3 * $Id: f-niceprime.c,v 1.4 2004/04/01 21:28:41 mdw Exp $
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 /*----- Revision history --------------------------------------------------*
32 * $Log: f-niceprime.c,v $
33 * Revision 1.4 2004/04/01 21:28:41 mdw
34 * Normal basis support (translates to poly basis internally). Rewrite
35 * EC and prime group table generators in awk, so that they can reuse data
36 * for repeated constants.
38 * Revision 1.3 2004/04/01 12:50:09 mdw
39 * Add cyclic group abstraction, with test code. Separate off exponentation
40 * functions for better static linking. Fix a buttload of bugs on the way.
41 * Generally ensure that negative exponents do inversion correctly. Add
42 * table of standard prime-field subgroups. (Binary field subgroups are
43 * currently unimplemented but easy to add if anyone ever finds a good one.)
45 * Revision 1.2 2004/03/27 17:54:11 mdw
46 * Standard curves and curve checking.
48 * Revision 1.1 2004/03/27 00:04:46 mdw
49 * Implement efficient reduction for pleasant-looking primes.
53 /*----- Header files ------------------------------------------------------*/
61 /*----- Main code ---------------------------------------------------------*/
68 /* --- Field operations --- */
70 static void fdestroy(field
*ff
)
71 { fctx
*f
= (fctx
*)ff
; mpreduce_destroy(&f
->r
); DESTROY(f
); }
73 static mp
*frand(field
*ff
, mp
*d
, grand
*r
)
74 { fctx
*f
= (fctx
*)ff
; return (mprand_range(d
, f
->r
.p
, r
, 0)); }
76 static int fzerop(field
*ff
, mp
*x
) { return (!MP_LEN(x
)); }
78 static mp
*fneg(field
*ff
, mp
*d
, mp
*x
)
79 { fctx
*f
= (fctx
*)ff
; return (mp_sub(d
, f
->r
.p
, x
)); }
81 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
82 fctx
*f
= (fctx
*)ff
; d
= mp_add(d
, x
, y
);
83 if (d
->f
& MP_NEG
) d
= mp_add(d
, d
, f
->r
.p
);
84 else if (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
88 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
89 fctx
*f
= (fctx
*)ff
; d
= mp_sub(d
, x
, y
);
90 if (d
->f
& MP_NEG
) d
= mp_add(d
, d
, f
->r
.p
);
91 else if (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
95 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
96 fctx
*f
= (fctx
*)ff
; d
= mp_mul(d
, x
, y
);
97 return (mpreduce_do(&f
->r
, d
, d
));
100 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
) {
101 fctx
*f
= (fctx
*)ff
; d
= mp_sqr(d
, x
);
102 return (mpreduce_do(&f
->r
, d
, d
));
105 static mp
*finv(field
*ff
, mp
*d
, mp
*x
)
106 { fctx
*f
= (fctx
*)ff
; mp_gcd(0, 0, &d
, f
->r
.p
, x
); return (d
); }
108 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
)
109 { fctx
*f
= (fctx
*)ff
; return (mpreduce_do(&f
->r
, d
, x
)); }
111 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
)
112 { fctx
*f
= (fctx
*)ff
; return (mp_modsqrt(d
, x
, f
->r
.p
)); }
114 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
) {
115 fctx
*f
= (fctx
*)ff
; d
= mp_lsl(d
, x
, 1);
116 if (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
120 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
) {
121 fctx
*f
= (fctx
*)ff
; MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
122 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3);
123 while (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
127 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
) {
128 fctx
*f
= (fctx
*)ff
; d
= mp_lsl(d
, x
, 2);
129 while (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
133 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
) {
134 fctx
*f
= (fctx
*)ff
;
135 if (!MP_LEN(x
)) { MP_COPY(x
); MP_DROP(d
); return (x
); }
136 if (x
->v
[0] & 1) { d
= mp_add(d
, x
, f
->r
.p
); x
= d
; }
137 return (mp_lsr(d
, x
, 1));
140 /* --- Field operations table --- */
142 static field_ops fops
= {
143 FTY_PRIME
, "niceprime",
144 fdestroy
, frand
, field_stdsamep
,
146 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
, fsqrt
,
148 fdbl
, ftpl
, fqdl
, fhlv
151 /* --- @field_niceprime@ --- *
153 * Arguments: @mp *p@ = the characteristic of the field
155 * Returns: A pointer to the field.
157 * Use: Creates a field structure for a prime field of size %$p$%,
158 * using efficient reduction for nice primes.
161 field
*field_niceprime(mp
*p
)
163 fctx
*f
= CREATE(fctx
);
167 f
->f
.nbits
= mp_bits(p
);
168 f
->f
.noctets
= (f
->f
.nbits
+ 7) >> 3;
169 mpreduce_create(&f
->r
, p
);
174 /*----- That's all, folks -------------------------------------------------*/