1 /* ecc-j-to-a.c
2 
3    Copyright (C) 2013 Niels Möller
4 
5    This file is part of GNU Nettle.
6 
7    GNU Nettle is free software: you can redistribute it and/or
8    modify it under the terms of either:
9 
10      * the GNU Lesser General Public License as published by the Free
11        Software Foundation; either version 3 of the License, or (at your
12        option) any later version.
13 
14    or
15 
16      * the GNU General Public License as published by the Free
17        Software Foundation; either version 2 of the License, or (at your
18        option) any later version.
19 
20    or both in parallel, as here.
21 
22    GNU Nettle is distributed in the hope that it will be useful,
23    but WITHOUT ANY WARRANTY; without even the implied warranty of
24    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
25    General Public License for more details.
26 
27    You should have received copies of the GNU General Public License and
28    the GNU Lesser General Public License along with this program.  If
29    not, see http://www.gnu.org/licenses/.
30 */
31 
32 /* Development of Nettle's ECC support was funded by the .SE Internet Fund. */
33 
34 #if HAVE_CONFIG_H
35 # include "config.h"
36 #endif
37 
38 #include "ecc.h"
39 #include "ecc-internal.h"
40 
41 void
ecc_j_to_a(const struct ecc_curve * ecc,int op,mp_limb_t * r,const mp_limb_t * p,mp_limb_t * scratch)42 ecc_j_to_a (const struct ecc_curve *ecc,
43 	    int op,
44 	    mp_limb_t *r, const mp_limb_t *p,
45 	    mp_limb_t *scratch)
46 {
47 #define izp   scratch
48 #define up   (scratch + 2*ecc->p.size)
49 #define iz2p (scratch + ecc->p.size)
50 #define iz3p (scratch + 2*ecc->p.size)
51 #define izBp (scratch + 3*ecc->p.size)
52 #define tp    scratch
53 
54   mp_limb_t cy;
55 
56   if (ecc->use_redc)
57     {
58       /* Set v = (r_z / B^2)^-1,
59 
60 	 r_x = p_x v^2 / B^3 =  ((v/B * v)/B * p_x)/B
61 	 r_y = p_y v^3 / B^4 = (((v/B * v)/B * v)/B * p_y)/B
62       */
63 
64       mpn_copyi (up, p + 2*ecc->p.size, ecc->p.size);
65       mpn_zero (up + ecc->p.size, ecc->p.size);
66       ecc->p.reduce (&ecc->p, up);
67       mpn_zero (up + ecc->p.size, ecc->p.size);
68       ecc->p.reduce (&ecc->p, up);
69 
70       ecc->p.invert (&ecc->p, izp, up, up + ecc->p.size);
71 
72       /* Divide this common factor by B */
73       mpn_copyi (izBp, izp, ecc->p.size);
74       mpn_zero (izBp + ecc->p.size, ecc->p.size);
75       ecc->p.reduce (&ecc->p, izBp);
76 
77       ecc_modp_mul (ecc, iz2p, izp, izBp);
78     }
79   else
80     {
81       /* Set s = p_z^{-1}, r_x = p_x s^2, r_y = p_y s^3 */
82 
83       mpn_copyi (up, p+2*ecc->p.size, ecc->p.size); /* p_z */
84       ecc->p.invert (&ecc->p, izp, up, up + ecc->p.size);
85 
86       ecc_modp_sqr (ecc, iz2p, izp);
87     }
88 
89   ecc_modp_mul (ecc, iz3p, iz2p, p);
90   /* ecc_modp (and ecc_modp_mul) may return a value up to 2p - 1, so
91      do a conditional subtraction. */
92   cy = mpn_sub_n (r, iz3p, ecc->p.m, ecc->p.size);
93   cnd_copy (cy, r, iz3p, ecc->p.size);
94 
95   if (op)
96     {
97       /* Skip y coordinate */
98       if (op > 1)
99 	{
100 	  /* Also reduce the x coordinate mod ecc->q. It should
101 	     already be < 2*ecc->q, so one subtraction should
102 	     suffice. */
103 	  cy = mpn_sub_n (scratch, r, ecc->q.m, ecc->p.size);
104 	  cnd_copy (cy == 0, r, scratch, ecc->p.size);
105 	}
106       return;
107     }
108   ecc_modp_mul (ecc, iz3p, iz2p, izp);
109   ecc_modp_mul (ecc, tp, iz3p, p + ecc->p.size);
110   /* And a similar subtraction. */
111   cy = mpn_sub_n (r + ecc->p.size, tp, ecc->p.m, ecc->p.size);
112   cnd_copy (cy, r + ecc->p.size, tp, ecc->p.size);
113 
114 #undef izp
115 #undef up
116 #undef iz2p
117 #undef iz3p
118 #undef tp
119 }
120