TwistedEdwards.php
Curves over a*x^2 + y^2 = 1 + d*x^2*y^2
http://www.secg.org/SEC2-Ver-1.0.pdf provides for curves with custom parameters. ie. the coefficients can be arbitrary set through specially formatted keys, etc. As such, Prime.php is built very generically and it's not able to take full advantage of curves with 0 coefficients to produce simplified point doubling, point addition. Twisted Edwards curves, in contrast, do not have a way, currently, to customize them. As such, we can omit the super generic stuff from this class and let the named curves (Ed25519 and Ed448) define their own custom tailored point addition and point doubling methods.
More info:
https://en.wikipedia.org/wiki/Twisted_Edwards_curve
PHP version 5 and 7
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- TwistedEdwards
- Curves over a*x^2 + y^2 = 1 + d*x^2*y^2