3 * $Id: f-prime.c,v 1.3.4.2 2004/03/20 00:13:31 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 1.3.4.2 2004/03/20 00:13:31 mdw
34 * Projective coordinates for prime curves
36 * Revision 1.3.4.1 2003/06/10 13:43:53 mdw
37 * Simple (non-projective) curves over prime fields now seem to work.
39 * Revision 1.3 2003/05/15 23:25:59 mdw
40 * Make elliptic curve stuff build.
42 * Revision 1.2 2002/01/13 13:48:44 mdw
45 * Revision 1.1 2001/04/29 18:12:33 mdw
50 /*----- Header files ------------------------------------------------------*/
57 /*----- Data structures ---------------------------------------------------*/
64 /*----- Main code ---------------------------------------------------------*/
66 /* --- Field operations --- */
68 static void fdestroy(field
*ff
)
71 mpmont_destroy(&f
->mm
);
75 static mp
*fin(field
*ff
, mp
*d
, mp
*x
)
78 mp_div(0, &d
, x
, f
->mm
.m
);
79 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
82 static mp
*fout(field
*ff
, mp
*d
, mp
*x
)
85 return (mpmont_reduce(&f
->mm
, d
, x
));
88 static int fzerop(field
*ff
, mp
*x
)
93 static mp
*fneg(field
*ff
, mp
*d
, mp
*x
)
96 return (mp_sub(d
, f
->mm
.m
, x
));
99 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
101 fctx
*f
= (fctx
*)ff
;
104 d
= mp_add(d
, d
, f
->mm
.m
);
105 else if (MP_CMP(d
, >, f
->mm
.m
))
106 d
= mp_sub(d
, d
, f
->mm
.m
);
110 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
112 fctx
*f
= (fctx
*)ff
;
115 d
= mp_add(d
, d
, f
->mm
.m
);
116 else if (MP_CMP(d
, >, f
->mm
.m
))
117 d
= mp_sub(d
, d
, f
->mm
.m
);
121 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
123 fctx
*f
= (fctx
*)ff
;
124 return (mpmont_mul(&f
->mm
, d
, x
, y
));
127 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
)
129 fctx
*f
= (fctx
*)ff
;
131 return (mpmont_reduce(&f
->mm
, d
, d
));
134 static mp
*finv(field
*ff
, mp
*d
, mp
*x
)
136 fctx
*f
= (fctx
*)ff
;
137 d
= mpmont_reduce(&f
->mm
, d
, x
);
138 mp_gcd(0, 0, &d
, f
->mm
.m
, d
);
139 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
142 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
)
144 fctx
*f
= (fctx
*)ff
;
145 mp_div(0, &d
, x
, f
->mm
.m
);
149 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
)
151 fctx
*f
= (fctx
*)ff
;
153 if (MP_CMP(d
, >, f
->mm
.m
))
154 d
= mp_sub(d
, d
, f
->mm
.m
);
158 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
)
160 fctx
*f
= (fctx
*)ff
;
161 MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
162 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3);
163 while (MP_CMP(d
, >, f
->mm
.m
))
164 d
= mp_sub(d
, d
, f
->mm
.m
);
168 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
)
170 fctx
*f
= (fctx
*)ff
;
172 while (MP_CMP(d
, >, f
->mm
.m
))
173 d
= mp_sub(d
, d
, f
->mm
.m
);
177 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
)
179 fctx
*f
= (fctx
*)ff
;
186 d
= mp_add(d
, x
, f
->mm
.m
);
189 return (mp_lsr(d
, x
, 1));
192 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
)
194 fctx
*f
= (fctx
*)ff
;
195 d
= mpmont_reduce(&f
->mm
, d
, x
);
196 d
= mp_modsqrt(d
, d
, f
->mm
.m
);
199 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
202 /* --- Field operations table --- */
204 static field_ops fops
= {
207 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
,
208 fdbl
, ftpl
, fqdl
, fhlv
, fsqrt
211 /* --- @field_prime@ --- *
213 * Arguments: @mp *p@ = the characteristic of the field
215 * Returns: A pointer to the field.
217 * Use: Creates a field structure for a prime field of size %$p$%,
218 * using Montgomery reduction for arithmetic.
221 field
*field_prime(mp
*p
)
223 fctx
*f
= CREATE(fctx
);
225 mpmont_create(&f
->mm
, p
);
231 /*----- That's all, folks -------------------------------------------------*/