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
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
|
/*
* Arithmetic for prime fields GF(p)
*
* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke
* 2009-2010 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#ifndef BOTAN_GFP_ELEMENT_H__
#define BOTAN_GFP_ELEMENT_H__
#include <botan/bigint.h>
#include <botan/gfp_modulus.h>
#include <iosfwd>
namespace Botan {
struct BOTAN_DLL Illegal_Transformation : public Exception
{
Illegal_Transformation(const std::string& err =
"Requested transformation is not possible") :
Exception(err) {}
};
/**
* This class represents one element in GF(p). Enables the convenient,
* transparent use of the montgomery multiplication.
*/
class BOTAN_DLL GFpElement
{
public:
/** construct an element of GF(p) with the given value.
* use_montg defaults to false and determines wether Montgomery
* multiplications will be use when applying operators *, *=
* @param p the prime number of the field
* @param value the element value
* @param use_montgm whether this object will use Montgomery multiplication
*/
GFpElement(const BigInt& p, const BigInt& value, bool use_montgm = false);
// GFpElement(const GFpElement& other) = default;
// const GFpElement& operator=(const GFpElement& other) = default;
/**
* Switch Montgomery multiplcation optimizations ON
*/
void turn_on_sp_red_mul() const;
/**
* Switch Montgomery multiplcation optimizations OFF
*/
void turn_off_sp_red_mul() const;
/**
* += Operator
* @param rhs the GFpElement to add to the local value
* @result *this
*/
GFpElement& operator+=(const GFpElement& rhs);
/**
* -= Operator
* @param rhs the GFpElement to subtract from the local value
* @result *this
*/
GFpElement& operator-=(const GFpElement& rhs);
/**
* *= Operator
* @param rhs the GFpElement to multiply with the local value
* @result *this
*/
GFpElement& operator*=(const GFpElement& rhs);
/**
* /= Operator
* @param rhs the GFpElement to divide the local value by
* @result *this
*/
GFpElement& operator/=(const GFpElement& rhs);
/**
* *= Operator
* @param rhs the value to multiply with the local value
* @result *this
*/
GFpElement& operator*=(u32bit rhs);
/**
* Negate internal value(*this *= -1 )
* @return *this
*/
GFpElement& negate();
/**
* Assigns the inverse of *this to *this, i.e.
* *this = (*this)^(-1)
* @result *this
*/
GFpElement& inverse_in_place();
/**
* checks whether the value is zero (without provoking
* a backtransformation to the ordinary-residue)
* @result true, if the value is zero, false otherwise.
*/
bool is_zero();
/**
* return prime number of GF(p)
* @result a prime number
*/
const BigInt& get_p() const;
/**
* Return the represented value in GF(p)
* @result The value in GF(p)
*/
const BigInt& get_value() const;
/**
* Tells whether this GFpElement is currently transformed to it´ m-residue,
* i.e. in the form x_bar = x * r mod m.
* @result true if it is currently transformed to it´s m-residue.
*/
bool is_trf_to_mres() const;
/**
* Transforms this to x_bar = x * r mod m
* @result return the value x_bar.
*/
const BigInt& get_mres() const;
/**
* Check, if montgomery multiplication is used.
* @result true, if montgomery multiplication is used, false otherwise
*/
bool is_use_montgm() const
{
return m_use_montgm;
}
/**
* Transforms the arguments in such way that either both
* are in m-residue representation (returns true) or both are
* in ordinary residue representation (returns false).
* m-residue is prefered in case of ambiguity.
* does not toggle m_use_montgm of the arguments.
* Don´t be confused about the constness of the arguments:
* the transformation between normal residue and m-residue is
* considered as leaving the object const.
* @param lhs the first operand to be aligned
* @param rhs the second operand to be aligned
* @result true if both are transformed to their m-residue,
* false it both are transformed to their normal residue.
*/
static bool align_operands_res(const GFpElement& lhs, const GFpElement& rhs);
/**
* swaps the states of *this and other, does not throw!
* @param other The value to swap with
*/
void swap(GFpElement& other);
private:
void ensure_montgm_precomp() const;
void trf_to_mres() const;
void trf_to_ordres() const;
mutable GFpModulus modulus;
mutable BigInt m_value; // ordinary residue or m-residue respectively
// data members for montgomery multiplication
mutable bool m_use_montgm;
mutable bool m_is_trf; // if m_value is montgomery
};
// relational operators
bool BOTAN_DLL operator==(const GFpElement& lhs, const GFpElement& rhs);
inline bool operator!=(const GFpElement& lhs, const GFpElement& rhs )
{
return !operator==(lhs, rhs);
}
// arithmetic operators
GFpElement BOTAN_DLL operator+(const GFpElement& lhs, const GFpElement& rhs);
GFpElement BOTAN_DLL operator-(const GFpElement& lhs, const GFpElement& rhs);
GFpElement BOTAN_DLL operator-(const GFpElement& lhs);
GFpElement BOTAN_DLL operator*(const GFpElement& lhs, const GFpElement& rhs);
GFpElement BOTAN_DLL operator/(const GFpElement& lhs, const GFpElement& rhs);
GFpElement BOTAN_DLL operator*(const GFpElement& lhs, u32bit rhs);
GFpElement BOTAN_DLL operator*(u32bit rhs, const GFpElement& lhs);
/**
* write a GFpElement to an output stream.
* @param output the output stream to write to
* @param elem the object to write
* @result the output stream
*/
BOTAN_DLL std::ostream& operator<<(std::ostream& output, const GFpElement& elem);
// return (*this)^(-1)
GFpElement BOTAN_DLL inverse(const GFpElement& elem);
// encoding and decoding
SecureVector<byte> BOTAN_DLL FE2OSP(const GFpElement& elem);
GFpElement BOTAN_DLL OS2FEP(MemoryRegion<byte> const& os, BigInt p);
inline void swap(GFpElement& x, GFpElement& y)
{
x.swap(y);
}
}
namespace std {
template<> inline
void swap<Botan::GFpElement>(Botan::GFpElement& x,
Botan::GFpElement& y)
{
x.swap(y);
}
}
#endif
|
