[Cryptography] Microsoft's new, free, crypto library dubbed FourQ

Rob S. rob.schneier1 at gmail.com
Sat Sep 19 14:38:02 EDT 2015

Tony Arcieri's post is full of misconceptions and mistakes.

First off, efficient scalar multiplications on the Kummer surface and the 
fast Kummer surface defined over GF(2^127-1) used by several recent 
implementations are due to Gaudry and Gaudry-Schost, respectively, not 
to "djb and friends".

Most of the recent Kummer implementations (see 
http://eprint.iacr.org/2012/670.pdf and 
http://eprint.iacr.org/2014/134.pdf) are fully optimized in assembly. 
Still, I see that FourQ is significantly faster when looking at different 
64-bit processors (check out Table 5 in the FourQ paper, 
http://eprint.iacr.org/2015/565.pdf). If one looks across different CPUs 
(not only one CPU in particular), FourQ is also shown to be up to 5 times 
faster than the NIST curve P-256 and close to 3 times faster than Cu
Curve25519. This is remarkable.   

I would like to see results on ARM though, but results so far are very 

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