.htaccess
9 months ago
Base.php
9 months ago
Binary.php
9 months ago
KoblitzPrime.php
9 months ago
Montgomery.php
9 months ago
Prime.php
9 months ago
TwistedEdwards.php
9 months ago
index.html
9 months ago
web.config
9 months ago
Binary.php
372 lines
| 1 | <?php |
| 2 | |
| 3 | /** |
| 4 | * Curves over y^2 + x*y = x^3 + a*x^2 + b |
| 5 | * |
| 6 | * These are curves used in SEC 2 over prime fields: http://www.secg.org/SEC2-Ver-1.0.pdf |
| 7 | * The curve is a weierstrass curve with a[3] and a[2] set to 0. |
| 8 | * |
| 9 | * Uses Jacobian Coordinates for speed if able: |
| 10 | * |
| 11 | * https://en.wikipedia.org/wiki/Jacobian_curve |
| 12 | * https://en.wikibooks.org/wiki/Cryptography/Prime_Curve/Jacobian_Coordinates |
| 13 | * |
| 14 | * PHP version 5 and 7 |
| 15 | * |
| 16 | * @author Jim Wigginton <terrafrost@php.net> |
| 17 | * @copyright 2017 Jim Wigginton |
| 18 | * @license http://www.opensource.org/licenses/mit-license.html MIT License |
| 19 | * @link http://pear.php.net/package/Math_BigInteger |
| 20 | */ |
| 21 | |
| 22 | declare(strict_types=1); |
| 23 | |
| 24 | namespace phpseclib3\Crypt\EC\BaseCurves; |
| 25 | |
| 26 | use phpseclib3\Exception\RuntimeException; |
| 27 | use phpseclib3\Exception\UnexpectedValueException; |
| 28 | use phpseclib3\Math\BigInteger; |
| 29 | use phpseclib3\Math\BinaryField; |
| 30 | use phpseclib3\Math\BinaryField\Integer as BinaryInteger; |
| 31 | use phpseclib3\Math\PrimeField\Integer; |
| 32 | |
| 33 | /** |
| 34 | * Curves over y^2 + x*y = x^3 + a*x^2 + b |
| 35 | * |
| 36 | * @author Jim Wigginton <terrafrost@php.net> |
| 37 | */ |
| 38 | class Binary extends Base |
| 39 | { |
| 40 | /** |
| 41 | * Binary Field Integer factory |
| 42 | * |
| 43 | * @var BinaryField |
| 44 | */ |
| 45 | protected $factory; |
| 46 | |
| 47 | /** |
| 48 | * Cofficient for x^1 |
| 49 | * |
| 50 | * @var object |
| 51 | */ |
| 52 | protected $a; |
| 53 | |
| 54 | /** |
| 55 | * Cofficient for x^0 |
| 56 | * |
| 57 | * @var object |
| 58 | */ |
| 59 | protected $b; |
| 60 | |
| 61 | /** |
| 62 | * Base Point |
| 63 | * |
| 64 | * @var object |
| 65 | */ |
| 66 | protected $p; |
| 67 | |
| 68 | /** |
| 69 | * The number one over the specified finite field |
| 70 | * |
| 71 | * @var object |
| 72 | */ |
| 73 | protected $one; |
| 74 | |
| 75 | /** |
| 76 | * The modulo |
| 77 | * |
| 78 | * @var array |
| 79 | */ |
| 80 | protected $modulo; |
| 81 | |
| 82 | /** |
| 83 | * The Order |
| 84 | * |
| 85 | * @var BigInteger |
| 86 | */ |
| 87 | protected $order; |
| 88 | |
| 89 | /** |
| 90 | * Sets the modulo |
| 91 | */ |
| 92 | public function setModulo(int ...$modulo): void |
| 93 | { |
| 94 | $this->modulo = $modulo; |
| 95 | $this->factory = new BinaryField(...$modulo); |
| 96 | |
| 97 | $this->one = $this->factory->newInteger("\1"); |
| 98 | } |
| 99 | |
| 100 | /** |
| 101 | * Set coefficients a and b |
| 102 | */ |
| 103 | public function setCoefficients(string $a, string $b): void |
| 104 | { |
| 105 | if (!isset($this->factory)) { |
| 106 | throw new RuntimeException('setModulo needs to be called before this method'); |
| 107 | } |
| 108 | $this->a = $this->factory->newInteger(pack('H*', $a)); |
| 109 | $this->b = $this->factory->newInteger(pack('H*', $b)); |
| 110 | } |
| 111 | |
| 112 | /** |
| 113 | * Set x and y coordinates for the base point |
| 114 | * |
| 115 | * @param string|BinaryInteger $x |
| 116 | * @param string|BinaryInteger $y |
| 117 | */ |
| 118 | public function setBasePoint($x, $y): void |
| 119 | { |
| 120 | switch (true) { |
| 121 | case !is_string($x) && !$x instanceof BinaryInteger: |
| 122 | throw new UnexpectedValueException('Argument 1 passed to Binary::setBasePoint() must be a string or an instance of BinaryField\Integer'); |
| 123 | case !is_string($y) && !$y instanceof BinaryInteger: |
