Internal, Fast "from scratch" Re-build of Paillier

[iamtrask]

Internal, Fast "from scratch" Re-build of Paillier

[iamtrask]

Rumor has it that the folks who built python-paillier are about to release a CUDA version

[iamtrask]

@samsontmr this one could be split into sub-tasks too based on the underlying architecture (C, Blas, and CUDA tickets)

[mortendahl]

just a few inputs:

• the existing phe Python lib uses GMP underneath (when available:
  https://github.com/n1analytics/python-paillier/blob/master/phe/util.py#L50) so the performance is already quite good

• I am not too optimistic about how much boost we'd get from using GPUs; my best guess is that a gain will most likely only show when dealing with several ciphertexts in parallel (to eg encrypt vectors)

• a (Python) lib where the encoding is decoupled from encryption would indeed be useful; the overflow detection built in phe can sometimes get a bit in the way

based on this it would seem reasonable to me to go with phe for now, and give this re-implementation task a somewhat low priority

[iamtrask]

@mortendahl given your feedback I'm inclined to agree.

[iamtrask]

assigned it to Lithium milestone (our latest one yet laid out), and it'll be a low priority there as well :)