418: GF2N ax,bc,a0,a1,a2,b0,b1,b2;
! 419: GF2N a2b0,a0b2,a2b1,a1b2,a02,a04,a22,a24,a0a2,a0a22,a1a2;
! 420: GF2N t,s,u,r0,r1,r00,r01,r02,r002,r003,r02q;
! 421: VECT r;
! 422: GF2N *vb,*rb;
! 423:
! 424: ecm_addcounter++;
! 425: /* addition with O */
! 426: if ( !p1 ) {
! 427: *rp = p2;
! 428: return;
! 429: }
! 430: if ( !p2 ) {
! 431: *rp = p1;
! 432: return;
! 433: }
! 434: vb = (GF2N *)BDY(ec); ax = vb[0]; bc = vb[1];
! 435: vb = (GF2N *)BDY(p1); a0 = vb[0]; a1 = vb[1]; a2 = vb[2];
! 436: vb = (GF2N *)BDY(p2); b0 = vb[0]; b1 = vb[1]; b2 = vb[2];
! 437:
! 438: mulgf2n(a2,b0,&a2b0); mulgf2n(a0,b2,&a0b2);
! 439: if ( !cmpgf2n(a2b0,a0b2) ) {
! 440: mulgf2n(a2,b1,&a2b1);
! 441: mulgf2n(a1,b2,&a1b2);
! 442: if ( !cmpgf2n(a2b1,a1b2) ) {
! 443: if ( !a0 )
! 444: *rp = 0;
! 445: else {
! 446: squaregf2n(a0,&a02); squaregf2n(a02,&a04);
! 447: squaregf2n(a2,&a22); squaregf2n(a22,&a24);
! 448: mulgf2n(a0,a2,&a0a2); squaregf2n(a0a2,&a0a22);
! 449: mulgf2n(bc,a24,&t); addgf2n(a04,t,&r0);
! 450: mulgf2n(a04,a0a2,&t); mulgf2n(a1,a2,&a1a2);
! 451: addgf2n(a02,a1a2,&s); addgf2n(s,a0a2,&u);
! 452: mulgf2n(u,r0,&s); addgf2n(t,s,&r1);
! 453:
! 454: MKVECT(r,3); rb = (GF2N *)r->body;
! 455: mulgf2n(r0,a0a2,&rb[0]); rb[1] = r1; mulgf2n(a0a22,a0a2,&rb[2]);
! 456: *rp = r;
! 457: }
! 458: } else
! 459: *rp = 0;
! 460: } else {
! 461: mulgf2n(a1,b2,&a1b2); addgf2n(a0b2,a2b0,&r00);
! 462: mulgf2n(a2,b1,&t); addgf2n(a1b2,t,&r01); mulgf2n(a2,b2,&r02);
! 463: squaregf2n(r00,&r002); mulgf2n(r002,r00,&r003);
! 464:
! 465: addgf2n(r00,r01,&t); mulgf2n(t,r01,&s); mulgf2n(s,r02,&t);
! 466: if ( ax ) {
! 467: mulgf2n(r02,ax,&r02q);
! 468: addgf2n(t,r003,&s); mulgf2n(r02q,r002,&t); addgf2n(s,t,&r0);
! 469: } else
! 470: addgf2n(t,r003,&r0);
! 471:
! 472: mulgf2n(a0b2,r002,&t); addgf2n(t,r0,&s); mulgf2n(r01,s,&t);
! 473: mulgf2n(r002,a1b2,&s); addgf2n(r0,s,&u); mulgf2n(r00,u,&s);
! 474: addgf2n(t,s,&r1);
! 475:
! 476: MKVECT(r,3); rb = (GF2N *)r->body;
! 477: mulgf2n(r0,r00,&rb[0]); rb[1] = r1; mulgf2n(r003,r02,&rb[2]);
! 478: *rp = r;
! 479: }
1.1 noro 480: }
481:
482: extern LM THREE_LM,FOUR_LM,EIGHT_LM;
483:
484: /* 0 < p < 2^16, 0 <= a,b < p */
485:
486: unsigned int ecm_count_order_gfp(p,a,b)
487: unsigned int p,a,b;
488: {
1.6 ! noro 489: unsigned int x,rhs,ord,t;
1.1 noro 490:
1.6 ! noro 491: for ( x = 0, ord = 1; x < p; x++ ) {
! 492: DMAR(x,x,a,p,t) /* t = x^2+a mod p */
! 493: DMAR(t,x,b,p,rhs) /* rhs = x*(x^2+a)+b mod p */
! 494: if ( !rhs )
! 495: ord++;
! 496: else if ( small_jacobi(rhs,p)==1 )
! 497: ord+=2;
! 498: }
! 499: return ord;
1.1 noro 500: }
501:
502: unsigned int ecm_count_order_gf2n(d,a,b)
503: UP2 d;
