3 * $Id: f-prime.c,v 1.9 2004/04/01 21:28:41 mdw Exp $
5 * Prime fields with Montgomery arithmetic
7 * (c) 2001 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 --------------------------------------------------*
33 * Revision 1.9 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 1.8 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 1.7 2004/03/27 17:54:11 mdw
46 * Standard curves and curve checking.
48 * Revision 1.6 2004/03/23 15:19:32 mdw
49 * Test elliptic curves more thoroughly.
51 * Revision 1.5 2004/03/23 12:08:26 mdw
52 * Random field-element selection.
54 * Revision 1.4 2004/03/21 22:52:06 mdw
55 * Merge and close elliptic curve branch.
57 * Revision 1.3.4.3 2004/03/21 22:39:46 mdw
58 * Elliptic curves on binary fields work.
60 * Revision 1.3.4.2 2004/03/20 00:13:31 mdw
61 * Projective coordinates for prime curves
63 * Revision 1.3.4.1 2003/06/10 13:43:53 mdw
64 * Simple (non-projective) curves over prime fields now seem to work.
66 * Revision 1.3 2003/05/15 23:25:59 mdw
67 * Make elliptic curve stuff build.
69 * Revision 1.2 2002/01/13 13:48:44 mdw
72 * Revision 1.1 2001/04/29 18:12:33 mdw
77 /*----- Header files ------------------------------------------------------*/
85 /*----- Main code ---------------------------------------------------------*/
92 /* --- Field operations --- */
94 static void fdestroy(field
*ff
)
95 { fctx
*f
= (fctx
*)ff
; mpmont_destroy(&f
->mm
); DESTROY(f
); }
97 static mp
*frand(field
*ff
, mp
*d
, grand
*r
)
98 { fctx
*f
= (fctx
*)ff
; return (mprand_range(d
, f
->mm
.m
, r
, 0)); }
100 static mp
*fin(field
*ff
, mp
*d
, mp
*x
) {
101 fctx
*f
= (fctx
*)ff
;
102 mp_div(0, &d
, x
, f
->mm
.m
);
103 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
106 static mp
*fout(field
*ff
, mp
*d
, mp
*x
)
107 { fctx
*f
= (fctx
*)ff
; return (mpmont_reduce(&f
->mm
, d
, x
)); }
109 static int fzerop(field
*ff
, mp
*x
) { return (!MP_LEN(x
)); }
111 static mp
*fneg(field
*ff
, mp
*d
, mp
*x
)
112 { fctx
*f
= (fctx
*)ff
; return (mp_sub(d
, f
->mm
.m
, x
)); }
114 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
115 fctx
*f
= (fctx
*)ff
; d
= mp_add(d
, x
, y
);
116 if (d
->f
& MP_NEG
) d
= mp_add(d
, d
, f
->mm
.m
);
117 else if (MP_CMP(d
, >, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
121 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
122 fctx
*f
= (fctx
*)ff
; d
= mp_sub(d
, x
, y
);
123 if (d
->f
& MP_NEG
) d
= mp_add(d
, d
, f
->mm
.m
);
124 else if (MP_CMP(d
, >, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
128 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
129 { fctx
*f
= (fctx
*)ff
; return (mpmont_mul(&f
->mm
, d
, x
, y
)); }
131 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
) {
132 fctx
*f
= (fctx
*)ff
; d
= mp_sqr(d
, x
);
133 return (mpmont_reduce(&f
->mm
, d
, d
));
136 static mp
*finv(field
*ff
, mp
*d
, mp
*x
) {
137 fctx
*f
= (fctx
*)ff
; d
= mpmont_reduce(&f
->mm
, d
, x
);
138 mp_gcd(0, 0, &d
, f
->mm
.m
, d
); return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
141 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
)
142 { fctx
*f
= (fctx
*)ff
; mp_div(0, &d
, x
, f
->mm
.m
); return (d
); }
144 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
) {
145 fctx
*f
= (fctx
*)ff
; d
= mpmont_reduce(&f
->mm
, d
, x
);
146 d
= mp_modsqrt(d
, d
, f
->mm
.m
); if (!d
) return (d
);
147 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
150 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
) {
151 fctx
*f
= (fctx
*)ff
; d
= mp_lsl(d
, x
, 1);
152 if (MP_CMP(d
, >, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
156 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
) {
157 fctx
*f
= (fctx
*)ff
; MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
158 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3);
159 while (MP_CMP(d
, >, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
163 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
) {
164 fctx
*f
= (fctx
*)ff
; d
= mp_lsl(d
, x
, 2);
165 while (MP_CMP(d
, >, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
169 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
) {
170 fctx
*f
= (fctx
*)ff
;
171 if (!MP_LEN(x
)) { MP_COPY(x
); MP_DROP(d
); return (x
); }
172 if (x
->v
[0] & 1) { d
= mp_add(d
, x
, f
->mm
.m
); x
= d
; }
173 return (mp_lsr(d
, x
, 1));
176 /* --- Field operations table --- */
178 static field_ops fops
= {
180 fdestroy
, frand
, field_stdsamep
,
182 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
, fsqrt
,
184 fdbl
, ftpl
, fqdl
, fhlv
187 /* --- @field_prime@ --- *
189 * Arguments: @mp *p@ = the characteristic of the field
191 * Returns: A pointer to the field.
193 * Use: Creates a field structure for a prime field of size %$p$%,
194 * using Montgomery reduction for arithmetic.
197 field
*field_prime(mp
*p
)
199 fctx
*f
= CREATE(fctx
);
201 mpmont_create(&f
->mm
, p
);
205 f
->f
.nbits
= mp_bits(p
);
206 f
->f
.noctets
= (f
->f
.nbits
+ 7) >> 3;
210 /*----- That's all, folks -------------------------------------------------*/