| 124 | throw new UnexpectedValueException('Argument 2 passed to Binary::setBasePoint() must be a string or an instance of BinaryField\Integer'); |
| 125 | } |
| 126 | if (!isset($this->factory)) { |
| 127 | throw new RuntimeException('setModulo needs to be called before this method'); |
| 128 | } |
| 129 | $this->p = [ |
| 130 | is_string($x) ? $this->factory->newInteger(pack('H*', $x)) : $x, |
| 131 | is_string($y) ? $this->factory->newInteger(pack('H*', $y)) : $y, |
| 132 | ]; |
| 133 | } |
| 134 | |
| 135 | /** |
| 136 | * Retrieve the base point as an array |
| 137 | * |
| 138 | * @return array |
| 139 | */ |
| 140 | public function getBasePoint() |
| 141 | { |
| 142 | if (!isset($this->factory)) { |
| 143 | throw new RuntimeException('setModulo needs to be called before this method'); |
| 144 | } |
| 145 | /* |
| 146 | if (!isset($this->p)) { |
| 147 | throw new \phpseclib3\Exception\RuntimeException('setBasePoint needs to be called before this method'); |
| 148 | } |
| 149 | */ |
| 150 | return $this->p; |
| 151 | } |
| 152 | |
| 153 | /** |
| 154 | * Adds two points on the curve |
| 155 | * |
| 156 | * @return FiniteField[] |
| 157 | */ |
| 158 | public function addPoint(array $p, array $q): array |
| 159 | { |
| 160 | if (!isset($this->factory)) { |
| 161 | throw new RuntimeException('setModulo needs to be called before this method'); |
| 162 | } |
| 163 | |
| 164 | if (!count($p) || !count($q)) { |
| 165 | if (count($q)) { |
| 166 | return $q; |
| 167 | } |
| 168 | if (count($p)) { |
| 169 | return $p; |
| 170 | } |
| 171 | return []; |
| 172 | } |
| 173 | |
| 174 | if (!isset($p[2]) || !isset($q[2])) { |
| 175 | throw new RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa'); |
| 176 | } |
| 177 | |
| 178 | if ($p[0]->equals($q[0])) { |
| 179 | return !$p[1]->equals($q[1]) ? [] : $this->doublePoint($p); |
| 180 | } |
| 181 | |
| 182 | // formulas from http://hyperelliptic.org/EFD/g12o/auto-shortw-jacobian.html |
| 183 | |
| 184 | [$x1, $y1, $z1] = $p; |
| 185 | [$x2, $y2, $z2] = $q; |
| 186 | |
| 187 | $o1 = $z1->multiply($z1); |
| 188 | $b = $x2->multiply($o1); |
| 189 | |
| 190 | if ($z2->equals($this->one)) { |
| 191 | $d = $y2->multiply($o1)->multiply($z1); |
| 192 | $e = $x1->add($b); |
| 193 | $f = $y1->add($d); |
| 194 | $z3 = $e->multiply($z1); |
| 195 | $h = $f->multiply($x2)->add($z3->multiply($y2)); |
| 196 | $i = $f->add($z3); |
| 197 | $g = $z3->multiply($z3); |
| 198 | $p1 = $this->a->multiply($g); |
| 199 | $p2 = $f->multiply($i); |
| 200 | $p3 = $e->multiply($e)->multiply($e); |
| 201 | $x3 = $p1->add($p2)->add($p3); |
| 202 | $y3 = $i->multiply($x3)->add($g->multiply($h)); |
| 203 | |
| 204 | return [$x3, $y3, $z3]; |
| 205 | } |
| 206 | |
| 207 | $o2 = $z2->multiply($z2); |
| 208 | $a = $x1->multiply($o2); |
| 209 | $c = $y1->multiply($o2)->multiply($z2); |
| 210 | $d = $y2->multiply($o1)->multiply($z1); |
| 211 | $e = $a->add($b); |
| 212 | $f = $c->add($d); |
| 213 | $g = $e->multiply($z1); |
| 214 | $h = $f->multiply($x2)->add($g->multiply($y2)); |
| 215 | $z3 = $g->multiply($z2); |
| 216 | $i = $f->add($z3); |
| 217 | $p1 = $this->a->multiply($z3->multiply($z3)); |
| 218 | $p2 = $f->multiply($i); |
| 219 | $p3 = $e->multiply($e)->multiply($e); |
| 220 | $x3 = $p1->add($p2)->add($p3); |
| 221 | $y3 = $i->multiply($x3)->add($g->multiply($g)->multiply($h)); |
| 222 | |
| 223 | return [$x3, $y3, $z3]; |
| 224 | } |
| 225 | |
| 226 | /** |
| 227 | * Doubles a point on a curve |
| 228 | * |
| 229 | * @return FiniteField[] |
| 230 | */ |
| 231 | public function doublePoint(array $p): array |
| 232 | { |
| 233 | if (!isset($this->factory)) { |
| 234 | throw new RuntimeException('setModulo needs to be called before this method'); |
| 235 | } |
| 236 | |
| 237 | if (!count($p)) { |
| 238 | return []; |
| 239 | } |
| 240 | |
| 241 | if (!isset($p[2])) { |
