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Old 2017-08-27, 22:12   #1
CRGreathouse's Avatar
Aug 2006

10111001011002 Posts
Default JKL-ECM: ECM using Hessian curves

Code and slides were recently posted here:

Any thoughts? It's not competitive -- "we do not outperform GMP-ECM in terms of speed. (Although it is close, and the gap narrows with larger inputs)." -- but that's without assembly or apparently that much optimization so it does look interesting. It describes itself as a sort of moral successor to EECM-MPFQ (ECM using Edwards Curves).
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Old 2017-09-06, 15:39   #2
chris2be8's Avatar
Sep 2009

5·383 Posts

Two thoughts:

The PDF has stats on pages 21 and 22 for finding primes that are 1 mod 3. Does that mean it can't find primes that are 2 mod 3?

The README says in part
If you are factoring numbers of the form

a^(2*x) + b^(2*y)

then try JKL-ECM with Edwards curves. The group order #E(F_p) will have a
prescribed factor of at least 16, and possibly 32.
That would apply to X^Y+Y^X where X and Y are both even.

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