blob: e378470f81079c62df61730d40ca9202848bb648 (
plain)
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
|
/*************************************************
* Modular Reducer Source File *
* (C) 1999-2008 The Botan Project *
*************************************************/
#include <botan/reducer.h>
#include <botan/numthry.h>
#include <botan/mp_core.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");
modulus = mod;
mod_words = modulus.sig_words();
modulus_2 = Botan::square(modulus);
mod2_words = modulus_2.sig_words();
mu = BigInt(BigInt::Power2, 2 * MP_WORD_BITS * mod_words) / modulus;
mu_words = mu.sig_words();
}
/*************************************************
* Barrett Reduction *
*************************************************/
BigInt Modular_Reducer::reduce(const BigInt& x) const
{
if(mod_words == 0)
throw Invalid_State("Modular_Reducer: Never initalized");
BigInt t1 = x;
t1.set_sign(BigInt::Positive);
if(t1 < modulus)
{
if(x.is_negative() && t1.is_nonzero())
return modulus - t1;
return x;
}
if(t1 >= modulus_2)
return (x % modulus);
t1 >>= (MP_WORD_BITS * (mod_words - 1));
t1 *= mu;
t1 >>= (MP_WORD_BITS * (mod_words + 1));
t1 *= modulus;
t1.mask_bits(MP_WORD_BITS * (mod_words+1));
BigInt t2 = x;
t2.set_sign(BigInt::Positive);
t2.mask_bits(MP_WORD_BITS * (mod_words+1));
t1 = t2 - t1;
if(t1.is_negative())
{
BigInt b_to_k1(BigInt::Power2, MP_WORD_BITS * (mod_words+1));
t1 += b_to_k1;
}
while(t1 >= modulus)
t1 -= modulus;
if(x.is_negative() && t1.is_nonzero())
t1 = modulus - t1;
return t1;
}
/*************************************************
* Multiply, followed by a reduction *
*************************************************/
BigInt Modular_Reducer::multiply(const BigInt& x, const BigInt& y) const
{
return reduce(x * y);
}
/*************************************************
* Square, followed by a reduction *
*************************************************/
BigInt Modular_Reducer::square(const BigInt& x) const
{
return reduce(Botan::square(x));
}
}
|
