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
|
/*
* Elliptic curves over GF(p)
*
* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke
* 2010-2011,2012,2014 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#ifndef BOTAN_GFP_CURVE_H__
#define BOTAN_GFP_CURVE_H__
#include <botan/numthry.h>
#include <memory>
namespace Botan {
class CurveGFp_Repr
{
public:
virtual ~CurveGFp_Repr() {}
virtual const BigInt& get_p() const = 0;
virtual const BigInt& get_a() const = 0;
virtual const BigInt& get_b() const = 0;
/*
* Returns to_curve_rep(get_a())
*/
virtual const BigInt& get_a_rep() const = 0;
/*
* Returns to_curve_rep(get_b())
*/
virtual const BigInt& get_b_rep() const = 0;
virtual void to_curve_rep(BigInt& x, secure_vector<word>& ws) const = 0;
virtual void from_curve_rep(BigInt& x, secure_vector<word>& ws) const = 0;
virtual void curve_mul(BigInt& z, const BigInt& x, const BigInt& y,
secure_vector<word>& ws) const = 0;
virtual void curve_sqr(BigInt& z, const BigInt& x,
secure_vector<word>& ws) const = 0;
};
/**
* This class represents an elliptic curve over GF(p)
*/
class BOTAN_DLL CurveGFp
{
public:
/**
* Create an uninitialized CurveGFp
*/
CurveGFp() {}
/**
* Construct the elliptic curve E: y^2 = x^3 + ax + b over GF(p)
* @param p prime number of the field
* @param a first coefficient
* @param b second coefficient
*/
CurveGFp(const BigInt& p, const BigInt& a, const BigInt& b) :
m_repr(choose_repr(p, a, b))
{
}
CurveGFp(const CurveGFp&) = default;
CurveGFp& operator=(const CurveGFp&) = default;
/**
* @return curve coefficient a
*/
const BigInt& get_a() const { return m_repr->get_a(); }
/**
* @return curve coefficient b
*/
const BigInt& get_b() const { return m_repr->get_b(); }
/**
* Get prime modulus of the field of the curve
* @return prime modulus of the field of the curve
*/
const BigInt& get_p() const { return m_repr->get_p(); }
const BigInt& get_a_rep() const { return m_repr->get_a_rep(); }
const BigInt& get_b_rep() const { return m_repr->get_b_rep(); }
void to_rep(BigInt& x, secure_vector<word>& ws) const
{
m_repr->to_curve_rep(x, ws);
}
void from_rep(BigInt& x, secure_vector<word>& ws) const
{
m_repr->from_curve_rep(x, ws);
}
BigInt from_rep(const BigInt& x, secure_vector<word>& ws) const
{
BigInt xt(x);
m_repr->from_curve_rep(xt, ws);
return xt;
}
void mul(BigInt& z, const BigInt& x, const BigInt& y, secure_vector<word>& ws) const
{
m_repr->curve_mul(z, x, y, ws);
}
BigInt mul(const BigInt& x, const BigInt& y, secure_vector<word>& ws) const
{
BigInt z;
m_repr->curve_mul(z, x, y, ws);
return z;
}
void sqr(BigInt& z, const BigInt& x, secure_vector<word>& ws) const
{
m_repr->curve_sqr(z, x, ws);
}
BigInt sqr(const BigInt& x, secure_vector<word>& ws) const
{
BigInt z;
m_repr->curve_sqr(z, x, ws);
return z;
}
void swap(CurveGFp& other)
{
std::swap(m_repr, other.m_repr);
}
private:
static std::shared_ptr<CurveGFp_Repr>
choose_repr(const BigInt& p, const BigInt& a, const BigInt& b);
std::shared_ptr<CurveGFp_Repr> m_repr;
};
/**
* Equality operator
* @param lhs a curve
* @param rhs a curve
* @return true iff lhs is the same as rhs
*/
inline bool operator==(const CurveGFp& lhs, const CurveGFp& rhs)
{
return (lhs.get_p() == rhs.get_p()) &&
(lhs.get_a() == rhs.get_a()) &&
(lhs.get_b() == rhs.get_b());
}
inline bool operator!=(const CurveGFp& lhs, const CurveGFp& rhs)
{
return !(lhs == rhs);
}
}
namespace std {
template<> inline
void swap<Botan::CurveGFp>(Botan::CurveGFp& curve1,
Botan::CurveGFp& curve2) noexcept
{
curve1.swap(curve2);
}
} // namespace std
#endif
|
