d9ec1acb29e64fa04ff444ca3638fb7f14f21124
5 * Prime fields with efficient reduction for special-form primes
7 * (c) 2004 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 /*----- Header files ------------------------------------------------------*/
38 /*----- Main code ---------------------------------------------------------*/
45 /* --- Field operations --- */
47 static void fdestroy(field
*ff
)
48 { fctx
*f
= (fctx
*)ff
; mpreduce_destroy(&f
->r
); DESTROY(f
); }
50 static mp
*frand(field
*ff
, mp
*d
, grand
*r
)
51 { fctx
*f
= (fctx
*)ff
; return (mprand_range(d
, f
->r
.p
, r
, 0)); }
53 static int fzerop(field
*ff
, mp
*x
) { return (MP_ZEROP(x
)); }
55 static mp
*fneg(field
*ff
, mp
*d
, mp
*x
)
56 { fctx
*f
= (fctx
*)ff
; return (mp_sub(d
, f
->r
.p
, x
)); }
58 static mp
*fadd(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
59 fctx
*f
= (fctx
*)ff
; d
= mp_add(d
, x
, y
);
60 if (MP_NEGP(d
)) d
= mp_add(d
, d
, f
->r
.p
);
61 else if (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
65 static mp
*fsub(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
66 fctx
*f
= (fctx
*)ff
; d
= mp_sub(d
, x
, y
);
67 if (MP_NEGP(d
)) d
= mp_add(d
, d
, f
->r
.p
);
68 else if (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
72 static mp
*fmul(field
*ff
, mp
*d
, mp
*x
, mp
*y
) {
73 fctx
*f
= (fctx
*)ff
; d
= mp_mul(d
, x
, y
);
74 return (mpreduce_do(&f
->r
, d
, d
));
77 static mp
*fsqr(field
*ff
, mp
*d
, mp
*x
) {
78 fctx
*f
= (fctx
*)ff
; d
= mp_sqr(d
, x
);
79 return (mpreduce_do(&f
->r
, d
, d
));
82 static mp
*finv(field
*ff
, mp
*d
, mp
*x
)
83 { fctx
*f
= (fctx
*)ff
; d
= mp_modinv(d
, x
, f
->r
.p
); return (d
); }
85 static mp
*freduce(field
*ff
, mp
*d
, mp
*x
)
86 { fctx
*f
= (fctx
*)ff
; return (mpreduce_do(&f
->r
, d
, x
)); }
88 static mp
*fsqrt(field
*ff
, mp
*d
, mp
*x
)
89 { fctx
*f
= (fctx
*)ff
; return (mp_modsqrt(d
, x
, f
->r
.p
)); }
91 static mp
*fdbl(field
*ff
, mp
*d
, mp
*x
) {
92 fctx
*f
= (fctx
*)ff
; d
= mp_lsl(d
, x
, 1);
93 if (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
97 static mp
*ftpl(field
*ff
, mp
*d
, mp
*x
) {
98 fctx
*f
= (fctx
*)ff
; MP_DEST(d
, MP_LEN(x
) + 1, x
->f
);
99 MPX_UMULN(d
->v
, d
->vl
, x
->v
, x
->vl
, 3);
100 while (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
104 static mp
*fqdl(field
*ff
, mp
*d
, mp
*x
) {
105 fctx
*f
= (fctx
*)ff
; d
= mp_lsl(d
, x
, 2);
106 while (MP_CMP(d
, >, f
->r
.p
)) d
= mp_sub(d
, d
, f
->r
.p
);
110 static mp
*fhlv(field
*ff
, mp
*d
, mp
*x
) {
111 fctx
*f
= (fctx
*)ff
;
112 if (MP_ZEROP(x
)) { MP_COPY(x
); MP_DROP(d
); return (x
); }
113 if (x
->v
[0] & 1) { d
= mp_add(d
, x
, f
->r
.p
); x
= d
; }
114 return (mp_lsr(d
, x
, 1));
117 /* --- Field operations table --- */
119 static const field_ops fops
= {
120 FTY_PRIME
, "niceprime",
121 fdestroy
, frand
, field_stdsamep
,
123 fzerop
, fneg
, fadd
, fsub
, fmul
, fsqr
, finv
, freduce
, fsqrt
,
125 fdbl
, ftpl
, fqdl
, fhlv
128 /* --- @field_niceprime@ --- *
130 * Arguments: @mp *p@ = the characteristic of the field
132 * Returns: A pointer to the field.
134 * Use: Creates a field structure for a prime field of size %$p$%,
135 * using efficient reduction for nice primes.
138 field
*field_niceprime(mp
*p
)
140 fctx
*f
= CREATE(fctx
);
144 f
->f
.nbits
= mp_bits(p
);
145 f
->f
.noctets
= (f
->f
.nbits
+ 7) >> 3;
146 mpreduce_create(&f
->r
, p
);
151 /*----- That's all, folks -------------------------------------------------*/