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
270
271
272
273
274
275
276
277
278
279
280
281
282
283
|
/*
* Point arithmetic on elliptic curves over GF(p)
*
* (C) 2007 Martin Doering, Christoph Ludwig, Falko Strenzke
* 2008-2011,2014 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 {
/**
* Exception thrown if you try to convert a zero point to an affine
* coordinate
*/
struct BOTAN_DLL Illegal_Transformation : public Exception
{
Illegal_Transformation(const std::string& err =
"Requested transformation is not possible") :
Exception(err) {}
};
/**
* Exception thrown if some form of illegal point is decoded
*/
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);
/**
* Copy constructor
*/
PointGFp(const PointGFp&) = default;
/**
* Move Constructor
*/
PointGFp(PointGFp&& other)
{
this->swap(other);
}
/**
* Standard Assignment
*/
PointGFp& operator=(const PointGFp&) = default;
/**
* Move Assignment
*/
PointGFp& operator=(PointGFp&& other)
{
if(this != &other)
this->swap(other);
return (*this);
}
/**
* 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);
/**
* += 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);
/**
* Multiexponentiation
* @param p1 a point
* @param z1 a scalar
* @param p2 a point
* @param z2 a scalar
* @result (p1 * z1 + p2 * z2)
*/
friend BOTAN_DLL PointGFp multi_exponentiate(
const PointGFp& p1, const BigInt& z1,
const PointGFp& p2, const BigInt& z2);
/**
* 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:
BigInt curve_mult(const BigInt& x, const BigInt& y) const
{
BigInt z;
curve.mul(z, x, y, ws);
return z;
}
void curve_mult(BigInt& z, const BigInt& x, const BigInt& y) const
{
curve.mul(z, x, y, ws);
}
BigInt curve_sqr(const BigInt& x) const
{
BigInt z;
curve.sqr(z, x, ws);
return z;
}
void curve_sqr(BigInt& z, const BigInt& x) const
{
curve.sqr(z, x, ws);
}
/**
* Point addition
* @param workspace temp space, at least 11 elements
*/
void add(const PointGFp& other, std::vector<BigInt>& workspace);
/**
* Point doubling
* @param workspace temp space, at least 9 elements
*/
void mult2(std::vector<BigInt>& workspace);
CurveGFp curve;
BigInt coord_x, coord_y, coord_z;
mutable secure_vector<word> ws; // workspace for Montgomery
};
// 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
secure_vector<byte> BOTAN_DLL EC2OSP(const PointGFp& point, byte format);
PointGFp BOTAN_DLL OS2ECP(const byte data[], size_t data_len,
const CurveGFp& curve);
template<typename Alloc>
PointGFp OS2ECP(const std::vector<byte, Alloc>& 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
|