## Twelfth Algorithmic Number Theory Symposium, Kaiserslautern, 2016

The Algorithmic Number Theory Symposium (ANTS-XII) took place at the Technical University of Kaiserslautern from August 29 to September 2, 2016.

Apart from the excellent invited lectures, the most memorable event of the conference was the late-night walk through the forest, illuminated by hand-held flaming torches, from the conference dinner at Bremerhof.

The Selfridge Prize was presented to J. Steffen Müller (Oldenburg) for the paper “Computing canonical heights on elliptic curves in quasi-linear time” by J. Steffen Müller and Michael Stoll.

The published papers are available in the LMS Journal of Computational Mathematics. Sadly this will be the final year that the proceedings appear in this journal, since the journal is being closed down.

There were relatively few papers with major relevance to ECC, but the following papers may be of some interest to readers of this blog:

• Chris Peikert “Finding Short Generators of Ideals, and Implications for Cryptography“. This was an overview of the work presented in his paper with Cramer, Ducas and Regev.
• Gary McGuire, Henriette Heer and Oisin Robinson “JKL-ECM: An implementation of ECM using Hessian curves”. The paper was about choosing elliptic curves in Hessian form with large torsion groups for the elliptic curve factoring method.
• Jung Hee Cheon, Jinhyuck Jeong and Changmin Lee “An algorithm for NTRU problems and cryptanalysis of the GGH multilinear map without an encoding of zero”. This paper is another nail in the coffin of multilinear maps.
• Francois Morain, Charlotte Scribot and Benjamin Smith “Computing cardinalities of $Q$-curve reductions over finite fields”. This was about a variant of the SEA method that is suitable for counting points on special curves with an endomorphism of a special type. Such curves are suitable for fast implementations of ECC, and so the method in this paper helps to speed up parameter generation when using such curves.
• Luca Defeo, Jerome Plût, Eric Schost and Cyril Hugounenq “Explicit isogenies in quadratic time in any characteristic”. The paper is about a Couveignes-type method for computing an explicit isogeny between two curves. This is a useful ingredient in point counting algorithms. The new method is appropriate when working in characteristic $p$ that is neither “large” nor “very small”.
• Jean-François Biasse, Claus Fieker and Michael Jacobson “Fast heuristic algorithms for computing relations in the class group of a quadratic order with applications to isogeny evaluation”. This paper is about the problem of “smoothing” an isogeny by reducing the ideal corresponding to it in the ideal class group of the order. It introduces some nice techniques that had not been used in this context previously.

The rump session contained a number of jokes about Australia and New Zealand. Aurore Guillevic mentioned some recent DLP records (mostly already mentioned on this blog). Rump session slides will be available eventually here.

The 2018 edition of the ANTS conference is expected to take place in Madison, Wisconsin.

— Steven Galbraith