3 * Prime fields with Montgomery arithmetic
5 * (c) 2001 Straylight/Edgeware
8 /*----- Licensing notice --------------------------------------------------*
10 * This file is part of Catacomb.
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.
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.
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,
28 /*----- Header files ------------------------------------------------------*/
34 #include "field-guts.h"
36 /*----- Main code ---------------------------------------------------------*/
38 /* --- Field operations --- */
40 static void fdestroy(field *ff) {
41 fctx_prime *f = (fctx_prime *)ff;
42 mpmont_destroy(&f->mm);
46 static mp *frand(field *ff, mp *d, grand *r) {
47 fctx_prime *f = (fctx_prime *)ff;
48 return (mprand_range(d, f->mm.m, r, 0));
51 static mp *fin(field *ff, mp *d, mp *x) {
52 fctx_prime *f = (fctx_prime *)ff;
53 mp_div(0, &d, x, f->mm.m);
54 return (mpmont_mul(&f->mm, d, d, f->mm.r2));
57 static mp *fout(field *ff, mp *d, mp *x) {
58 fctx_prime *f = (fctx_prime *)ff;
59 return (mpmont_reduce(&f->mm, d, x));
62 static int fzerop(field *ff, mp *x) { return (MP_ZEROP(x)); }
64 static mp *fneg(field *ff, mp *d, mp *x) {
65 fctx_prime *f = (fctx_prime *)ff;
66 return (mp_sub(d, f->mm.m, x));
69 static mp *fadd(field *ff, mp *d, mp *x, mp *y) {
70 fctx_prime *f = (fctx_prime *)ff; d = mp_add(d, x, y);
71 if (MP_NEGP(d)) d = mp_add(d, d, f->mm.m);
72 else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
76 static mp *fsub(field *ff, mp *d, mp *x, mp *y) {
77 fctx_prime *f = (fctx_prime *)ff; d = mp_sub(d, x, y);
78 if (MP_NEGP(d)) d = mp_add(d, d, f->mm.m);
79 else if (MP_CMP(d, >, f->mm.m)) d = mp_sub(d, d, f->mm.m);
83 static mp *fmul(field *ff, mp *d, mp *x, mp *y) {
84 fctx_prime *f = (fctx_prime *)ff;
85 return (mpmont_mul(&f->mm, d, x, y));
88 static mp *fsqr(field *ff, mp *d, mp *x) {
89 fctx_prime *f = (fctx_prime *)ff; d = mp_sqr(d, x);
90 return (mpmont_reduce(&f->mm, d, d));
93 static mp *finv(field *ff, mp *d, mp *x) {
94 fctx_prime *f = (fctx_prime *)ff; d = mpmont_reduce(&f->mm, d, x);
95 d = mp_modinv(d, d, f->mm.m); return (mpmont_mul(&f->mm, d, d, f->mm.r2));
98 static mp *freduce(field *ff, mp *d, mp *x) {
99 fctx_prime *f = (fctx_prime *)ff;
100 mp_div(0, &d, x, f->mm.m);
104 static mp *fsqrt(field *ff, mp *d, mp *x) {
105 fctx_prime *f = (fctx_prime *)ff; d = mpmont_reduce(&f->mm, d, x);
106 d = mp_modsqrt(d, d, f->mm.m); if (!d) return (d);
107 return (mpmont_mul(&f->mm, d, d, f->mm.r2));
110 static mp *fdbl(field *ff, mp *d, mp *x) {
111 fctx_prime *f = (fctx_prime *)ff; d = mp_lsl(d, x, 1);
112 if (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m);
116 static mp *ftpl(field *ff, mp *d, mp *x) {
117 fctx_prime *f = (fctx_prime *)ff; MP_DEST(d, MP_LEN(x) + 1, x->f);
118 MPX_UMULN(d->v, d->vl, x->v, x->vl, 3); d->f &= ~MP_UNDEF;
119 while (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m);
123 static mp *fqdl(field *ff, mp *d, mp *x) {
124 fctx_prime *f = (fctx_prime *)ff; d = mp_lsl(d, x, 2);
125 while (MP_CMP(d, >=, f->mm.m)) d = mp_sub(d, d, f->mm.m);
129 static mp *fhlv(field *ff, mp *d, mp *x) {
130 fctx_prime *f = (fctx_prime *)ff;
131 if (MP_ZEROP(x)) { MP_COPY(x); MP_DROP(d); return (x); }
132 if (x->v[0] & 1) { d = mp_add(d, x, f->mm.m); x = d; }
133 return (mp_lsr(d, x, 1));
136 /* --- Field operations table --- */
138 static const field_ops fops = {
140 fdestroy, frand, field_stdsamep,
142 fzerop, fneg, fadd, fsub, fmul, fsqr, finv, freduce, fsqrt,
144 fdbl, ftpl, fqdl, fhlv
147 /* --- @field_prime@ --- *
149 * Arguments: @mp *p@ = the characteristic of the field
151 * Returns: A pointer to the field or null.
153 * Use: Creates a field structure for a prime field of size %$p$%,
154 * using Montgomery reduction for arithmetic.
157 field *field_prime(mp *p)
161 f = CREATE(fctx_prime);
163 if (mpmont_create(&f->mm, p)) {
170 f->f.nbits = mp_bits(p);
171 f->f.noctets = (f->f.nbits + 7) >> 3;
176 /*----- That's all, folks -------------------------------------------------*/