News Archive 5

Michael Cheng kindly sent me a modified version of PBC 0.4.7 which can be compiled using Microsoft Visual C++. I have made it available on the download page.

I have not tried it myself as I don’t have this particular compiler handy.

I patched a memory leak reported by Michael Cheng. I forgot to free a temporary variable when I added Lucas sequences (which speed up D and G pairings).

Applied patch by Joe Cooley that addresses configure.ac issues and fixes a bug in example/zss.c.

A fairly lowlevel bug had somehow escaped my attention for quite some time. Comparing zero elements previously returned the wrong result, due to a simple logic bug in montfp.c.

Simple final powering optimizations were applied to D and G pairings.

Fortunately for me, Paul Miller tests each version extensively soon after release. In version 0.4.5 he found a bug that I had overlooked for one of the usual reasons: "the modification is so trivial that it can’t possibly cause problems!". Luckily the bug wasn’t difficult to fix.

I finally implemented what I call type G pairings, which are curves of embedding degree 10 found by David Freeman.

They’re a bit slow at the moment, but I hope to speed them up soon. Interestingly, Katherine Stange’s elliptic net algorithm for computing a type G pairing is about the same speed as Miller’s algorithm, but this is without using (signed) sliding windows for the latter.