3 * Prime fields with efficient reduction for special-form primes
5 * (c) 2004 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 ------------------------------------------------------*/
33 #include "field-guts.h"
36 /*----- Main code ---------------------------------------------------------*/
38 /* --- Field operations --- */
40 static void fdestroy(field
*ff
) {
41 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
42 mpreduce_destroy(&f
->r
);
46 static mp
*frand(field
*ff
, mp
*d
, grand
*r
) {
47 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
48 return (mprand_range(d
, f
->r
.p
, r
, 0));
51 static int fzerop(field
*ff
, mp
*x
) { return (MP_ZEROP(x
)); }
53 static mp
*fneg(field
*ff
, mp
*d
, mp
*x
) {
54 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
55 if (MP_ZEROP(x
)) { if (d
!= x
) mp_drop(d
); return (MP_COPY(x
)); }
56 else return (mp_sub(d
, f
->r
.p
, x
));
59 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
60 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_add(d
, x
, y
);
61 if (MP_NEGP(d
)) d
= mp_add(d
, d
, f
->r
.p
);
62 else if (MP_CMP(d
, >=, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
66 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
67 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_sub(d
, x
, y
);
68 if (MP_NEGP(d
)) d
= mp_add(d
, d
, f
->r
.p
);
69 else if (MP_CMP(d
, >=, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
73 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
74 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_mul(d
, x
, y
);
75 return (mpreduce_do(&f
->r
, d
, d
));
78 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
) {
79 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_sqr(d
, x
);
80 return (mpreduce_do(&f
->r
, d
, d
));
83 static mp
*finv(field
*ff
, mp
*d
, mp
*x
) {
84 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
85 d
= mp_modinv(d
, x
, f
->r
.p
);
89 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
) {
90 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
91 return (mpreduce_do(&f
->r
, d
, x
));
94 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
) {
95 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
96 return (mp_modsqrt(d
, x
, f
->r
.p
));
99 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
) {
100 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_lsl(d
, x
, 1);
101 if (MP_CMP(d
, >=, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
105 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
) {
106 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
107 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3); d
->f
&= ~MP_UNDEF
;
108 while (MP_CMP(d
, >=, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
112 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
) {
113 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_lsl(d
, x
, 2);
114 while (MP_CMP(d
, >=, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
118 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
) {
119 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
120 if (MP_ZEROP(x
)) { MP_COPY(x
); MP_DROP(d
); return (x
); }
121 if (x
->v
[0] & 1) { d
= mp_add(d
, x
, f
->r
.p
); x
= d
; }
122 return (mp_lsr(d
, x
, 1));
125 /* --- Field operations table --- */
127 static const field_ops fops
= {
128 FTY_PRIME
, "niceprime",
129 fdestroy
, frand
, field_stdsamep
,
131 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
, fsqrt
,
133 fdbl
, ftpl
, fqdl
, fhlv
136 /* --- @field_niceprime@ --- *
138 * Arguments: @mp *p@ = the characteristic of the field
140 * Returns: A pointer to the field, or null.
142 * Use: Creates a field structure for a prime field of size %$p$%,
143 * using efficient reduction for nice primes.
146 field
*field_niceprime(mp
*p
)
148 fctx_niceprime
*f
= CREATE(fctx_niceprime
);
152 f
->f
.nbits
= mp_bits(p
);
153 f
->f
.noctets
= (f
->f
.nbits
+ 7) >> 3;
154 if (mpreduce_create(&f
->r
, p
)) {
163 /*----- That's all, folks -------------------------------------------------*/