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
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
|
/*
* Arithmetic for point groups of elliptic curves over GF(p)
*
* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke
* 2008-2010 Jack Lloyd
*
* Distributed under the terms of the Botan license
*/
#ifndef BOTAN_POINT_GFP_H__
#define BOTAN_POINT_GFP_H__
#include <botan/curve_gfp.h>
#include <vector>
namespace Botan {
struct BOTAN_DLL Illegal_Transformation : public Exception
{
Illegal_Transformation(const std::string& err =
"Requested transformation is not possible") :
Exception(err) {}
};
struct BOTAN_DLL Illegal_Point : public Exception
{
Illegal_Point(const std::string& err = "Malformed ECP point detected") :
Exception(err) {}
};
/**
* This class represents one point on a curve of GF(p)
*/
class BOTAN_DLL PointGFp
{
public:
enum Compression_Type {
UNCOMPRESSED = 0,
COMPRESSED = 1,
HYBRID = 2
};
/**
* Construct an uninitialized PointGFp
*/
PointGFp() {}
/**
* Construct the zero point
* @param curve The base curve
*/
PointGFp(const CurveGFp& curve);
/**
* Construct a point from its affine coordinates
* @param curve the base curve
* @param x affine x coordinate
* @param y affine y coordinate
*/
PointGFp(const CurveGFp& curve, const BigInt& x, const BigInt& y);
//PointGFp(const PointGFp& other) = default;
//PointGFp& operator=(const PointGFp& other) = default;
/**
* += Operator
* @param rhs the PointGFp to add to the local value
* @result resulting PointGFp
*/
PointGFp& operator+=(const PointGFp& rhs);
/**
* -= Operator
* @param rhs the PointGFp to subtract from the local value
* @result resulting PointGFp
*/
PointGFp& operator-=(const PointGFp& rhs);
/**
* *= Operator
* @param scalar the PointGFp to multiply with *this
* @result resulting PointGFp
*/
PointGFp& operator*=(const BigInt& scalar);
/**
* Multiplication Operator
* @param scalar the scalar value
* @param point the point value
* @return scalar*point on the curve
*/
friend BOTAN_DLL PointGFp operator*(const BigInt& scalar, const PointGFp& point);
/**
* Negate this point
* @return *this
*/
PointGFp& negate()
{
if(!is_zero())
coord_y = curve.get_p() - coord_y;
return *this;
}
/**
* Return base curve of this point
* @result the curve over GF(p) of this point
*/
const CurveGFp& get_curve() const { return curve; }
/**
* get affine x coordinate
* @result affine x coordinate
*/
BigInt get_affine_x() const;
/**
* get affine y coordinate
* @result affine y coordinate
*/
BigInt get_affine_y() const;
/**
* Is this the point at infinity?
* @result true, if this point is at infinity, false otherwise.
*/
bool is_zero() const
{ return (coord_x.is_zero() && coord_z.is_zero()); }
/**
* Checks whether the point is to be found on the underlying
* curve; used to prevent fault attacks.
* @return if the point is on the curve
*/
bool on_the_curve() const;
/**
* swaps the states of *this and other, does not throw!
* @param other the object to swap values with
*/
void swap(PointGFp& other);
/**
* Equality operator
*/
bool operator==(const PointGFp& other) const;
private:
class Workspace
{
public:
Workspace(u32bit p_words) :
ws_monty(2*(p_words+2)), ws_bn(12) {}
SecureVector<word> ws_monty;
std::vector<BigInt> ws_bn;
};
/**
* Montgomery multiplication/reduction
* @param x first multiplicand
* @param y second multiplicand
* @param workspace temp space
*/
BigInt monty_mult(const BigInt& x, const BigInt& y,
MemoryRegion<word>& workspace) const
{
BigInt result;
monty_mult(result, x, y, workspace);
return result;
}
/**
* Montgomery multiplication/reduction
* @param z output
* @param x first multiplicand
* @param y second multiplicand
* @param workspace temp space
*/
void monty_mult(BigInt& z,
const BigInt& x, const BigInt& y,
MemoryRegion<word>& workspace) const;
/**
* Montgomery squaring/reduction
* @param x multiplicand
* @param workspace temp space
*/
BigInt monty_sqr(const BigInt& x,
MemoryRegion<word>& workspace) const
{
BigInt result;
monty_sqr(result, x, workspace);
return result;
}
/**
* Montgomery squaring/reduction
* @param z output
* @param x multiplicand
* @param workspace temp space
*/
void monty_sqr(BigInt& z, const BigInt& x,
MemoryRegion<word>& workspace) const;
/**
* Point addition
*/
void add(const PointGFp& other, Workspace& workspace);
/**
* Point doubling
* @param workspace temp space
*/
void mult2(Workspace& workspace);
CurveGFp curve;
BigInt coord_x, coord_y, coord_z;
};
// relational operators
inline bool operator!=(const PointGFp& lhs, const PointGFp& rhs)
{
return !(rhs == lhs);
}
// arithmetic operators
inline PointGFp operator-(const PointGFp& lhs)
{
return PointGFp(lhs).negate();
}
inline PointGFp operator+(const PointGFp& lhs, const PointGFp& rhs)
{
PointGFp tmp(lhs);
return tmp += rhs;
}
inline PointGFp operator-(const PointGFp& lhs, const PointGFp& rhs)
{
PointGFp tmp(lhs);
return tmp -= rhs;
}
inline PointGFp operator*(const PointGFp& point, const BigInt& scalar)
{
return scalar * point;
}
// encoding and decoding
SecureVector<byte> BOTAN_DLL EC2OSP(const PointGFp& point, byte format);
PointGFp BOTAN_DLL OS2ECP(const byte data[], u32bit data_len,
const CurveGFp& curve);
inline PointGFp OS2ECP(const MemoryRegion<byte>& data, const CurveGFp& curve)
{ return OS2ECP(&data[0], data.size(), curve); }
}
namespace std {
template<>
inline void swap<Botan::PointGFp>(Botan::PointGFp& x, Botan::PointGFp& y)
{ x.swap(y); }
}
#endif
|
