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Curves over y^2 = x^3 + a*x + x Technically, a Montgomery curve has a coefficient for y^2 but for Curve25519 and Curve448 that coefficient is 1.
| Author: | Jim Wigginton |
| Copyright: | 2019 Jim Wigginton |
| License: | http://www.opensource.org/licenses/mit-license.html MIT License |
| Link: | http://pear.php.net/package/Math_BigInteger |
| File Size: | 279 lines (7 kb) |
| Included or required: | 0 times |
| Referenced: | 0 times |
| Includes or requires: | 0 files |
Montgomery:: (8 methods):
setModulo()
setCoefficients()
setBasePoint()
getBasePoint()
doubleAndAddPoint()
multiplyPoint()
convertToInternal()
convertToAffine()
Class: Montgomery - X-Ref
Curves over y^2 = x^3 + a*x + x| setModulo(BigInteger $modulo) X-Ref |
| Sets the modulo |
| setCoefficients(BigInteger $a) X-Ref |
| Set coefficients a |
| setBasePoint($x, $y) X-Ref |
| Set x and y coordinates for the base point return: PrimeInteger[] param: BigInteger|PrimeInteger $x param: BigInteger|PrimeInteger $y |
| getBasePoint() X-Ref |
| Retrieve the base point as an array return: array |
| doubleAndAddPoint(array $p, array $q, PrimeInteger $x1) X-Ref |
| Doubles and adds a point on a curve See https://tools.ietf.org/html/draft-ietf-tls-curve25519-01#appendix-A.1.3 return: FiniteField[][] |
| multiplyPoint(array $p, BigInteger $d) X-Ref |
| Multiply a point on the curve by a scalar Uses the montgomery ladder technique as described here: https://en.wikipedia.org/wiki/Elliptic_curve_point_multiplication#Montgomery_ladder https://github.com/phpecc/phpecc/issues/16#issuecomment-59176772 return: array |
| convertToInternal(array $p) X-Ref |
| Converts an affine point to an XZ coordinate From https://hyperelliptic.org/EFD/g1p/auto-montgom-xz.html XZ coordinates represent x y as X Z satsfying the following equations: x=X/Z return: \phpseclib3\Math\PrimeField\Integer[] |
| convertToAffine(array $p) X-Ref |
| Returns the affine point return: \phpseclib3\Math\PrimeField\Integer[] |