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brainpoolP160t1.php

brainpoolP160t1

This curve is a twisted version of brainpoolP160r1 with A = -3. With brainpool, the curves ending in r1 are the "regular" curves and the curves ending in "t1" are the twisted version of the r1 curves. Per https://tools.ietf.org/html/rfc5639#page-7 you can convert a point on an r1 curve to a point on a t1 curve thusly:

F(x,y) := (x*Z^2, y*Z^3)

The advantage of A = -3 is that some of the point doubling and point addition can be slightly optimized. See http://hyperelliptic.org/EFD/g1p/auto-shortw-projective-3.html vs http://hyperelliptic.org/EFD/g1p/auto-shortw-projective.html for example.

phpseclib does not currently take advantage of this optimization opportunity

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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brainpoolP160t1
Curves over y^2 = x^3 + a*x + b

        
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