1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
|
/*
* Montgomery Reduction
* (C) 1999-2011 Jack Lloyd
* 2006 Luca Piccarreta
* 2016 Matthias Gierlings
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/internal/mp_core.h>
#include <botan/internal/mp_madd.h>
#include <botan/internal/mp_asmi.h>
#include <botan/internal/ct_utils.h>
#include <botan/mem_ops.h>
#include <botan/exceptn.h>
namespace Botan {
/*
* Montgomery Reduction Algorithm
*/
void bigint_monty_redc(word z[],
const word p[], size_t p_size, word p_dash,
word ws[], size_t ws_size)
{
const size_t z_size = 2*(p_size+1);
if(ws_size < z_size)
throw Invalid_Argument("bigint_monty_redc workspace too small");
CT::poison(z, z_size);
CT::poison(p, p_size);
CT::poison(ws, 2*(p_size+1));
/*
Montgomery reduction - product scanning form
https://www.iacr.org/archive/ches2005/006.pdf
https://eprint.iacr.org/2013/882.pdf
https://www.microsoft.com/en-us/research/wp-content/uploads/1996/01/j37acmon.pdf
*/
word w2 = 0, w1 = 0, w0 = 0;
w0 = z[0];
ws[0] = w0 * p_dash;
word3_muladd(&w2, &w1, &w0, ws[0], p[0]);
w0 = w1;
w1 = w2;
w2 = 0;
for(size_t i = 1; i != p_size; ++i)
{
for(size_t j = 0; j < i; ++j)
{
word3_muladd(&w2, &w1, &w0, ws[j], p[i-j]);
}
word3_add(&w2, &w1, &w0, z[i]);
ws[i] = w0 * p_dash;
word3_muladd(&w2, &w1, &w0, ws[i], p[0]);
w0 = w1;
w1 = w2;
w2 = 0;
}
for(size_t i = p_size; i != 2*p_size; ++i)
{
for(size_t j = i - p_size + 1; j != p_size; ++j)
{
word3_muladd(&w2, &w1, &w0, ws[j], p[i-j]);
}
word3_add(&w2, &w1, &w0, z[i]);
ws[i-p_size] = w0;
w0 = w1;
w1 = w2;
w2 = 0;
}
word3_add(&w2, &w1, &w0, z[z_size-1]);
ws[p_size] = w0;
ws[p_size+1] = w1;
/*
* The result might need to be reduced mod p. To avoid a timing
* channel, always perform the subtraction. If in the compution
* of x - p a borrow is required then x was already < p.
*
* x starts at ws[0] and is p_size+1 bytes long.
* x - p starts at ws[p_size+1] and is also p_size+1 bytes log
*
* Select which address to copy from indexing off of the final
* borrow.
*/
// word borrow = bigint_sub3(ws + p_size + 1, ws, p_size + 1, p, p_size);
word borrow = 0;
for(size_t i = 0; i != p_size; ++i)
ws[p_size + 1 + i] = word_sub(ws[i], p[i], &borrow);
ws[2*p_size+1] = word_sub(ws[p_size], 0, &borrow);
CT::conditional_copy_mem(borrow, z, ws, ws + (p_size + 1), (p_size + 1));
clear_mem(z + p_size + 1, z_size - p_size - 1);
CT::unpoison(z, z_size);
CT::unpoison(p, p_size);
CT::unpoison(ws, 2*(p_size+1));
// This check comes after we've used it but that's ok here
CT::unpoison(&borrow, 1);
BOTAN_ASSERT(borrow == 0 || borrow == 1, "Expected borrow");
}
}
|
