3 * $Id: f-prime.c,v 1.8 2004/04/01 12:50:09 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 1.8 2004/04/01 12:50:09 mdw
34 * Add cyclic group abstraction, with test code. Separate off exponentation
35 * functions for better static linking. Fix a buttload of bugs on the way.
36 * Generally ensure that negative exponents do inversion correctly. Add
37 * table of standard prime-field subgroups. (Binary field subgroups are
38 * currently unimplemented but easy to add if anyone ever finds a good one.)
40 * Revision 1.7 2004/03/27 17:54:11 mdw
41 * Standard curves and curve checking.
43 * Revision 1.6 2004/03/23 15:19:32 mdw
44 * Test elliptic curves more thoroughly.
46 * Revision 1.5 2004/03/23 12:08:26 mdw
47 * Random field-element selection.
49 * Revision 1.4 2004/03/21 22:52:06 mdw
50 * Merge and close elliptic curve branch.
52 * Revision 1.3.4.3 2004/03/21 22:39:46 mdw
53 * Elliptic curves on binary fields work.
55 * Revision 1.3.4.2 2004/03/20 00:13:31 mdw
56 * Projective coordinates for prime curves
58 * Revision 1.3.4.1 2003/06/10 13:43:53 mdw
59 * Simple (non-projective) curves over prime fields now seem to work.
61 * Revision 1.3 2003/05/15 23:25:59 mdw
62 * Make elliptic curve stuff build.
64 * Revision 1.2 2002/01/13 13:48:44 mdw
67 * Revision 1.1 2001/04/29 18:12:33 mdw
72 /*----- Header files ------------------------------------------------------*/
80 /*----- Data structures ---------------------------------------------------*/
87 /*----- Main code ---------------------------------------------------------*/
89 /* --- Field operations --- */
91 static void fdestroy(field
*ff
)
94 mpmont_destroy(&f
->mm
);
98 static mp
*frand(field
*ff
, mp
*d
, grand
*r
)
100 fctx
*f
= (fctx
*)ff
;
101 return (mprand_range(d
, f
->mm
.m
, r
, 0));
104 static mp
*fin(field
*ff
, mp
*d
, mp
*x
)
106 fctx
*f
= (fctx
*)ff
;
107 mp_div(0, &d
, x
, f
->mm
.m
);
108 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
111 static mp
*fout(field
*ff
, mp
*d
, mp
*x
)
113 fctx
*f
= (fctx
*)ff
;
114 return (mpmont_reduce(&f
->mm
, d
, x
));
117 static int fzerop(field
*ff
, mp
*x
)
122 static mp
*fneg(field
*ff
, mp
*d
, mp
*x
)
124 fctx
*f
= (fctx
*)ff
;
125 return (mp_sub(d
, f
->mm
.m
, x
));
128 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
130 fctx
*f
= (fctx
*)ff
;
133 d
= mp_add(d
, d
, f
->mm
.m
);
134 else if (MP_CMP(d
, >, f
->mm
.m
))
135 d
= mp_sub(d
, d
, f
->mm
.m
);
139 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
141 fctx
*f
= (fctx
*)ff
;
144 d
= mp_add(d
, d
, f
->mm
.m
);
145 else if (MP_CMP(d
, >, f
->mm
.m
))
146 d
= mp_sub(d
, d
, f
->mm
.m
);
150 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
152 fctx
*f
= (fctx
*)ff
;
153 return (mpmont_mul(&f
->mm
, d
, x
, y
));
156 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
)
158 fctx
*f
= (fctx
*)ff
;
160 return (mpmont_reduce(&f
->mm
, d
, d
));
163 static mp
*finv(field
*ff
, mp
*d
, mp
*x
)
165 fctx
*f
= (fctx
*)ff
;
166 d
= mpmont_reduce(&f
->mm
, d
, x
);
167 mp_gcd(0, 0, &d
, f
->mm
.m
, d
);
168 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
171 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
)
173 fctx
*f
= (fctx
*)ff
;
174 mp_div(0, &d
, x
, f
->mm
.m
);
178 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
)
180 fctx
*f
= (fctx
*)ff
;
181 d
= mpmont_reduce(&f
->mm
, d
, x
);
182 d
= mp_modsqrt(d
, d
, f
->mm
.m
);
185 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
188 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
)
190 fctx
*f
= (fctx
*)ff
;
192 if (MP_CMP(d
, >, f
->mm
.m
))
193 d
= mp_sub(d
, d
, f
->mm
.m
);
197 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
)
199 fctx
*f
= (fctx
*)ff
;
200 MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
201 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3);
202 while (MP_CMP(d
, >, f
->mm
.m
))
203 d
= mp_sub(d
, d
, f
->mm
.m
);
207 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
)
209 fctx
*f
= (fctx
*)ff
;
211 while (MP_CMP(d
, >, f
->mm
.m
))
212 d
= mp_sub(d
, d
, f
->mm
.m
);
216 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
)
218 fctx
*f
= (fctx
*)ff
;
225 d
= mp_add(d
, x
, f
->mm
.m
);
228 return (mp_lsr(d
, x
, 1));
231 /* --- Field operations table --- */
233 static field_ops fops
= {
235 fdestroy
, frand
, field_stdsamep
,
237 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
, fsqrt
,
239 fdbl
, ftpl
, fqdl
, fhlv
242 /* --- @field_prime@ --- *
244 * Arguments: @mp *p@ = the characteristic of the field
246 * Returns: A pointer to the field.
248 * Use: Creates a field structure for a prime field of size %$p$%,
249 * using Montgomery reduction for arithmetic.
252 field
*field_prime(mp
*p
)
254 fctx
*f
= CREATE(fctx
);
256 mpmont_create(&f
->mm
, p
);
260 f
->f
.nbits
= mp_bits(p
);
261 f
->f
.noctets
= (f
->f
.nbits
+ 7) >> 3;
265 /*----- That's all, folks -------------------------------------------------*/