504: GF2N a,b;
505: {
1.6 ! noro 506: error("ecm_count_order_gf2n : not implemented yet");
! 507: /* NOTREACHED */
! 508: return 0;
1.1 noro 509: }
510:
511: /* ec = [AX,BC] */
512:
513: void ecm_add_gfp(p1,p2,ec,pr)
514: VECT p1,p2,ec;
515: VECT *pr;
516: {
1.6 ! noro 517: LM aa,bb,x1,y1,z1,x2,y2,z2,x1z2,v1,y1z2,u1,u2,v2,v3,z1z2;
! 518: LM v2x1z2,a1,x3,y3,z3,w1,s1,s2,s3,s1y1,b1,h1;
! 519: LM t,s,u;
! 520: LM *vb;
! 521: VECT r;
! 522:
! 523: ecm_addcounter++;
! 524: /* addition with O */
! 525: if( !p1 ) {
! 526: *pr = p2;
! 527: return;
! 528: }
! 529: if( !p2 ) {
! 530: *pr = p1;
! 531: return;
! 532: }
! 533:
! 534: /* set parameters */
! 535:
! 536: /* aa = ec[0]; bb = ec[1]; */
! 537: vb = (LM *)BDY(ec); aa = vb[0]; bb = vb[1];
! 538:
! 539: /* x1 = p1[0]; y1 = p1[1]; z1 = p1[2]; */
! 540: vb = (LM *)BDY(p1); x1 = vb[0]; y1 = vb[1]; z1 = vb[2];
! 541:
! 542: /* x2 = p2[0]; y2 = p2[1]; z2 = p2[2]; */
! 543: vb = (LM *)BDY(p2); x2 = vb[0]; y2 = vb[1]; z2 = vb[2];
! 544:
! 545: /* addition */
! 546:
! 547: /* x1z2 = (x1*z2) %p; */
! 548: mullm(x1,z2,&x1z2);
! 549:
! 550: /* v1 = (x2*z1-x1z2) %p; */
! 551: lm_lazy = 1;
! 552: mullm(x2,z1,&t); sublm(t,x1z2,&s);
! 553: lm_lazy = 0; simplm(s,&v1);
! 554:
! 555: /* y1z2 = (y1*z2) %p; */
! 556: mullm(y1,z2,&y1z2);
! 557:
! 558: /* u1 = (y2*z1-y1z2) %p; */
! 559: lm_lazy = 1;
! 560: mullm(y2,z1,&t); sublm(t,y1z2,&s);
! 561: lm_lazy = 0; simplm(s,&u1);
! 562:
! 563: if( v1 != 0 ) {
! 564: /* u2 = (u1*u1) %p; */
! 565: mullm(u1,u1,&u2);
! 566:
! 567: /* v2 = (v1*v1) %p; */
! 568: mullm(v1,v1,&v2);
! 569:
! 570: /* v3 = (v1*v2) %p; */
! 571: mullm(v1,v2,&v3);
! 572:
! 573: /* z1z2 = (z1*z2) %p; */
! 574: mullm(z1,z2,&z1z2);
! 575:
! 576: /* v2x1z2 = (v2*x1z2) %p; */
! 577: mullm(v2,x1z2,&v2x1z2);
! 578:
! 579: /* a1 = (u2*z1z2-v3-2*v2x1z2) %p; */
! 580: lm_lazy = 1;
! 581: mullm(u2,z1z2,&t); addlm(v2x1z2,v2x1z2,&s);
! 582: addlm(v3,s,&u); sublm(t,u,&s);
! 583: lm_lazy = 0; simplm(s,&a1);
! 584:
! 585: /* x3 = ( v1 * a1 ) %p; */
! 586: mullm(v1,a1,&x3);
! 587:
! 588: /* y3 = ( u1 * ( v2x1z2 - a1 ) - v3 * y1z2 ) %p; */
! 589: lm_lazy = 1;
! 590: sublm(v2x1z2,a1,&t); mullm(u1,t,&s); mullm(v3,y1z2,&u); sublm(s,u,&t);
! 591: lm_lazy = 0; simplm(t,&y3);
! 592:
! 593: /* z3 = ( v3 * z1z2 ) %p; */
! 594: mullm(v3,z1z2,&z3);
! 595: } else if( u1 == 0 ) {
! 596: /* w1 = (aa*z1*z1+3*x1*x1) %p; */
! 597: lm_lazy = 1;
! 598: mullm(z1,z1,&t); mullm(aa,t,&s);
! 599: mullm(x1,x1,&t); mullm(THREE_LM,t,&u); addlm(s,u,&t);
! 600: lm_lazy = 0; simplm(t,&w1);
! 601:
! 602: /* s1 = (y1*z1) %p; */
! 603: mullm(y1,z1,&s1);
! 604:
! 605: /* s2 = (s1*s1) %p; */
! 606: mullm(s1,s1,&s2);
