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
|
<?php
/**
* Curves over a*x^2 + y^2 = 1 + d*x^2*y^2
*
* http://www.secg.org/SEC2-Ver-1.0.pdf provides for curves with custom parameters.
* ie. the coefficients can be arbitrary set through specially formatted keys, etc.
* As such, Prime.php is built very generically and it's not able to take full
* advantage of curves with 0 coefficients to produce simplified point doubling,
* point addition. Twisted Edwards curves, in contrast, do not have a way, currently,
* to customize them. As such, we can omit the super generic stuff from this class
* and let the named curves (Ed25519 and Ed448) define their own custom tailored
* point addition and point doubling methods.
*
* More info:
*
* https://en.wikipedia.org/wiki/Twisted_Edwards_curve
*
* PHP version 5 and 7
*
* @author Jim Wigginton <[email protected]>
* @copyright 2017 Jim Wigginton
* @license http://www.opensource.org/licenses/mit-license.html MIT License
* @link http://pear.php.net/package/Math_BigInteger
*/
namespace phpseclib3\Crypt\EC\BaseCurves;
use phpseclib3\Math\BigInteger;
use phpseclib3\Math\PrimeField;
use phpseclib3\Math\PrimeField\Integer as PrimeInteger;
/**
* Curves over a*x^2 + y^2 = 1 + d*x^2*y^2
*
* @author Jim Wigginton <[email protected]>
*/
class TwistedEdwards extends Base
{
/**
* The modulo
*
* @var BigInteger
*/
protected $modulo;
/**
* Cofficient for x^2
*
* @var object
*/
protected $a;
/**
* Cofficient for x^2*y^2
*
* @var object
*/
protected $d;
/**
* Base Point
*
* @var object[]
*/
protected $p;
/**
* The number zero over the specified finite field
*
* @var object
*/
protected $zero;
/**
* The number one over the specified finite field
*
* @var object
*/
protected $one;
/**
* The number two over the specified finite field
*
* @var object
*/
protected $two;
/**
* Sets the modulo
*/
public function setModulo(BigInteger $modulo)
{
$this->modulo = $modulo;
$this->factory = new PrimeField($modulo);
$this->zero = $this->factory->newInteger(new BigInteger(0));
$this->one = $this->factory->newInteger(new BigInteger(1));
$this->two = $this->factory->newInteger(new BigInteger(2));
}
/**
* Set coefficients a and b
*/
public function setCoefficients(BigInteger $a, BigInteger $d)
{
if (!isset($this->factory)) {
throw new \RuntimeException('setModulo needs to be called before this method');
}
$this->a = $this->factory->newInteger($a);
$this->d = $this->factory->newInteger($d);
}
/**
* Set x and y coordinates for the base point
*/
public function setBasePoint($x, $y)
{
switch (true) {
case !$x instanceof BigInteger && !$x instanceof PrimeInteger:
throw new \UnexpectedValueException('Argument 1 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
case !$y instanceof BigInteger && !$y instanceof PrimeInteger:
throw new \UnexpectedValueException('Argument 2 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
}
if (!isset($this->factory)) {
throw new \RuntimeException('setModulo needs to be called before this method');
}
$this->p = [
$x instanceof BigInteger ? $this->factory->newInteger($x) : $x,
$y instanceof BigInteger ? $this->factory->newInteger($y) : $y
];
}
/**
* Returns the a coefficient
*
* @return \phpseclib3\Math\PrimeField\Integer
*/
public function getA()
{
return $this->a;
}
/**
* Returns the a coefficient
*
* @return \phpseclib3\Math\PrimeField\Integer
*/
public function getD()
{
return $this->d;
}
/**
* Retrieve the base point as an array
*
* @return array
*/
public function getBasePoint()
{
if (!isset($this->factory)) {
throw new \RuntimeException('setModulo needs to be called before this method');
}
/*
if (!isset($this->p)) {
throw new \RuntimeException('setBasePoint needs to be called before this method');
}
*/
return $this->p;
}
/**
* Returns the affine point
*
* @return \phpseclib3\Math\PrimeField\Integer[]
*/
public function convertToAffine(array $p)
{
if (!isset($p[2])) {
return $p;
}
list($x, $y, $z) = $p;
$z = $this->one->divide($z);
return [
$x->multiply($z),
$y->multiply($z)
];
}
/**
* Returns the modulo
*
* @return \phpseclib3\Math\BigInteger
*/
public function getModulo()
{
return $this->modulo;
}
/**
* Tests whether or not the x / y values satisfy the equation
*
* @return boolean
*/
public function verifyPoint(array $p)
{
list($x, $y) = $p;
$x2 = $x->multiply($x);
$y2 = $y->multiply($y);
$lhs = $this->a->multiply($x2)->add($y2);
$rhs = $this->d->multiply($x2)->multiply($y2)->add($this->one);
return $lhs->equals($rhs);
}
}
|
