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
|
#ifndef CRYPTOPP_MODARITH_H
#define CRYPTOPP_MODARITH_H
// implementations are in integer.cpp
#include "cryptlib.h"
#include "misc.h"
#include "integer.h"
#include "algebra.h"
NAMESPACE_BEGIN(CryptoPP)
CRYPTOPP_DLL_TEMPLATE_CLASS AbstractGroup<Integer>;
CRYPTOPP_DLL_TEMPLATE_CLASS AbstractRing<Integer>;
CRYPTOPP_DLL_TEMPLATE_CLASS AbstractEuclideanDomain<Integer>;
//! ring of congruence classes modulo n
/*! \note this implementation represents each congruence class as the smallest non-negative integer in that class */
class CRYPTOPP_DLL ModularArithmetic : public AbstractRing<Integer>
{
public:
typedef int RandomizationParameter;
typedef Integer Element;
ModularArithmetic(const Integer &modulus = Integer::One())
: m_modulus(modulus), m_result((word)0, modulus.reg.size()) {}
ModularArithmetic(const ModularArithmetic &ma)
: m_modulus(ma.m_modulus), m_result((word)0, m_modulus.reg.size()) {}
ModularArithmetic(BufferedTransformation &bt); // construct from BER encoded parameters
virtual ModularArithmetic * Clone() const {return new ModularArithmetic(*this);}
void DEREncode(BufferedTransformation &bt) const;
void DEREncodeElement(BufferedTransformation &out, const Element &a) const;
void BERDecodeElement(BufferedTransformation &in, Element &a) const;
const Integer& GetModulus() const {return m_modulus;}
void SetModulus(const Integer &newModulus) {m_modulus = newModulus; m_result.reg.resize(m_modulus.reg.size());}
virtual bool IsMontgomeryRepresentation() const {return false;}
virtual Integer ConvertIn(const Integer &a) const
{return a%m_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 m_result1 = a*b%m_modulus;}
const Integer& Square(const Integer &a) const
{return m_result1 = a.Squared()%m_modulus;}
bool IsUnit(const Integer &a) const
{return Integer::Gcd(a, m_modulus).IsUnit();}
const Integer& MultiplicativeInverse(const Integer &a) const
{return m_result1 = a.InverseMod(m_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 (m_modulus-1).BitCount();}
unsigned int MaxElementByteLength() const
{return (m_modulus-1).ByteCount();}
Element RandomElement( RandomNumberGenerator &rng , const RandomizationParameter &ignore_for_now = 0 ) const
// left RandomizationParameter arg as ref in case RandomizationParameter becomes a more complicated struct
{
return Element( rng , Integer( (long) 0) , m_modulus - Integer( (long) 1 ) ) ;
}
bool operator==(const ModularArithmetic &rhs) const
{return m_modulus == rhs.m_modulus;}
static const RandomizationParameter DefaultRandomizationParameter ;
protected:
Integer m_modulus;
mutable Integer m_result, m_result1;
};
// const ModularArithmetic::RandomizationParameter ModularArithmetic::DefaultRandomizationParameter = 0 ;
//! do modular arithmetics in Montgomery representation for increased speed
/*! \note the Montgomery representation represents each congruence class [a] as a*r%n, where r is a convenient power of 2 */
class CRYPTOPP_DLL MontgomeryRepresentation : public ModularArithmetic
{
public:
MontgomeryRepresentation(const Integer &modulus); // modulus must be odd
virtual ModularArithmetic * Clone() const {return new MontgomeryRepresentation(*this);}
bool IsMontgomeryRepresentation() const {return true;}
Integer ConvertIn(const Integer &a) const
{return (a<<(WORD_BITS*m_modulus.reg.size()))%m_modulus;}
Integer ConvertOut(const Integer &a) const;
const Integer& MultiplicativeIdentity() const
{return m_result1 = Integer::Power2(WORD_BITS*m_modulus.reg.size())%m_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<Integer>::CascadeExponentiate(x, e1, y, e2);}
void SimultaneousExponentiate(Element *results, const Element &base, const Integer *exponents, unsigned int exponentsCount) const
{AbstractRing<Integer>::SimultaneousExponentiate(results, base, exponents, exponentsCount);}
private:
Integer m_u;
mutable IntegerSecBlock m_workspace;
};
NAMESPACE_END
#endif
|
