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
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
|
/*
Copyright (c) 2000, 2012, Oracle and/or its affiliates. All rights reserved.
This program is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; version 2 of the License.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program; see the file COPYING. If not, write to the
Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston,
MA 02110-1301 USA.
*/
/* based on Wei Dai's modarith.h from CryptoPP */
#ifndef TAO_CRYPT_MODARITH_HPP
#define TAO_CRYPT_MODARITH_HPP
#include "misc.hpp"
#include "algebra.hpp"
namespace TaoCrypt {
// ModularArithmetic
class ModularArithmetic : public AbstractRing
{
public:
typedef int RandomizationParameter;
typedef Integer Element;
ModularArithmetic(const Integer &modulus = Integer::One())
: modulus(modulus), result((word)0, modulus.reg_.size()) {}
ModularArithmetic(const ModularArithmetic &ma)
: AbstractRing(),
modulus(ma.modulus), result((word)0, modulus.reg_.size()) {}
const Integer& GetModulus() const {return modulus;}
void SetModulus(const Integer &newModulus)
{
modulus = newModulus;
result.reg_.resize(modulus.reg_.size());
}
virtual bool IsMontgomeryRepresentation() const {return false;}
virtual Integer ConvertIn(const Integer &a) const
{return a%modulus;}
virtual Integer ConvertOut(const Integer &a) const
{return a;}
const Integer& Half(const Integer &a) const;
bool Equal(const Integer &a, const Integer &b) const
{return a==b;}
const Integer& Identity() const
{return Integer::Zero();}
const Integer& Add(const Integer &a, const Integer &b) const;
Integer& Accumulate(Integer &a, const Integer &b) const;
const Integer& Inverse(const Integer &a) const;
const Integer& Subtract(const Integer &a, const Integer &b) const;
Integer& Reduce(Integer &a, const Integer &b) const;
const Integer& Double(const Integer &a) const
{return Add(a, a);}
const Integer& MultiplicativeIdentity() const
{return Integer::One();}
const Integer& Multiply(const Integer &a, const Integer &b) const
{return result1 = a*b%modulus;}
const Integer& Square(const Integer &a) const
{return result1 = a.Squared()%modulus;}
bool IsUnit(const Integer &a) const
{return Integer::Gcd(a, modulus).IsUnit();}
const Integer& MultiplicativeInverse(const Integer &a) const
{return result1 = a.InverseMod(modulus);}
const Integer& Divide(const Integer &a, const Integer &b) const
{return Multiply(a, MultiplicativeInverse(b));}
Integer CascadeExponentiate(const Integer &x, const Integer &e1,
const Integer &y, const Integer &e2) const;
void SimultaneousExponentiate(Element *results, const Element &base,
const Integer *exponents, unsigned int exponentsCount) const;
unsigned int MaxElementBitLength() const
{return (modulus-1).BitCount();}
unsigned int MaxElementByteLength() const
{return (modulus-1).ByteCount();}
static const RandomizationParameter DefaultRandomizationParameter;
protected:
Integer modulus;
mutable Integer result, result1;
};
//! do modular arithmetics in Montgomery representation for increased speed
class MontgomeryRepresentation : public ModularArithmetic
{
public:
MontgomeryRepresentation(const Integer &modulus); // modulus must be odd
bool IsMontgomeryRepresentation() const {return true;}
Integer ConvertIn(const Integer &a) const
{return (a<<(WORD_BITS*modulus.reg_.size()))%modulus;}
Integer ConvertOut(const Integer &a) const;
const Integer& MultiplicativeIdentity() const
{return result1 = Integer::Power2(WORD_BITS*modulus.reg_.size())%modulus;}
const Integer& Multiply(const Integer &a, const Integer &b) const;
const Integer& Square(const Integer &a) const;
const Integer& MultiplicativeInverse(const Integer &a) const;
Integer CascadeExponentiate(const Integer &x, const Integer &e1,
const Integer &y, const Integer &e2) const
{return AbstractRing::CascadeExponentiate(x, e1, y, e2);}
void SimultaneousExponentiate(Element *results, const Element &base,
const Integer *exponents, unsigned int exponentsCount) const
{AbstractRing::SimultaneousExponentiate(results, base,
exponents, exponentsCount);}
private:
Integer u;
mutable AlignedWordBlock workspace;
};
} // namespace
#endif // TAO_CRYPT_MODARITH_HPP
|
