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Curves over y^2 + x*y = x^3 + a*x^2 + b These are curves used in SEC 2 over prime fields: http://www.secg.org/SEC2-Ver-1.0.pdf The curve is a weierstrass curve with a[3] and a[2] set to 0.
| Author: | Jim Wigginton |
| Copyright: | 2017 Jim Wigginton |
| License: | http://www.opensource.org/licenses/mit-license.html MIT License |
| Link: | http://pear.php.net/package/Math_BigInteger |
| File Size: | 373 lines (10 kb) |
| Included or required: | 0 times |
| Referenced: | 0 times |
| Includes or requires: | 0 files |
Binary:: (13 methods):
setModulo()
setCoefficients()
setBasePoint()
getBasePoint()
addPoint()
doublePoint()
derivePoint()
verifyPoint()
getModulo()
getA()
getB()
convertToAffine()
convertToInternal()
| setModulo(...$modulo) X-Ref |
| Sets the modulo |
| setCoefficients($a, $b) X-Ref |
| Set coefficients a and b param: string $a param: string $b |
| setBasePoint($x, $y) X-Ref |
| Set x and y coordinates for the base point param: string|BinaryInteger $x param: string|BinaryInteger $y |
| getBasePoint() X-Ref |
| Retrieve the base point as an array return: array |
| addPoint(array $p, array $q) X-Ref |
| Adds two points on the curve return: FiniteField[] |
| doublePoint(array $p) X-Ref |
| Doubles a point on a curve return: FiniteField[] |
| derivePoint($m) X-Ref |
| Returns the X coordinate and the derived Y coordinate Not supported because it is covered by patents. Quoting https://www.openssl.org/docs/man1.1.0/apps/ecparam.html , "Due to patent issues the compressed option is disabled by default for binary curves and can be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at compile time." return: array |
| verifyPoint(array $p) X-Ref |
| Tests whether or not the x / y values satisfy the equation return: boolean |
| getModulo() X-Ref |
| Returns the modulo return: \phpseclib3\Math\BigInteger |
| getA() X-Ref |
| Returns the a coefficient return: \phpseclib3\Math\PrimeField\Integer |
| getB() X-Ref |
| Returns the a coefficient return: \phpseclib3\Math\PrimeField\Integer |
| convertToAffine(array $p) X-Ref |
| Returns the affine point A Jacobian Coordinate is of the form (x, y, z). To convert a Jacobian Coordinate to an Affine Point you do (x / z^2, y / z^3) return: \phpseclib3\Math\PrimeField\Integer[] |
| convertToInternal(array $p) X-Ref |
| Converts an affine point to a jacobian coordinate return: \phpseclib3\Math\PrimeField\Integer[] |