5 * Prime fields with efficient reduction for special-form primes
7 * (c) 2004 Straylight/Edgeware
10 /*----- Licensing notice --------------------------------------------------*
12 * This file is part of Catacomb.
14 * Catacomb is free software; you can redistribute it and/or modify
15 * it under the terms of the GNU Library General Public License as
16 * published by the Free Software Foundation; either version 2 of the
17 * License, or (at your option) any later version.
19 * Catacomb is distributed in the hope that it will be useful,
20 * but WITHOUT ANY WARRANTY; without even the implied warranty of
21 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
22 * GNU Library General Public License for more details.
24 * You should have received a copy of the GNU Library General Public
25 * License along with Catacomb; if not, write to the Free
26 * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
30 /*----- Header files ------------------------------------------------------*/
35 #include "field-guts.h"
38 /*----- Main code ---------------------------------------------------------*/
40 /* --- Field operations --- */
42 static void fdestroy(field
*ff
) {
43 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
44 mpreduce_destroy(&f
->r
);
48 static mp
*frand(field
*ff
, mp
*d
, grand
*r
) {
49 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
50 return (mprand_range(d
, f
->r
.p
, r
, 0));
53 static int fzerop(field
*ff
, mp
*x
) { return (MP_ZEROP(x
)); }
55 static mp
*fneg(field
*ff
, mp
*d
, mp
*x
) {
56 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
57 return (mp_sub(d
, f
->r
.p
, x
));
60 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
61 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_add(d
, x
, y
);
62 if (MP_NEGP(d
)) d
= mp_add(d
, d
, f
->r
.p
);
63 else if (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
67 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
68 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_sub(d
, x
, y
);
69 if (MP_NEGP(d
)) d
= mp_add(d
, d
, f
->r
.p
);
70 else if (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
74 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
75 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_mul(d
, x
, y
);
76 return (mpreduce_do(&f
->r
, d
, d
));
79 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
) {
80 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_sqr(d
, x
);
81 return (mpreduce_do(&f
->r
, d
, d
));
84 static mp
*finv(field
*ff
, mp
*d
, mp
*x
) {
85 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
86 d
= mp_modinv(d
, x
, f
->r
.p
);
90 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
) {
91 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
92 return (mpreduce_do(&f
->r
, d
, x
));
95 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
) {
96 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
97 return (mp_modsqrt(d
, x
, f
->r
.p
));
100 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
) {
101 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_lsl(d
, x
, 1);
102 if (MP_CMP(d
, >=, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
106 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
) {
107 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
108 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3); d
->f
&= ~MP_UNDEF
;
109 while (MP_CMP(d
, >=, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
113 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
) {
114 fctx_niceprime
*f
= (fctx_niceprime
*)ff
; d
= mp_lsl(d
, x
, 2);
115 while (MP_CMP(d
, >=, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
119 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
) {
120 fctx_niceprime
*f
= (fctx_niceprime
*)ff
;
121 if (MP_ZEROP(x
)) { MP_COPY(x
); MP_DROP(d
); return (x
); }
122 if (x
->v
[0] & 1) { d
= mp_add(d
, x
, f
->r
.p
); x
= d
; }
123 return (mp_lsr(d
, x
, 1));
126 /* --- Field operations table --- */
128 static const field_ops fops
= {
129 FTY_PRIME
, "niceprime",
130 fdestroy
, frand
, field_stdsamep
,
132 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
, fsqrt
,
134 fdbl
, ftpl
, fqdl
, fhlv
137 /* --- @field_niceprime@ --- *
139 * Arguments: @mp *p@ = the characteristic of the field
141 * Returns: A pointer to the field, or null.
143 * Use: Creates a field structure for a prime field of size %$p$%,
144 * using efficient reduction for nice primes.
147 field
*field_niceprime(mp
*p
)
149 fctx_niceprime
*f
= CREATE(fctx_niceprime
);
153 f
->f
.nbits
= mp_bits(p
);
154 f
->f
.noctets
= (f
->f
.nbits
+ 7) >> 3;
155 if (mpreduce_create(&f
->r
, p
)) {
164 /*----- That's all, folks -------------------------------------------------*/