1
|
|
|
<?php |
2
|
|
|
|
3
|
|
|
/*********************************************************************** |
4
|
|
|
Copyright (C) 2012 Matyas Danter |
5
|
|
|
|
6
|
|
|
Permission is hereby granted, free of charge, to any person obtaining |
7
|
|
|
a copy of this software and associated documentation files (the "Software"), |
8
|
|
|
to deal in the Software without restriction, including without limitation |
9
|
|
|
the rights to use, copy, modify, merge, publish, distribute, sublicense, |
10
|
|
|
and/or sell copies of the Software, and to permit persons to whom the |
11
|
|
|
Software is furnished to do so, subject to the following conditions: |
12
|
|
|
|
13
|
|
|
The above copyright notice and this permission notice shall be included |
14
|
|
|
in all copies or substantial portions of the Software. |
15
|
|
|
|
16
|
|
|
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS |
17
|
|
|
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, |
18
|
|
|
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL |
19
|
|
|
THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES |
20
|
|
|
OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, |
21
|
|
|
ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR |
22
|
|
|
OTHER DEALINGS IN THE SOFTWARE. |
23
|
|
|
*************************************************************************/ |
24
|
|
|
|
25
|
|
|
namespace Jose\Component\Core\Util\Ecc\Primitives; |
26
|
|
|
|
27
|
|
|
use Jose\Component\Core\Util\Ecc\Math\GmpMath; |
28
|
|
|
use Jose\Component\Core\Util\Ecc\Math\ModularArithmetic; |
29
|
|
|
|
30
|
|
|
/** |
31
|
|
|
* This class is a representation of an EC over a field modulo a prime number |
32
|
|
|
* |
33
|
|
|
* Important objectives for this class are: |
34
|
|
|
* - Does the curve contain a point? |
35
|
|
|
* - Comparison of two curves. |
36
|
|
|
*/ |
37
|
|
|
final class CurveFp |
38
|
|
|
{ |
39
|
|
|
|
40
|
|
|
/** |
41
|
|
|
* @var CurveParameters |
42
|
|
|
*/ |
43
|
|
|
private $parameters; |
44
|
|
|
|
45
|
|
|
/** |
46
|
|
|
* |
47
|
|
|
* @var GmpMath |
48
|
|
|
*/ |
49
|
|
|
private $adapter; |
50
|
|
|
|
51
|
|
|
/** |
52
|
|
|
* |
53
|
|
|
* @var ModularArithmetic |
54
|
|
|
*/ |
55
|
|
|
private $modAdapter; |
56
|
|
|
|
57
|
|
|
/** |
58
|
|
|
* Constructor that sets up the instance variables. |
59
|
|
|
* |
60
|
|
|
* @param CurveParameters $parameters |
61
|
|
|
*/ |
62
|
|
|
public function __construct(CurveParameters $parameters) |
63
|
|
|
{ |
64
|
|
|
$this->parameters = $parameters; |
65
|
|
|
$this->adapter = new GmpMath(); |
66
|
|
|
$this->modAdapter = new ModularArithmetic($this->parameters->getPrime()); |
67
|
|
|
} |
68
|
|
|
|
69
|
|
|
/** |
70
|
|
|
* @return ModularArithmetic |
71
|
|
|
*/ |
72
|
|
|
public function getModAdapter(): ModularArithmetic |
73
|
|
|
{ |
74
|
|
|
return $this->modAdapter; |
75
|
|
|
} |
76
|
|
|
|
77
|
|
|
/** |
78
|
|
|
* @param \GMP $x |
79
|
|
|
* @param \GMP $y |
80
|
|
|
* @param \GMP|null $order |
