845490200b44be805127ab949f1c0604269254d3
3 * $Id: f-prime.c,v 1.4 2004/03/21 22:52:06 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 1.4 2004/03/21 22:52:06 mdw
34 * Merge and close elliptic curve branch.
36 * Revision 1.3.4.3 2004/03/21 22:39:46 mdw
37 * Elliptic curves on binary fields work.
39 * Revision 1.3.4.2 2004/03/20 00:13:31 mdw
40 * Projective coordinates for prime curves
42 * Revision 1.3.4.1 2003/06/10 13:43:53 mdw
43 * Simple (non-projective) curves over prime fields now seem to work.
45 * Revision 1.3 2003/05/15 23:25:59 mdw
46 * Make elliptic curve stuff build.
48 * Revision 1.2 2002/01/13 13:48:44 mdw
51 * Revision 1.1 2001/04/29 18:12:33 mdw
56 /*----- Header files ------------------------------------------------------*/
63 /*----- Data structures ---------------------------------------------------*/
70 /*----- Main code ---------------------------------------------------------*/
72 /* --- Field operations --- */
74 static void fdestroy(field
*ff
)
77 mpmont_destroy(&f
->mm
);
81 static mp
*fin(field
*ff
, mp
*d
, mp
*x
)
84 mp_div(0, &d
, x
, f
->mm
.m
);
85 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
88 static mp
*fout(field
*ff
, mp
*d
, mp
*x
)
91 return (mpmont_reduce(&f
->mm
, d
, x
));
94 static int fzerop(field
*ff
, mp
*x
)
99 static mp
*fneg(field
*ff
, mp
*d
, mp
*x
)
101 fctx
*f
= (fctx
*)ff
;
102 return (mp_sub(d
, f
->mm
.m
, x
));
105 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
107 fctx
*f
= (fctx
*)ff
;
110 d
= mp_add(d
, d
, f
->mm
.m
);
111 else if (MP_CMP(d
, >, f
->mm
.m
))
112 d
= mp_sub(d
, d
, f
->mm
.m
);
116 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
118 fctx
*f
= (fctx
*)ff
;
121 d
= mp_add(d
, d
, f
->mm
.m
);
122 else if (MP_CMP(d
, >, f
->mm
.m
))
123 d
= mp_sub(d
, d
, f
->mm
.m
);
127 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
)
129 fctx
*f
= (fctx
*)ff
;
130 return (mpmont_mul(&f
->mm
, d
, x
, y
));
133 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
)
135 fctx
*f
= (fctx
*)ff
;
137 return (mpmont_reduce(&f
->mm
, d
, d
));
140 static mp
*finv(field
*ff
, mp
*d
, mp
*x
)
142 fctx
*f
= (fctx
*)ff
;
143 d
= mpmont_reduce(&f
->mm
, d
, x
);
144 mp_gcd(0, 0, &d
, f
->mm
.m
, d
);
145 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
148 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
)
150 fctx
*f
= (fctx
*)ff
;
151 mp_div(0, &d
, x
, f
->mm
.m
);
155 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
)
157 fctx
*f
= (fctx
*)ff
;
158 d
= mpmont_reduce(&f
->mm
, d
, x
);
159 d
= mp_modsqrt(d
, d
, f
->mm
.m
);
162 return (mpmont_mul(&f
->mm
, d
, d
, f
->mm
.r2
));
165 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
)
167 fctx
*f
= (fctx
*)ff
;
169 if (MP_CMP(d
, >, f
->mm
.m
))
170 d
= mp_sub(d
, d
, f
->mm
.m
);
174 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
)
176 fctx
*f
= (fctx
*)ff
;
177 MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
178 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3);
179 while (MP_CMP(d
, >, f
->mm
.m
))
180 d
= mp_sub(d
, d
, f
->mm
.m
);
184 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
)
186 fctx
*f
= (fctx
*)ff
;
188 while (MP_CMP(d
, >, f
->mm
.m
))
189 d
= mp_sub(d
, d
, f
->mm
.m
);
193 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
)
195 fctx
*f
= (fctx
*)ff
;
202 d
= mp_add(d
, x
, f
->mm
.m
);
205 return (mp_lsr(d
, x
, 1));
208 /* --- Field operations table --- */
210 static field_ops fops
= {
213 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
, fsqrt
,
215 fdbl
, ftpl
, fqdl
, fhlv
218 /* --- @field_prime@ --- *
220 * Arguments: @mp *p@ = the characteristic of the field
222 * Returns: A pointer to the field.
224 * Use: Creates a field structure for a prime field of size %$p$%,
225 * using Montgomery reduction for arithmetic.
228 field
*field_prime(mp
*p
)
230 fctx
*f
= CREATE(fctx
);
232 mpmont_create(&f
->mm
, p
);
238 /*----- That's all, folks -------------------------------------------------*/