[curves] Sandy2x

[Michael Hamburg]

Interestingly, the new Intel optimization manual says that Skylake can issue (V)PMULQDQ twice every cycle instead of once, presumably even for 4-way (256-bit) multiplications.  So “Sandy2x” and other designs with similar strategies (including for Goldilocks) should be competitive on Skylake as well.

Cheers,
— Mike

> On Sep 29, 2015, at 10:29 PM, Trevor Perrin <trevp at trevp.net> wrote:
> 
> Tung Chou's "Sandy2x" code for 25519 on Sandy Bridge and Ivy Bridge is
> around 10-20% faster than other implementations:
> 
> https://eprint.iacr.org/2015/943
> 
> Speedup is attributed to using the 2-way 32x32->64 vectorized
> multiplier (vpmuludq) instead of the 64x64->128 serialized multiplier.
> 
> The paper doesn't say whether this strategy also pays off on Haswell
> (which seems to be lagging in 25519 performance?):
> 
> https://docs.google.com/spreadsheets/d/1SO3NGX-EgIZ1slw9uExb5FoeFy5TVkuA2lEutP6roYI/edit#gid=0
> 
> 
> Trevor
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