! 607:
! 608: /* s3 = (s1*s2) %p; */
! 609: mullm(s1,s2,&s3);
! 610:
! 611: /* s1y1 = (s1*y1) %p; */
! 612: mullm(s1,y1,&s1y1);
! 613:
! 614: /* b1 = (s1y1*x1) %p; */
! 615: mullm(s1y1,x1,&b1);
! 616:
! 617: /* h1 = (w1*w1-8*b1) %p; */
! 618: lm_lazy = 1;
! 619: mullm(w1,w1,&t); mullm(EIGHT_LM,b1,&s); sublm(t,s,&u);
! 620: lm_lazy = 0; simplm(u,&h1);
! 621:
! 622: /* x3 = ( 2 * h1 * s1 ) %p; */
! 623: lm_lazy = 1;
! 624: mullm(h1,s1,&t); addlm(t,t,&s);
! 625: lm_lazy = 0; simplm(s,&x3);
! 626:
! 627: /* y3 = ( w1 * ( 4 * b1 - h1 ) - 8 * s1y1 * s1y1 ) %p; */
! 628: lm_lazy = 1;
! 629: mullm(FOUR_LM,b1,&t); sublm(t,h1,&s); mullm(w1,s,&u);
! 630: mullm(s1y1,s1y1,&t); mullm(EIGHT_LM,t,&s); sublm(u,s,&t);
! 631: lm_lazy = 0; simplm(t,&y3);
! 632:
! 633: /* z3 = ( 8 * s3 ) %p; */
! 634: mullm(EIGHT_LM,s3,&z3);
! 635: } else {
! 636: *pr = 0;
! 637: return;
! 638: }
! 639: if ( !z3 )
! 640: *pr = 0;
! 641: else {
! 642: MKVECT(r,3); *pr = r;
! 643: vb = (LM *)BDY(r); vb[0] = x3; vb[1] = y3; vb[2] = z3;
! 644: }
1.1 noro 645: }
646:
647: void ecm_chsgn_ff(p,pr)
648: VECT p;
649: VECT *pr;
650: {
1.6 ! noro 651: Obj x,y,z;
! 652: LM tl;
! 653: GF2N tg;
! 654: Obj *vb;
! 655: VECT r;
! 656:
! 657: if( !p ) {
! 658: *pr = 0;
! 659: return;
! 660: }
! 661:
! 662: /* x = p[0]; y = p[1]; z = p[2]; */
! 663: vb = (Obj *)BDY(p); x = vb[0]; y = vb[1]; z = vb[2];
! 664: switch ( current_ff ) {
! 665: case FF_GFP:
! 666: if ( !y )
! 667: *pr = p;
! 668: else {
! 669: chsgnlm((LM)y,&tl);
! 670: MKVECT(r,3); *pr = r;
! 671: vb = (Obj *)BDY(r); vb[0] = x; vb[1] = (Obj)tl; vb[2] = z;
! 672: }
! 673: break;
! 674: case FF_GF2N:
! 675: addgf2n((GF2N)x,(GF2N)y,&tg);
! 676: MKVECT(r,3); *pr = r;
! 677: vb = (Obj *)BDY(r); vb[0] = x; vb[1] = (Obj)tg; vb[2] = z;
! 678: break;
! 679: default:
! 680: error("ecm_chsgn_ff : current_ff is not set");
! 681: }
1.1 noro 682: }
683:
684: void ecm_sub_ff(p1,p2,ec,pr)
685: VECT p1,p2,ec;
686: VECT *pr;
687: {
1.6 ! noro 688: VECT mp2;
1.1 noro 689:
1.6 ! noro 690: ecm_chsgn_ff(p2,&mp2);
! 691: ecm_add_ff(p1,mp2,ec,pr);
1.1 noro 692: }
693:
694: /* tplist = [[t,p],...]; t:interger, p=[p0,p1]:point (vector) */
695:
696: int comp_kip(a,b)
697: struct oKeyIndexPair *a,*b;
698: {
1.6 ! noro 699: unsigned int ka,kb;
1.1 noro 700:
1.6 ! noro 701: ka = a->key; kb = b->key;
! 702: if ( ka > kb )
! 703: return 1;
! 704: else if ( ka < kb )
! 705: return -1;
! 706: else
! 707: return 0;
1.1 noro 708: }
709:
710: #define EC_GET_XZ(p,x,z) \
1.6 ! noro 711: if ( !(p) ) {\
! 712: (x)=0; (z)=(LM)ONE;\
! 713: } else { \
! 714: LM *vb;\
! 715: vb = (LM *)BDY((VECT)(p));\
! 716: (x) = vb[0]; (z) = vb[2];\
