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
|
/*
* Montgomery Reduction
* (C) 1999-2011 Jack Lloyd
* 2006 Luca Piccarreta
*
* 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/mem_ops.h>
namespace Botan {
extern "C" {
/*
* Montgomery Reduction Algorithm
*/
void bigint_monty_redc(word z[],
const word p[], size_t p_size,
word p_dash, word ws[])
{
const size_t z_size = 2*(p_size+1);
const size_t blocks_of_8 = p_size - (p_size % 8);
for(size_t i = 0; i != p_size; ++i)
{
word* z_i = z + i;
const word y = z_i[0] * p_dash;
/*
bigint_linmul3(ws, p, p_size, y);
bigint_add2(z_i, z_size - i, ws, p_size+1);
*/
word carry = 0;
for(size_t j = 0; j != blocks_of_8; j += 8)
carry = word8_madd3(z_i + j, p + j, y, carry);
for(size_t j = blocks_of_8; j != p_size; ++j)
z_i[j] = word_madd3(p[j], y, z_i[j], &carry);
word z_sum = z_i[p_size] + carry;
carry = (z_sum < z_i[p_size]);
z_i[p_size] = z_sum;
for(size_t j = p_size + 1; carry && j != z_size - i; ++j)
{
++z_i[j];
carry = !z_i[j];
}
}
/*
* 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 - p starts at ws[0] and is p_size+1 bytes long
* x starts at ws[p_size+1] and is also p_size+1 bytes log
* (that's the copy_mem)
*
* Select which address to copy from indexing off of the final
* borrow.
*/
word borrow = 0;
for(size_t i = 0; i != p_size; ++i)
ws[i] = word_sub(z[p_size + i], p[i], &borrow);
ws[p_size] = word_sub(z[p_size+p_size], 0, &borrow);
BOTAN_ASSERT(borrow == 0 || borrow == 1, "Expected borrow");
copy_mem(ws + p_size + 1, z + p_size, p_size + 1);
copy_mem(z, ws + borrow*(p_size+1), p_size + 1);
clear_mem(z + p_size + 1, z_size - p_size - 1);
}
void bigint_monty_mul(word z[], size_t z_size,
const word x[], size_t x_size, size_t x_sw,
const word y[], size_t y_size, size_t y_sw,
const word p[], size_t p_size, word p_dash,
word ws[])
{
bigint_mul(&z[0], z_size, &ws[0],
&x[0], x_size, x_sw,
&y[0], y_size, y_sw);
bigint_monty_redc(&z[0],
&p[0], p_size, p_dash,
&ws[0]);
}
void bigint_monty_sqr(word z[], size_t z_size,
const word x[], size_t x_size, size_t x_sw,
const word p[], size_t p_size, word p_dash,
word ws[])
{
bigint_sqr(&z[0], z_size, &ws[0],
&x[0], x_size, x_sw);
bigint_monty_redc(&z[0],
&p[0], p_size, p_dash,
&ws[0]);
}
}
}
|