| 242 | throw new RuntimeException('Affine coordinates need to be manually converted to "Jacobi" coordinates or vice versa'); |
| 243 | } |
| 244 | |
| 245 | // formulas from http://hyperelliptic.org/EFD/g12o/auto-shortw-jacobian.html |
| 246 | |
| 247 | [$x1, $y1, $z1] = $p; |
| 248 | |
| 249 | $a = $x1->multiply($x1); |
| 250 | $b = $a->multiply($a); |
| 251 | |
| 252 | if ($z1->equals($this->one)) { |
| 253 | $x3 = $b->add($this->b); |
| 254 | $z3 = clone $x1; |
| 255 | $p1 = $a->add($y1)->add($z3)->multiply($this->b); |
| 256 | $p2 = $a->add($y1)->multiply($b); |
| 257 | $y3 = $p1->add($p2); |
| 258 | |
| 259 | return [$x3, $y3, $z3]; |
| 260 | } |
| 261 | |
| 262 | $c = $z1->multiply($z1); |
| 263 | $d = $c->multiply($c); |
| 264 | $x3 = $b->add($this->b->multiply($d->multiply($d))); |
| 265 | $z3 = $x1->multiply($c); |
| 266 | $p1 = $b->multiply($z3); |
| 267 | $p2 = $a->add($y1->multiply($z1))->add($z3)->multiply($x3); |
| 268 | $y3 = $p1->add($p2); |
| 269 | |
| 270 | return [$x3, $y3, $z3]; |
| 271 | } |
| 272 | |
| 273 | /** |
| 274 | * Returns the X coordinate and the derived Y coordinate |
| 275 | * |
| 276 | * Not supported because it is covered by patents. |
| 277 | * Quoting https://www.openssl.org/docs/man1.1.0/apps/ecparam.html , |
| 278 | * |
| 279 | * "Due to patent issues the compressed option is disabled by default for binary curves |
| 280 | * and can be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at |
| 281 | * compile time." |
| 282 | */ |
| 283 | public function derivePoint($m): array |
| 284 | { |
| 285 | throw new RuntimeException('Point compression on binary finite field elliptic curves is not supported'); |
| 286 | } |
| 287 | |
| 288 | /** |
| 289 | * Tests whether or not the x / y values satisfy the equation |
| 290 | * |
| 291 | * @return boolean |
| 292 | */ |
| 293 | public function verifyPoint(array $p): bool |
| 294 | { |
| 295 | [$x, $y] = $p; |
| 296 | $lhs = $y->multiply($y); |
| 297 | $lhs = $lhs->add($x->multiply($y)); |
| 298 | $x2 = $x->multiply($x); |
| 299 | $x3 = $x2->multiply($x); |
| 300 | $rhs = $x3->add($this->a->multiply($x2))->add($this->b); |
| 301 | |
| 302 | return $lhs->equals($rhs); |
| 303 | } |
| 304 | |
| 305 | /** |
| 306 | * Returns the modulo |
| 307 | */ |
| 308 | public function getModulo(): array |
| 309 | { |
| 310 | return $this->modulo; |
| 311 | } |
| 312 | |
| 313 | /** |
| 314 | * Returns the a coefficient |
| 315 | * |
| 316 | * @return Integer |
| 317 | */ |
| 318 | public function getA() |
| 319 | { |
| 320 | return $this->a; |
| 321 | } |
| 322 | |
| 323 | /** |
| 324 | * Returns the a coefficient |
| 325 | * |
| 326 | * @return Integer |
| 327 | */ |
| 328 | public function getB() |
| 329 | { |
| 330 | return $this->b; |
| 331 | } |
| 332 | |
| 333 | /** |
| 334 | * Returns the affine point |
| 335 | * |
| 336 | * A Jacobian Coordinate is of the form (x, y, z). |
| 337 | * To convert a Jacobian Coordinate to an Affine Point |
| 338 | * you do (x / z^2, y / z^3) |
| 339 | * |
| 340 | * @return Integer[] |
| 341 | */ |
| 342 | public function convertToAffine(array $p): array |
| 343 | { |
| 344 | if (!isset($p[2])) { |
| 345 | return $p; |
| 346 | } |
| 347 | [$x, $y, $z] = $p; |
| 348 | $z = $this->one->divide($z); |
| 349 | $z2 = $z->multiply($z); |
| 350 | return [ |
| 351 | $x->multiply($z2), |
| 352 | $y->multiply($z2)->multiply($z), |
| 353 | ]; |
| 354 | } |
| 355 | |
| 356 | /** |
| 357 | * Converts an affine point to a jacobian coordinate |
| 358 | * |
| 359 | * @return Integer[] |
| 360 | */ |
| 361 | public function convertToInternal(array $p): array |
| 362 | { |
| 363 | if (isset($p[2])) { |
| 364 | return $p; |
| 365 | } |
| 366 | |
| 367 | $p[2] = clone $this->one; |
| 368 | $p['fresh'] = true; |
| 369 | return $p; |
| 370 | } |
| 371 | } |
| 372 |