3 * $Id: f-prime.c,v 1.10 2004/04/02 01:03:49 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 1.10 2004/04/02 01:03:49 mdw
34 * Miscellaneous constification.
36 * Revision 1.9 2004/04/01 21:28:41 mdw
37 * Normal basis support (translates to poly basis internally). Rewrite
38 * EC and prime group table generators in awk, so that they can reuse data
39 * for repeated constants.
41 * Revision 1.8 2004/04/01 12:50:09 mdw
42 * Add cyclic group abstraction, with test code. Separate off exponentation
43 * functions for better static linking. Fix a buttload of bugs on the way.
44 * Generally ensure that negative exponents do inversion correctly. Add
45 * table of standard prime-field subgroups. (Binary field subgroups are
46 * currently unimplemented but easy to add if anyone ever finds a good one.)
48 * Revision 1.7 2004/03/27 17:54:11 mdw
49 * Standard curves and curve checking.
51 * Revision 1.6 2004/03/23 15:19:32 mdw
52 * Test elliptic curves more thoroughly.
54 * Revision 1.5 2004/03/23 12:08:26 mdw
55 * Random field-element selection.
57 * Revision 1.4 2004/03/21 22:52:06 mdw
58 * Merge and close elliptic curve branch.
60 * Revision 1.3.4.3 2004/03/21 22:39:46 mdw
61 * Elliptic curves on binary fields work.
63 * Revision 1.3.4.2 2004/03/20 00:13:31 mdw
64 * Projective coordinates for prime curves
66 * Revision 1.3.4.1 2003/06/10 13:43:53 mdw
67 * Simple (non-projective) curves over prime fields now seem to work.
69 * Revision 1.3 2003/05/15 23:25:59 mdw
70 * Make elliptic curve stuff build.
72 * Revision 1.2 2002/01/13 13:48:44 mdw
75 * Revision 1.1 2001/04/29 18:12:33 mdw
80 /*----- Header files ------------------------------------------------------*/
88 /*----- Main code ---------------------------------------------------------*/
95 /* --- Field operations --- */
97 static void fdestroy(field
*ff
)
98 { fctx
*f
= (fctx
*)ff
; mpmont_destroy(&f
->mm
); DESTROY(f
); }
100 static mp
*frand(field
*ff
, mp
*d
, grand
*r
)
101 { fctx
*f
= (fctx
*)ff
; return (mprand_range(d
, f
->mm
.m
, r
, 0)); }
103 static mp
*fin(field
*ff
, mp
*d
, mp
*x
) {
104 fctx
*f
= (fctx
*)ff
;
105 mp_div(0, &d
, x
, f
->mm
.m
);
106 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
109 static mp
*fout(field
*ff
, mp
*d
, mp
*x
)
110 { fctx
*f
= (fctx
*)ff
; return (mpmont_reduce(&f
->mm
, d
, x
)); }
112 static int fzerop(field
*ff
, mp
*x
) { return (!MP_LEN(x
)); }
114 static mp
*fneg(field
*ff
, mp
*d
, mp
*x
)
115 { fctx
*f
= (fctx
*)ff
; return (mp_sub(d
, f
->mm
.m
, x
)); }
117 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
118 fctx
*f
= (fctx
*)ff
; d
= mp_add(d
, x
, y
);
119 if (d
->f
& MP_NEG
) d
= mp_add(d
, d
, f
->mm
.m
);
120 else if (MP_CMP(d
, >, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
124 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
125 fctx
*f
= (fctx
*)ff
; d
= mp_sub(d
, x
, y
);
126 if (d
->f
& MP_NEG
) d
= mp_add(d
, d
, f
->mm
.m
);
127 else if (MP_CMP(d
, >, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
131 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
132 { fctx
*f
= (fctx
*)ff
; return (mpmont_mul(&f
->mm
, d
, x
, y
)); }
134 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
) {
135 fctx
*f
= (fctx
*)ff
; d
= mp_sqr(d
, x
);
136 return (mpmont_reduce(&f
->mm
, d
, d
));
139 static mp
*finv(field
*ff
, mp
*d
, mp
*x
) {
140 fctx
*f
= (fctx
*)ff
; d
= mpmont_reduce(&f
->mm
, d
, x
);
141 mp_gcd(0, 0, &d
, f
->mm
.m
, d
); return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
144 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
)
145 { fctx
*f
= (fctx
*)ff
; mp_div(0, &d
, x
, f
->mm
.m
); return (d
); }
147 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
) {
148 fctx
*f
= (fctx
*)ff
; d
= mpmont_reduce(&f
->mm
, d
, x
);
149 d
= mp_modsqrt(d
, d
, f
->mm
.m
); if (!d
) return (d
);
150 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
153 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
) {
154 fctx
*f
= (fctx
*)ff
; d
= mp_lsl(d
, x
, 1);
155 if (MP_CMP(d
, >, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
159 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
) {
160 fctx
*f
= (fctx
*)ff
; MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
161 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3);
162 while (MP_CMP(d
, >, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
166 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
) {
167 fctx
*f
= (fctx
*)ff
; d
= mp_lsl(d
, x
, 2);
168 while (MP_CMP(d
, >, f
->mm
.m
)) d
= mp_sub(d
, d
, f
->mm
.m
);
172 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
) {
173 fctx
*f
= (fctx
*)ff
;
174 if (!MP_LEN(x
)) { MP_COPY(x
); MP_DROP(d
); return (x
); }
175 if (x
->v
[0] & 1) { d
= mp_add(d
, x
, f
->mm
.m
); x
= d
; }
176 return (mp_lsr(d
, x
, 1));
179 /* --- Field operations table --- */
181 static const field_ops fops
= {
183 fdestroy
, frand
, field_stdsamep
,
185 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
, fsqrt
,
187 fdbl
, ftpl
, fqdl
, fhlv
190 /* --- @field_prime@ --- *
192 * Arguments: @mp *p@ = the characteristic of the field
194 * Returns: A pointer to the field.
196 * Use: Creates a field structure for a prime field of size %$p$%,
197 * using Montgomery reduction for arithmetic.
200 field
*field_prime(mp
*p
)
202 fctx
*f
= CREATE(fctx
);
204 mpmont_create(&f
->mm
, p
);
208 f
->f
.nbits
= mp_bits(p
);
209 f
->f
.noctets
= (f
->f
.nbits
+ 7) >> 3;
213 /*----- That's all, folks -------------------------------------------------*/