KoblitzPrime.php
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".
For these generalized Koblitz curves $b$ doesn't have to be 0 or 1. Whether or not $a$ has any restrictions on it is unclear, however, for all the GF(P) Koblitz curves defined in SEC2 v1.0 $a$ is $0$ so all of the methods defined herein will assume that it is.
I suppose we could rename the $b$ coefficient to $a$, however, the documentation refers to $b$ so we'll just keep it.
If a later version of SEC2 comes out wherein some $a$ values are non-zero we can create a new method for those. eg. KoblitzA1Prime.php or something.
PHP version 5 and 7
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- KoblitzPrime
- Curves over y^2 = x^3 + b