! 717: }
1.1 noro 718:
719: #define EC_GET_XZ_GF2N(p,x,z) \
1.6 ! noro 720: if ( !(p) ) {\
! 721: (x)=0; (z)=(GF2N)ONE;\
! 722: } else { \
! 723: GF2N *vb;\
! 724: vb = (GF2N *)BDY((VECT)(p));\
! 725: (x) = vb[0]; (z) = vb[2];\
! 726: }
1.1 noro 727:
728: void compute_all_key_homo_gfp(pa,len,ka)
729: VECT *pa;
730: int len;
731: unsigned int *ka;
732: {
1.6 ! noro 733: LM *b,*x,*z;
! 734: int i;
! 735: LM t,s,m;
! 736:
! 737: b = (LM *)ALLOCA((len+1)*sizeof(LM));
! 738: x = (LM *)ALLOCA(len*sizeof(LM));
! 739: z = (LM *)ALLOCA(len*sizeof(LM));
! 740: MKLM(ONEN,b[0]);
! 741: for ( i = 1; i <= len; i++ ) {
! 742: EC_GET_XZ(pa[i-1],x[i-1],z[i-1]);
! 743: mullm(b[i-1],z[i-1],&b[i]);
! 744: }
! 745: /* b[0] = 1 */
! 746: divlm(b[0],b[len],&m);
! 747: for ( i = len-1; i >= 0; i-- ) {
! 748: mullm(m,b[i],&s); mullm(s,x[i],&t); s = t;
! 749: ka[i] = s ? s->body->b[0] : 0; ka[i] |= 0x80000000;
! 750: mullm(m,z[i],&s); m = s;
! 751: }
1.1 noro 752: }
753:
754: void compute_all_key_homo_gf2n(pa,len,ka)
755: VECT *pa;
756: int len;
757: unsigned int *ka;
758: {
1.6 ! noro 759: GF2N *b,*x,*z;
! 760: int i;
! 761: GF2N t,s,m;
! 762:
! 763: b = (GF2N *)ALLOCA((len+1)*sizeof(Q));
! 764: x = (GF2N *)ALLOCA(len*sizeof(Q));
! 765: z = (GF2N *)ALLOCA(len*sizeof(Q));
! 766: MKGF2N(ONEUP2,b[0]);
! 767: for ( i = 1; i <= len; i++ ) {
! 768: EC_GET_XZ_GF2N(pa[i-1],x[i-1],z[i-1]);
! 769: mulgf2n(b[i-1],z[i-1],&b[i]);
! 770: }
! 771: invgf2n(b[len],&m);
! 772: for ( i = len-1; i >= 0; i-- ) {
! 773: mulgf2n(m,b[i],&s); mulgf2n(s,x[i],&t); s = t;
! 774: ka[i] = s ? s->body->b[0] : 0; ka[i] |= 0x80000000;
! 775: mulgf2n(m,z[i],&s); m = s;
! 776: }
1.1 noro 777: }
778:
779: unsigned int separate_vect(v,n)
780: double *v;
781: int n;
782: {
1.6 ! noro 783: unsigned int max = 1<<n;
! 784: unsigned int i,j,i0;
! 785: double all,a,total,m;
! 786:
! 787: for ( i = 0, all = 1; i < (unsigned int)n; i++ )
! 788: all *= v[i];
! 789:
! 790: for ( i = 0, m = 0; i < max; i++ ) {
! 791: for ( a = 1, j = 0; j < (unsigned int)n; j++ )
! 792: if ( i & (1<<j) )
! 793: a *= v[j];
! 794: total = a+(all/a)*2;
! 795: if ( !m || total < m ) {
! 796: m = total;
! 797: i0 = i;
! 798: }
! 799: }
! 800: return i0;
1.1 noro 801: }
802:
803: void ecm_find_match(g,ng,b,nb,r)
804: unsigned int *g;
805: int ng;
806: unsigned int *b;
807: int nb;
808: LIST *r;
809: {
1.6 ! noro 810: int i,j;
! 811: Q iq,jq;
! 812: NODE n0,n1,c0,c;
! 813: LIST l;
! 814:
! 815: for ( i = 0, c0 = 0; i < ng; i++ ) {
! 816: j = find_match(g[i],b,nb);
! 817: if ( j >= 0 ) {
! 818: STOQ(i,iq); STOQ(j,jq);
! 819: MKNODE(n1,jq,0); MKNODE(n0,iq,n1); MKLIST(l,n0);
