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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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category

Crypt

author

Jim Wigginton terrafrost@php.net

copyright

2017 Jim Wigginton

license

http://www.opensource.org/licenses/mit-license.html MIT License

link
http://pear.php.net/package/Math_BigInteger

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KoblitzPrime
Curves over y^2 = x^3 + b

        
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