1. The ECC 2019 conference took place in Bochum in December. Slides from some of the talks (including the rump session) are available here.
2. ASIACRYPT 2019 took place in Kobe, Japan in December. It was a very well organised conference.
The Best Paper award went to Thomas Debris-Alazard, Nicolas Sendrier and Jean-Pierre Tillich for the paper “Wave: A New Family of Trapdoor One-Way Preimage Sampleable Functions Based on Codes”. This paper gives a post-quantum signature scheme (of the “hash and sign” type) from error-correcting codes. Ward Beullens has written a blog post on this paper in the COSIC blog.
There were two conference sessions on isogenies, featuring these papers:
- Ward Beullens, Thorsten Kleinjung and Fréderik Vercauteren “CSI-FiSh: Efficient Isogeny based Signatures through Class Group Computations”. This paper introduces an isogeny signature scheme of the type originally proposed by Stolbunov (also discussed by De Feo and me in the appendix of our “SeaSign” paper). The key step is a large class group computation for one specific parameter (ie one prime).
- Luca De Feo, Simon Masson, Christophe Petit and Antonio Sanso “Verifiable Delay Functions from Supersingular Isogenies and Pairings”. Computing a sequence of isogenies is a natural “delay function” (in the sense that the computation cannot be sped up using parallel computing). The paper shows how to get a delay function whose result can be checked efficiently, by using pairings. Carl Bootland has blogged about this talk.
- Xiu Xu, Haiyang Xue, Kunpeng Wang, Man Ho Au and Song Tian “Strongly Secure Authenticated Key Exchange from Supersingular Isogenies”. The paper gives an authenticated key exchange scheme based on isogenies, with very strong security properties in the CK+ model (and the random oracle model).
- Michael Naehrig and Joost Renes “Dual Isogenies and Their Application to Public-key Compression for Isogeny-based Cryptography”. The paper has some nice ideas about compression.
- Suhri Kim, Kisoon Yoon, Young-Ho Park and Seokhie Hong “Optimized Method for Computing Odd-Degree Isogenies on Edwards Curves”. The paper introduces some nice isogeny formulas, that are similar to formulas already known for Montgomery curves.
- Salim Ali Altuğ and Yilei Chen “Hard Isogeny Problems over RSA Moduli and Groups with Infeasible Inversion”. The paper has fascinating ideas about constructing something like a group with infeasible inversion.
The invited talks were both about blockchain, so I don’t mention them here.
You can read about several other papers on the COSIC blog. Recordings were made of the talks, and will go on the iacr youtube channel eventually.
The rump session, hosted by Mehdi Tibouchi, featured a Samurai warrior to make sure speakers kept to time.
3. Recall the Multiparty Non-Interactive Key Exchange From Isogenies on Elliptic Curves (mentioned in this blog post. It was relying on an invariant of products of elliptic curves. Recently Eric Rains, Karl Rubin, Travis Scholl, Shahed Sharif and Alice Silverberg have posted on arxiv the paper “Algebraic maps constant on isomorphism classes of unpolarized abelian varieties are constant”, which gives additional evidence that a useful invariant doesn’t exist.
4. Advance notice for ECC 2020 in Taiwan! You will find information here.
— Steven Galbraith