! 820: NEXTNODE(c0,c);
! 821: BDY(c) = (pointer)l;
! 822: }
! 823: }
! 824: if ( c0 )
! 825: NEXT(c) = 0;
! 826: MKLIST(*r,c0);
1.1 noro 827: }
828:
829: int find_match(k,key,n)
830: unsigned int k;
831: unsigned int *key;
832: int n;
833: {
1.6 ! noro 834: int s,e,m;
1.1 noro 835:
1.6 ! noro 836: for ( s = 0, e = n; (e-s) > 1; ) {
! 837: m = (s+e)/2;
! 838: if ( k==key[m] )
! 839: return m;
! 840: else if ( k > key[m] )
! 841: s = m;
! 842: else
! 843: e = m;
! 844: }
! 845: if ( k == key[s] )
! 846: return s;
! 847: else
! 848: return -1;
1.1 noro 849: }
850:
851: int nextvect1(vect,bound)
852: VECT vect,bound;
853: {
1.6 ! noro 854: int size,i,a;
! 855: Q *vb,*bb;
1.1 noro 856:
1.6 ! noro 857: size = vect->len;
! 858: vb = (Q *)vect->body;
! 859: bb = (Q *)bound->body;
! 860: for ( i = size-1; i >= 0; i-- )
! 861: if ( (a=QTOS(vb[i])) < QTOS(bb[i]) ) {
! 862: a++; STOQ(a,vb[i]);
! 863: break;
! 864: } else
! 865: vb[i] = 0;
! 866: return i;
1.1 noro 867: }
868:
869: void sort_ktarray(karray,tarray,rp)
870: VECT karray,tarray;
871: LIST *rp;
872: {
1.6 ! noro 873: NODE r,r1;
! 874: int i,i0,k,len,same,tsame;
! 875: struct oKeyIndexPair *kip;
! 876: VECT key,value,v;
! 877: Q *tb,*samebuf;
! 878: USINT *kb;
! 879: Obj *svb;
! 880: USINT *skb;
! 881:
! 882: len = karray->len;
! 883: kb = (USINT *)karray->body;
! 884:
! 885: kip = (struct oKeyIndexPair *)ALLOCA(len*sizeof(struct oKeyIndexPair));
! 886: for ( i = 0; i < len; i++ ) {
! 887: kip[i].key = BDY(kb[i]); kip[i].index = i;
! 888: }
! 889: qsort((void *)kip,len,sizeof(struct oKeyIndexPair),
! 890: (int (*)(const void *,const void *))comp_kip);
! 891:
! 892: for ( same = tsame = i = i0 = 0, k = 1; i < len; i++, tsame++ )
! 893: if ( kip[i0].key != kip[i].key ) {
! 894: i0 = i; k++;
! 895: same = MAX(tsame,same);
! 896: tsame = 0;
! 897: }
! 898: same = MAX(tsame,same);
! 899: samebuf = (Q *)ALLOCA(same*sizeof(Q));
! 900:
! 901: MKVECT(key,k); skb = (USINT *)BDY(key);
! 902: MKVECT(value,k); svb = (Obj *)BDY(value);
! 903:
! 904: tb = (Q *)tarray->body;
! 905: for ( same = i = i0 = k = 0; i <= len; i++ ) {
! 906: if ( i == len || kip[i0].key != kip[i].key ) {
! 907: skb[k] = kb[kip[i0].index];
! 908: if ( same > 1 ) {
! 909: MKVECT(v,same);
! 910: bcopy((char *)samebuf,(char *)v->body,same*sizeof(Q));
! 911: svb[k] = (Obj)v;
! 912: } else
! 913: svb[k] = (Obj)samebuf[0];
! 914: i0 = i;
! 915: k++;
! 916: same = 0;
! 917: if ( i == len )
! 918: break;
! 919: }
! 920: samebuf[same++] = tb[kip[i].index];
! 921: }
! 922: MKNODE(r1,value,0); MKNODE(r,key,r1); MKLIST(*rp,r);
1.1 noro 923: }
924:
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