3 * $Id: f-prime.c,v 1.3.4.3 2004/03/21 22:39:46 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 1.3.4.3 2004/03/21 22:39:46 mdw
34 * Elliptic curves on binary fields work.
36 * Revision 1.3.4.2 2004/03/20 00:13:31 mdw
37 * Projective coordinates for prime curves
39 * Revision 1.3.4.1 2003/06/10 13:43:53 mdw
40 * Simple (non-projective) curves over prime fields now seem to work.
42 * Revision 1.3 2003/05/15 23:25:59 mdw
43 * Make elliptic curve stuff build.
45 * Revision 1.2 2002/01/13 13:48:44 mdw
48 * Revision 1.1 2001/04/29 18:12:33 mdw
53 /*----- Header files ------------------------------------------------------*/
60 /*----- Data structures ---------------------------------------------------*/
67 /*----- Main code ---------------------------------------------------------*/
69 /* --- Field operations --- */
71 static void fdestroy(field
*ff
)
74 mpmont_destroy(&f
->mm
);
78 static mp
*fin(field
*ff
, mp
*d
, mp
*x
)
81 mp_div(0, &d
, x
, f
->mm
.m
);
82 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
85 static mp
*fout(field
*ff
, mp
*d
, mp
*x
)
88 return (mpmont_reduce(&f
->mm
, d
, x
));
91 static int fzerop(field
*ff
, mp
*x
)
96 static mp
*fneg(field
*ff
, mp
*d
, mp
*x
)
99 return (mp_sub(d
, f
->mm
.m
, x
));
102 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
104 fctx
*f
= (fctx
*)ff
;
107 d
= mp_add(d
, d
, f
->mm
.m
);
108 else if (MP_CMP(d
, >, f
->mm
.m
))
109 d
= mp_sub(d
, d
, f
->mm
.m
);
113 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
115 fctx
*f
= (fctx
*)ff
;
118 d
= mp_add(d
, d
, f
->mm
.m
);
119 else if (MP_CMP(d
, >, f
->mm
.m
))
120 d
= mp_sub(d
, d
, f
->mm
.m
);
124 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
126 fctx
*f
= (fctx
*)ff
;
127 return (mpmont_mul(&f
->mm
, d
, x
, y
));
130 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
)
132 fctx
*f
= (fctx
*)ff
;
134 return (mpmont_reduce(&f
->mm
, d
, d
));
137 static mp
*finv(field
*ff
, mp
*d
, mp
*x
)
139 fctx
*f
= (fctx
*)ff
;
140 d
= mpmont_reduce(&f
->mm
, d
, x
);
141 mp_gcd(0, 0, &d
, f
->mm
.m
, d
);
142 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
145 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
)
147 fctx
*f
= (fctx
*)ff
;
148 mp_div(0, &d
, x
, f
->mm
.m
);
152 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
)
154 fctx
*f
= (fctx
*)ff
;
155 d
= mpmont_reduce(&f
->mm
, d
, x
);
156 d
= mp_modsqrt(d
, d
, f
->mm
.m
);
159 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
162 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
)
164 fctx
*f
= (fctx
*)ff
;
166 if (MP_CMP(d
, >, f
->mm
.m
))
167 d
= mp_sub(d
, d
, f
->mm
.m
);
171 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
)
173 fctx
*f
= (fctx
*)ff
;
174 MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
175 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3);
176 while (MP_CMP(d
, >, f
->mm
.m
))
177 d
= mp_sub(d
, d
, f
->mm
.m
);
181 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
)
183 fctx
*f
= (fctx
*)ff
;
185 while (MP_CMP(d
, >, f
->mm
.m
))
186 d
= mp_sub(d
, d
, f
->mm
.m
);
190 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
)
192 fctx
*f
= (fctx
*)ff
;
199 d
= mp_add(d
, x
, f
->mm
.m
);
202 return (mp_lsr(d
, x
, 1));
205 /* --- Field operations table --- */
207 static field_ops fops
= {
210 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
, fsqrt
,
212 fdbl
, ftpl
, fqdl
, fhlv
215 /* --- @field_prime@ --- *
217 * Arguments: @mp *p@ = the characteristic of the field
219 * Returns: A pointer to the field.
221 * Use: Creates a field structure for a prime field of size %$p$%,
222 * using Montgomery reduction for arithmetic.
225 field
*field_prime(mp
*p
)
227 fctx
*f
= CREATE(fctx
);
229 mpmont_create(&f
->mm
, p
);
235 /*----- That's all, folks -------------------------------------------------*/