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 -------------------------------------------------*/