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 if (MP_ZEROP(x
)) { if (d
!= x
) mp_drop(d
); return (MP_COPY(x
)); }
67 else return (mp_sub(d
, f
->mm
.m
, x
));
70 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
71 fctx_prime
*f
= (fctx_prime
*)ff
; d
= mp_add(d
, x
, y
);
72 if (MP_NEGP(d
)) d
= mp_add(d
, d
, f
->mm
.m
);
73 else if (MP_CMP(d
, >=, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
77 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
78 fctx_prime
*f
= (fctx_prime
*)ff
; d
= mp_sub(d
, x
, y
);
79 if (MP_NEGP(d
)) d
= mp_add(d
, d
, f
->mm
.m
);
80 else if (MP_CMP(d
, >=, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
84 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
85 fctx_prime
*f
= (fctx_prime
*)ff
;
86 return (mpmont_mul(&f
->mm
, d
, x
, y
));
89 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
) {
90 fctx_prime
*f
= (fctx_prime
*)ff
; d
= mp_sqr(d
, x
);
91 return (mpmont_reduce(&f
->mm
, d
, d
));
94 static mp
*finv(field
*ff
, mp
*d
, mp
*x
) {
95 fctx_prime
*f
= (fctx_prime
*)ff
; d
= mpmont_reduce(&f
->mm
, d
, x
);
96 d
= mp_modinv(d
, d
, f
->mm
.m
); return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
99 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
) {
100 fctx_prime
*f
= (fctx_prime
*)ff
;
101 mp_div(0, &d
, x
, f
->mm
.m
);
105 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
) {
106 fctx_prime
*f
= (fctx_prime
*)ff
; d
= mpmont_reduce(&f
->mm
, d
, x
);
107 d
= mp_modsqrt(d
, d
, f
->mm
.m
); if (!d
) return (d
);
108 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
111 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
) {
112 fctx_prime
*f
= (fctx_prime
*)ff
; d
= mp_lsl(d
, x
, 1);
113 if (MP_CMP(d
, >=, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
117 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
) {
118 fctx_prime
*f
= (fctx_prime
*)ff
; MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
119 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3); d
->f
&= ~MP_UNDEF
;
120 while (MP_CMP(d
, >=, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
124 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
) {
125 fctx_prime
*f
= (fctx_prime
*)ff
; d
= mp_lsl(d
, x
, 2);
126 while (MP_CMP(d
, >=, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
130 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
) {
131 fctx_prime
*f
= (fctx_prime
*)ff
;
132 if (MP_ZEROP(x
)) { MP_COPY(x
); MP_DROP(d
); return (x
); }
133 if (x
->v
[0] & 1) { d
= mp_add(d
, x
, f
->mm
.m
); x
= d
; }
134 return (mp_lsr(d
, x
, 1));
137 /* --- Field operations table --- */
139 static const field_ops fops
= {
141 fdestroy
, frand
, field_stdsamep
,
143 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
, fsqrt
,
145 fdbl
, ftpl
, fqdl
, fhlv
148 /* --- @field_prime@ --- *
150 * Arguments: @mp *p@ = the characteristic of the field
152 * Returns: A pointer to the field or null.
154 * Use: Creates a field structure for a prime field of size %$p$%,
155 * using Montgomery reduction for arithmetic.
158 field
*field_prime(mp
*p
)
162 f
= CREATE(fctx_prime
);
164 if (mpmont_create(&f
->mm
, p
)) {
171 f
->f
.nbits
= mp_bits(p
);
172 f
->f
.noctets
= (f
->f
.nbits
+ 7) >> 3;
177 /*----- That's all, folks -------------------------------------------------*/