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 return (mp_sub(d
, f
->r
.p
, x
));
58 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
59 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_add(d
, x
, y
);
60 if (MP_NEGP(d
)) d
= mp_add(d
, d
, f
->r
.p
);
61 else if (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
65 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
66 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_sub(d
, x
, y
);
67 if (MP_NEGP(d
)) d
= mp_add(d
, d
, f
->r
.p
);
68 else if (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
72 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
73 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_mul(d
, x
, y
);
74 return (mpreduce_do(&f
->r
, d
, d
));
77 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
) {
78 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_sqr(d
, x
);
79 return (mpreduce_do(&f
->r
, d
, d
));
82 static mp
*finv(field
*ff
, mp
*d
, mp
*x
) {
83 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
84 d
= mp_modinv(d
, x
, f
->r
.p
);
88 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
) {
89 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
90 return (mpreduce_do(&f
->r
, d
, x
));
93 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
) {
94 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
95 return (mp_modsqrt(d
, x
, f
->r
.p
));
98 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
) {
99 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_lsl(d
, x
, 1);
100 if (MP_CMP(d
, >=, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
104 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
) {
105 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
106 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3); d
->f
&= ~MP_UNDEF
;
107 while (MP_CMP(d
, >=, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
111 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
) {
112 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_lsl(d
, x
, 2);
113 while (MP_CMP(d
, >=, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
117 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
) {
118 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
119 if (MP_ZEROP(x
)) { MP_COPY(x
); MP_DROP(d
); return (x
); }
120 if (x
->v
[0] & 1) { d
= mp_add(d
, x
, f
->r
.p
); x
= d
; }
121 return (mp_lsr(d
, x
, 1));
124 /* --- Field operations table --- */
126 static const field_ops fops
= {
127 FTY_PRIME
, "niceprime",
128 fdestroy
, frand
, field_stdsamep
,
130 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
, fsqrt
,
132 fdbl
, ftpl
, fqdl
, fhlv
135 /* --- @field_niceprime@ --- *
137 * Arguments: @mp *p@ = the characteristic of the field
139 * Returns: A pointer to the field, or null.
141 * Use: Creates a field structure for a prime field of size %$p$%,
142 * using efficient reduction for nice primes.
145 field
*field_niceprime(mp
*p
)
147 fctx_niceprime
*f
= CREATE(fctx_niceprime
);
151 f
->f
.nbits
= mp_bits(p
);
152 f
->f
.noctets
= (f
->f
.nbits
+ 7) >> 3;
153 if (mpreduce_create(&f
->r
, p
)) {
162 /*----- That's all, folks -------------------------------------------------*/