81
|
|
|
* |
82
|
|
|
* @return Point |
83
|
|
|
*/ |
84
|
|
|
public function getPoint(\GMP $x, \GMP $y, ?\GMP $order = null): Point |
85
|
|
|
{ |
86
|
|
|
return new Point($this, $x, $y, $order); |
87
|
|
|
} |
88
|
|
|
|
89
|
|
|
/** |
90
|
|
|
* @return Point |
91
|
|
|
*/ |
92
|
|
|
public function getInfinity(): Point |
93
|
|
|
{ |
94
|
|
|
return new Point($this, gmp_init(0, 10), gmp_init(0, 10), null, true); |
95
|
|
|
} |
96
|
|
|
|
97
|
|
|
/** |
98
|
|
|
* @param \GMP $x |
99
|
|
|
* @param \GMP $y |
100
|
|
|
* @param \GMP $order |
101
|
|
|
* |
102
|
|
|
* @return GeneratorPoint |
103
|
|
|
*/ |
104
|
|
|
public function getGenerator(\GMP $x, \GMP $y, \GMP $order): GeneratorPoint |
105
|
|
|
{ |
106
|
|
|
return new GeneratorPoint($this, $x, $y, $order); |
107
|
|
|
} |
108
|
|
|
|
109
|
|
|
/** |
110
|
|
|
* @param \GMP $x |
111
|
|
|
* @param \GMP $y |
112
|
|
|
* @return bool |
113
|
|
|
*/ |
114
|
|
|
public function contains(\GMP $x, \GMP $y): bool |
115
|
|
|
{ |
116
|
|
|
$math = $this->adapter; |
117
|
|
|
|
118
|
|
|
$eq_zero = $math->equals( |
119
|
|
|
$this->modAdapter->sub( |
120
|
|
|
$math->pow($y, 2), |
121
|
|
|
$math->add( |
122
|
|
|
$math->add( |
123
|
|
|
$math->pow($x, 3), |
124
|
|
|
$math->mul($this->getA(), $x) |
125
|
|
|
), |
126
|
|
|
$this->getB() |
127
|
|
|
) |
128
|
|
|
), |
129
|
|
|
gmp_init(0, 10) |
130
|
|
|
); |
131
|
|
|
|
132
|
|
|
return $eq_zero; |
133
|
|
|
} |
134
|
|
|
|
135
|
|
|
/** |
136
|
|
|
* @return \GMP |
137
|
|
|
*/ |
138
|
|
|
public function getA(): \GMP |
139
|
|
|
{ |
140
|
|
|
return $this->parameters->getA(); |
141
|
|
|
} |
142
|
|
|
|
143
|
|
|
/** |
144
|
|
|
* @return \GMP |
145
|
|
|
*/ |
146
|
|
|
public function getB(): \GMP |
147
|
|
|
{ |
148
|
|
|
return $this->parameters->getB(); |
149
|
|
|
} |
150
|
|
|
|
151
|
|
|
/** |
152
|
|
|
* @return \GMP |
153
|
|
|
*/ |
154
|
|
|
public function getPrime(): \GMP |
155
|
|
|
{ |
156
|
|
|
return $this->parameters->getPrime(); |
157
|
|
|
} |
158
|
|
|
|
159
|
|
|
/** |
160
|
|
|
* @return int |
161
|
|
|
*/ |
162
|
|
|
public function getSize(): int |
163
|
|
|
{ |
164
|
|
|
return $this->parameters->getSize(); |
165
|
|
|
} |
166
|
|
|
|
167
|
|
|
/** |
168
|
|
|
* @param CurveFp $other |
169
|
|
|
* |
170
|
|
|
* @return int |
171
|
|
|
*/ |
172
|
|
|
public function cmp(CurveFp $other): int |
173
|
|
|
{ |
174
|
|
|
$math = $this->adapter; |
175
|
|
|
|
176
|
|
|
$equal = $math->equals($this->getA(), $other->getA()); |
177
|
|
|
$equal &= $math->equals($this->getB(), $other->getB()); |
178
|
|
|
$equal &= $math->equals($this->getPrime(), $other->getPrime()); |
179
|
|
|
|
180
|
|
|
return $equal ? 0 : 1; |
181
|
|
|
} |
182
|
|
|
|
183
|
|
|
/** |
184
|
|
|
* @param CurveFp $other |
185
|
|
|
* |
186
|
|
|
* @return bool |
187
|
|
|
*/ |
188
|
|
|
public function equals(CurveFp $other): bool |
189
|
|
|
{ |
190
|
|
|
return $this->cmp($other) === 0; |
191
|
|
|
} |
192
|
|
|
} |
193
|
|
|
|