1 /* mpn_sec_pi1_div_qr, mpn_sec_pi1_div_r -- Compute Q = floor(U / V), U = U
2 mod V. Side-channel silent under the assumption that the used instructions
3 are side-channel silent.
4
5 Contributed to the GNU project by Torbjörn Granlund.
6
7 THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES. IT IS ONLY
8 SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES. IN FACT, IT IS ALMOST
9 GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
10
11 Copyright 2011-2013 Free Software Foundation, Inc.
12
13 This file is part of the GNU MP Library.
14
15 The GNU MP Library is free software; you can redistribute it and/or modify
16 it under the terms of either:
17
18 * the GNU Lesser General Public License as published by the Free
19 Software Foundation; either version 3 of the License, or (at your
20 option) any later version.
21
22 or
23
24 * the GNU General Public License as published by the Free Software
25 Foundation; either version 2 of the License, or (at your option) any
26 later version.
27
28 or both in parallel, as here.
29
30 The GNU MP Library is distributed in the hope that it will be useful, but
31 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
32 or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
33 for more details.
34
35 You should have received copies of the GNU General Public License and the
36 GNU Lesser General Public License along with the GNU MP Library. If not,
37 see https://www.gnu.org/licenses/. */
38
39 #include "gmp-impl.h"
40 #include "longlong.h"
41
42 /* This side-channel silent division algorithm reduces the partial remainder by
43 GMP_NUMB_BITS/2 bits at a time, compared to GMP_NUMB_BITS for the main
44 division algorithm. We actually do not insist on reducing by exactly
45 GMP_NUMB_BITS/2, but may leave a partial remainder that is D*B^i to 3D*B^i
46 too large (B is the limb base, D is the divisor, and i is the induction
47 variable); the subsequent step will handle the extra partial remainder bits.
48
49 With that partial remainder reduction, each step generates a quotient "half
50 limb". The outer loop generates two quotient half limbs, an upper (q1h) and
51 a lower (q0h) which are stored sparsely in separate limb arrays. These
52 arrays are added at the end; using separate arrays avoids data-dependent
53 carry propagation which could else pose a side-channel leakage problem.
54
55 The quotient half limbs may be between -3 to 0 from the accurate value
56 ("accurate" being the one which corresponds to a reduction to a principal
57 partial remainder). Too small quotient half limbs correspond to too large
58 remainders, which we reduce later, as described above.
59
60 In order to keep quotients from getting too big, corresponding to a negative
61 partial remainder, we use an inverse which is slightly smaller than usually.
62 */
63
64 #if OPERATION_sec_pi1_div_qr
65 /* Needs (dn + 1) + (nn - dn) + (nn - dn) = 2nn - dn + 1 limbs at tp. */
66 #define FNAME mpn_sec_pi1_div_qr
67 #define Q(q) q,
68 #define RETTYPE mp_limb_t
69 #endif
70 #if OPERATION_sec_pi1_div_r
71 /* Needs (dn + 1) limbs at tp. */
72 #define FNAME mpn_sec_pi1_div_r
73 #define Q(q)
74 #define RETTYPE void
75 #endif
76
77 RETTYPE
78 FNAME (Q(mp_ptr qp)
79 mp_ptr np, mp_size_t nn,
80 mp_srcptr dp, mp_size_t dn,
81 mp_limb_t dinv,
82 mp_ptr tp)
83 {
84 mp_limb_t nh, cy, q1h, q0h, dummy, cnd;
85 mp_size_t i;
86 mp_ptr hp;
87 #if OPERATION_sec_pi1_div_qr
88 mp_limb_t qh;
89 mp_ptr qlp, qhp;
90 #endif
91
92 ASSERT (dn >= 1);
93 ASSERT (nn >= dn);
94 ASSERT ((dp[dn - 1] & GMP_NUMB_HIGHBIT) != 0);
95
96 if (nn == dn)
97 {
98 cy = mpn_sub_n (np, np, dp, dn);
99 mpn_cnd_add_n (cy, np, np, dp, dn);
100 #if OPERATION_sec_pi1_div_qr
101 return 1 - cy;
102 #else
103 return;
104 #endif
105 }
106
107 /* Create a divisor copy shifted half a limb. */
108 hp = tp; /* (dn + 1) limbs */
109 hp[dn] = mpn_lshift (hp, dp, dn, GMP_NUMB_BITS / 2);
110
111 #if OPERATION_sec_pi1_div_qr
112 qlp = tp + (dn + 1); /* (nn - dn) limbs */
113 qhp = tp + (nn + 1); /* (nn - dn) limbs */
114 #endif
115
116 np += nn - dn;
117 nh = 0;
118
119 for (i = nn - dn - 1; i >= 0; i--)
120 {
121 np--;
122
123 nh = (nh << GMP_NUMB_BITS/2) + (np[dn] >> GMP_NUMB_BITS/2);
124 umul_ppmm (q1h, dummy, nh, dinv);
125 q1h += nh;
126 #if OPERATION_sec_pi1_div_qr
127 qhp[i] = q1h;
128 #endif
129 mpn_submul_1 (np, hp, dn + 1, q1h);
130
131 nh = np[dn];
132 umul_ppmm (q0h, dummy, nh, dinv);
133 q0h += nh;
134 #if OPERATION_sec_pi1_div_qr
135 qlp[i] = q0h;
136 #endif
137 nh -= mpn_submul_1 (np, dp, dn, q0h);
138 }
139
140 /* 1st adjustment depends on extra high remainder limb. */
141 cnd = nh != 0; /* FIXME: cmp-to-int */
142 #if OPERATION_sec_pi1_div_qr
143 qlp[0] += cnd;
144 #endif
145 nh -= mpn_cnd_sub_n (cnd, np, np, dp, dn);
146
147 /* 2nd adjustment depends on remainder/divisor comparison as well as whether
148 extra remainder limb was nullified by previous subtract. */
149 cy = mpn_sub_n (np, np, dp, dn);
150 cy = cy - nh;
151 #if OPERATION_sec_pi1_div_qr
152 qlp[0] += 1 - cy;
153 #endif
154 mpn_cnd_add_n (cy, np, np, dp, dn);
155
156 /* 3rd adjustment depends on remainder/divisor comparison. */
157 cy = mpn_sub_n (np, np, dp, dn);
158 #if OPERATION_sec_pi1_div_qr
159 qlp[0] += 1 - cy;
160 #endif
161 mpn_cnd_add_n (cy, np, np, dp, dn);
162
163 #if OPERATION_sec_pi1_div_qr
164 /* Combine quotient halves into final quotient. */
165 qh = mpn_lshift (qhp, qhp, nn - dn, GMP_NUMB_BITS/2);
166 qh += mpn_add_n (qp, qhp, qlp, nn - dn);
167
168 return qh;
169 #else
170 return;
171 #endif
172 }