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
|
/*
* Modular Reducer
* (C) 1999-2011,2018 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include <botan/reducer.h>
namespace Botan {
/*
* Modular_Reducer Constructor
*/
Modular_Reducer::Modular_Reducer(const BigInt& mod)
{
if(mod <= 0)
throw Invalid_Argument("Modular_Reducer: modulus must be positive");
m_modulus = mod;
m_mod_words = m_modulus.sig_words();
m_modulus_2 = Botan::square(m_modulus);
m_mu = BigInt::power_of_2(2 * BOTAN_MP_WORD_BITS * m_mod_words) / m_modulus;
}
/*
* Barrett Reduction
*/
BigInt Modular_Reducer::reduce(const BigInt& x) const
{
if(m_mod_words == 0)
throw Invalid_State("Modular_Reducer: Never initalized");
const size_t x_sw = x.sig_words();
if(x_sw >= (2*m_mod_words - 1) && x.cmp(m_modulus_2, false) >= 0)
{
// too big, fall back to normal division
return (x % m_modulus);
}
secure_vector<word> ws;
BigInt t1 = x;
t1.set_sign(BigInt::Positive);
t1 >>= (BOTAN_MP_WORD_BITS * (m_mod_words - 1));
t1.mul(m_mu, ws);
t1 >>= (BOTAN_MP_WORD_BITS * (m_mod_words + 1));
// TODO add masked mul to avoid computing high bits
t1.mul(m_modulus, ws);
t1.mask_bits(BOTAN_MP_WORD_BITS * (m_mod_words + 1));
t1.rev_sub(x.data(), std::min(x_sw, m_mod_words + 1), ws);
if(t1.is_negative())
{
if(ws.size() < m_mod_words + 2)
ws.resize(m_mod_words + 2);
clear_mem(ws.data(), ws.size());
ws[m_mod_words + 1] = 1;
t1.add(ws.data(), m_mod_words + 2, BigInt::Positive);
}
t1.reduce_below(m_modulus, ws);
if(x.is_negative() && t1.is_nonzero())
{
t1.rev_sub(m_modulus.data(), m_modulus.size(), ws);
}
return t1;
}
}
|
