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Generalized Koblitz Curves over y^2 = x^3 + b. According to http://www.secg.org/SEC2-Ver-1.0.pdf Koblitz curves are over the GF(2**m) finite field. Both the $a$ and $b$ coefficients are either 0 or 1. However, SEC2 generalizes the definition to include curves over GF(P) "which possess an efficiently computable endomorphism".
| 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: | 335 lines (10 kb) |
| Included or required: | 0 times |
| Referenced: | 0 times |
| Includes or requires: | 0 files |
KoblitzPrime:: (6 methods):
multiplyAddPoints()
doublePointHelper()
jacobianDoublePoint()
jacobianDoublePointMixed()
verifyPoint()
extendedGCD()
Class: KoblitzPrime - X-Ref
Curves over y^2 = x^3 + b| multiplyAddPoints(array $points, array $scalars) X-Ref |
| Multiply and Add Points Uses a efficiently computable endomorphism to achieve a slight speedup Adapted from: https://github.com/indutny/elliptic/blob/725bd91/lib/elliptic/curve/short.js#L219 return: int[] |
| doublePointHelper(array $p) X-Ref |
| Returns the numerator and denominator of the slope return: FiniteField[] |
| jacobianDoublePoint(array $p) X-Ref |
| Doubles a jacobian coordinate on the curve See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l return: FiniteField[] |
| jacobianDoublePointMixed(array $p) X-Ref |
| Doubles a "fresh" jacobian coordinate on the curve See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-mdbl-2007-bl return: FiniteField[] |
| verifyPoint(array $p) X-Ref |
| Tests whether or not the x / y values satisfy the equation return: boolean |
| extendedGCD(BigInteger $u, BigInteger $v) X-Ref |
| Calculates the parameters needed from the Euclidean algorithm as discussed at http://diamond.boisestate.edu/~liljanab/MATH308/GuideToECC.pdf#page=148 return: BigInteger[] param: BigInteger $u param: BigInteger $v |