TwistedEdwards.php — JetBackup – Backup, Restore & Migrate 3.1.13.4

backup / src / JetBackup / 3rdparty / phpseclib3 / Crypt / EC / BaseCurves / TwistedEdwards.php

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TwistedEdwards.php

216 lines

1	<?php
2
3	/**
4	* Curves over ax^2 + y^2 = 1 + dx^2*y^2
5	*
6	* http://www.secg.org/SEC2-Ver-1.0.pdf provides for curves with custom parameters.
7	* ie. the coefficients can be arbitrary set through specially formatted keys, etc.
8	* As such, Prime.php is built very generically and it's not able to take full
9	* advantage of curves with 0 coefficients to produce simplified point doubling,
10	* point addition. Twisted Edwards curves, in contrast, do not have a way, currently,
11	* to customize them. As such, we can omit the super generic stuff from this class
12	* and let the named curves (Ed25519 and Ed448) define their own custom tailored
13	* point addition and point doubling methods.
14	*
15	* More info:
16	*
17	* https://en.wikipedia.org/wiki/Twisted_Edwards_curve
18	*
19	* PHP version 5 and 7
20	*
21	* @author Jim Wigginton <terrafrost@php.net>
22	* @copyright 2017 Jim Wigginton
23	* @license http://www.opensource.org/licenses/mit-license.html MIT License
24	* @link http://pear.php.net/package/Math_BigInteger
25	*/
26
27	declare(strict_types=1);
28
29	namespace phpseclib3\Crypt\EC\BaseCurves;
30
31	use phpseclib3\Exception\RuntimeException;
32	use phpseclib3\Exception\UnexpectedValueException;
33	use phpseclib3\Math\BigInteger;
34	use phpseclib3\Math\PrimeField;
35	use phpseclib3\Math\PrimeField\Integer as PrimeInteger;
36
37	/**
38	* Curves over ax^2 + y^2 = 1 + dx^2*y^2
39	*
40	* @author Jim Wigginton <terrafrost@php.net>
41	*/
42	class TwistedEdwards extends Base
43	{
44	/**
45	* The modulo
46	*
47	* @var BigInteger
48	*/
49	protected $modulo;
50
51	/**
52	* Cofficient for x^2
53	*
54	* @var object
55	*/
56	protected $a;
57
58	/**
59	* Cofficient for x^2*y^2
60	*
61	* @var object
62	*/
63	protected $d;
64
65	/**
66	* Base Point
67	*
68	* @var object[]
69	*/
70	protected $p;
71
72	/**
73	* The number zero over the specified finite field
74	*
75	* @var object
76	*/
77	protected $zero;
78
79	/**
80	* The number one over the specified finite field
81	*
82	* @var object
83	*/
84	protected $one;
85
86	/**
87	* The number two over the specified finite field
88	*
89	* @var object
90	*/
91	protected $two;
92
93	/**
94	* Sets the modulo
95	*/
96	public function setModulo(BigInteger $modulo): void
97	{
98	$this->modulo = $modulo;
99	$this->factory = new PrimeField($modulo);
100	$this->zero = $this->factory->newInteger(new BigInteger(0));
101	$this->one = $this->factory->newInteger(new BigInteger(1));
102	$this->two = $this->factory->newInteger(new BigInteger(2));
103	}
104
105	/**
106	* Set coefficients a and b
107	*/
108	public function setCoefficients(BigInteger $a, BigInteger $d): void
109	{
110	if (!isset($this->factory)) {
111	throw new RuntimeException('setModulo needs to be called before this method');
112	}
113	$this->a = $this->factory->newInteger($a);
114	$this->d = $this->factory->newInteger($d);
115	}
116
117	/**
118	* Set x and y coordinates for the base point
119	*/
120	public function setBasePoint($x, $y): void
121	{
122	switch (true) {
123	case !$x instanceof BigInteger && !$x instanceof PrimeInteger:
124	throw new UnexpectedValueException('Argument 1 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
125	case !$y instanceof BigInteger && !$y instanceof PrimeInteger:
126	throw new UnexpectedValueException('Argument 2 passed to Prime::setBasePoint() must be an instance of either BigInteger or PrimeField\Integer');
127	}
128	if (!isset($this->factory)) {
129	throw new RuntimeException('setModulo needs to be called before this method');
130	}
131	$this->p = [
132	$x instanceof BigInteger ? $this->factory->newInteger($x) : $x,
133	$y instanceof BigInteger ? $this->factory->newInteger($y) : $y,
134	];
135	}
136
137	/**
138	* Returns the a coefficient
139	*
140	* @return PrimeInteger
141	*/
142	public function getA()
143	{
144	return $this->a;
145	}
146
147	/**
148	* Returns the a coefficient
149	*
150	* @return PrimeInteger
151	*/
152	public function getD()
153	{
154	return $this->d;
155	}
156
157	/**
158	* Retrieve the base point as an array
159	*/
160	public function getBasePoint(): array
161	{
162	if (!isset($this->factory)) {
163	throw new RuntimeException('setModulo needs to be called before this method');
164	}
165	/*
166	if (!isset($this->p)) {
167	throw new \phpseclib3\Exception\RuntimeException('setBasePoint needs to be called before this method');
168	}
169	*/
170	return $this->p;
171	}
172
173	/**
174	* Returns the affine point
175	*
176	* @return PrimeInteger[]
177	*/
178	public function convertToAffine(array $p): array
179	{
180	if (!isset($p[2])) {
181	return $p;
182	}
183	[$x, $y, $z] = $p;
184	$z = $this->one->divide($z);
185	return [
186	$x->multiply($z),
187	$y->multiply($z),
188	];
189	}
190
191	/**
192	* Returns the modulo
193	*/
194	public function getModulo(): BigInteger
195	{
196	return $this->modulo;
197	}
198
199	/**
200	* Tests whether or not the x / y values satisfy the equation
201	*
202	* @return boolean
203	*/
204	public function verifyPoint(array $p): bool
205	{
206	[$x, $y] = $p;
207	$x2 = $x->multiply($x);
208	$y2 = $y->multiply($y);
209
210	$lhs = $this->a->multiply($x2)->add($y2);
211	$rhs = $this->d->multiply($x2)->multiply($y2)->add($this->one);
212
213	return $lhs->equals($rhs);
214	}
215	}
216