5 * Prime fields with Montgomery arithmetic
7 * (c) 2001 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
30 /*----- Header files ------------------------------------------------------*/
36 #include "field-guts.h"
38 /*----- Main code ---------------------------------------------------------*/
40 /* --- Field operations --- */
42 static void fdestroy(field *ff) {
43 fctx_prime *f = (fctx_prime *)ff;
44 mpmont_destroy(&f->mm);
48 static mp *frand(field *ff, mp *d, grand *r) {
49 fctx_prime *f = (fctx_prime *)ff;
50 return (mprand_range(d, f->mm.m, r, 0));
53 static mp *fin(field *ff, mp *d, mp *x) {
54 fctx_prime *f = (fctx_prime *)ff;
55 mp_div(0, &d, x, f->mm.m);
56 return (mpmont_mul(&f->mm, d, d, f->mm.r2));
59 static mp *fout(field *ff, mp *d, mp *x) {
60 fctx_prime *f = (fctx_prime *)ff;
61 return (mpmont_reduce(&f->mm, d, x));
64 static int fzerop(field *ff, mp *x) { return (MP_ZEROP(x)); }
66 static mp *fneg(field *ff, mp *d, mp *x) {
67 fctx_prime *f = (fctx_prime *)ff;
68 return (mp_sub(d, f->mm.m, x));
71 static mp *fadd(field *ff, mp *d, mp *x, mp *y) {
72 fctx_prime *f = (fctx_prime *)ff; d = mp_add(d, x, y);
73 if (MP_NEGP(d)) d = mp_add(d, d, f->mm.m);
74 else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
78 static mp *fsub(field *ff, mp *d, mp *x, mp *y) {
79 fctx_prime *f = (fctx_prime *)ff; d = mp_sub(d, x, y);
80 if (MP_NEGP(d)) d = mp_add(d, d, f->mm.m);
81 else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
85 static mp *fmul(field *ff, mp *d, mp *x, mp *y) {
86 fctx_prime *f = (fctx_prime *)ff;
87 return (mpmont_mul(&f->mm, d, x, y));
90 static mp *fsqr(field *ff, mp *d, mp *x) {
91 fctx_prime *f = (fctx_prime *)ff; d = mp_sqr(d, x);
92 return (mpmont_reduce(&f->mm, d, d));
95 static mp *finv(field *ff, mp *d, mp *x) {
96 fctx_prime *f = (fctx_prime *)ff; d = mpmont_reduce(&f->mm, d, x);
97 d = mp_modinv(d, d, f->mm.m); return (mpmont_mul(&f->mm, d, d, f->mm.r2));
100 static mp *freduce(field *ff, mp *d, mp *x) {
101 fctx_prime *f = (fctx_prime *)ff;
102 mp_div(0, &d, x, f->mm.m);
106 static mp *fsqrt(field *ff, mp *d, mp *x) {
107 fctx_prime *f = (fctx_prime *)ff; d = mpmont_reduce(&f->mm, d, x);
108 d = mp_modsqrt(d, d, f->mm.m); if (!d) return (d);
109 return (mpmont_mul(&f->mm, d, d, f->mm.r2));
112 static mp *fdbl(field *ff, mp *d, mp *x) {
113 fctx_prime *f = (fctx_prime *)ff; d = mp_lsl(d, x, 1);
114 if (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m);
118 static mp *ftpl(field *ff, mp *d, mp *x) {
119 fctx_prime *f = (fctx_prime *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f);
120 MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); d->f &= ~MP_UNDEF;
121 while (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m);
125 static mp *fqdl(field *ff, mp *d, mp *x) {
126 fctx_prime *f = (fctx_prime *)ff; d = mp_lsl(d, x, 2);
127 while (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m);
131 static mp *fhlv(field *ff, mp *d, mp *x) {
132 fctx_prime *f = (fctx_prime *)ff;
133 if (MP_ZEROP(x)) { MP_COPY(x); MP_DROP(d); return (x); }
134 if (x->v[0] & 1) { d = mp_add(d, x, f->mm.m); x = d; }
135 return (mp_lsr(d, x, 1));
138 /* --- Field operations table --- */
140 static const field_ops fops = {
142 fdestroy, frand, field_stdsamep,
144 fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt,
146 fdbl, ftpl, fqdl, fhlv
149 /* --- @field_prime@ --- *
151 * Arguments: @mp *p@ = the characteristic of the field
153 * Returns: A pointer to the field or null.
155 * Use: Creates a field structure for a prime field of size %$p$%,
156 * using Montgomery reduction for arithmetic.
159 field *field_prime(mp *p)
163 f = CREATE(fctx_prime);
165 if (mpmont_create(&f->mm, p)) {
172 f->f.nbits = mp_bits(p);
173 f->f.noctets = (f->f.nbits + 7) >> 3;
178 /*----- That's all, folks -------------------------------------------------*/