10:00am - 12:00pmIsogenies in Cryptography
Chair(s): Tanja Lange (Eindhoven University of Technology, Netherlands, The), Chloe Martindale (Eindhoven University of Technology, Netherlands, The), Lorenz Panny (Eindhoven University of Technology, Netherlands, The)
The isogeny graph of elliptic curves over finite fields has long been a subject of study in algebraic geometry and number theory. During the past 10 years several authors have shown multiple applications in cryptology. One interesting feature is that systems built on isogenies seem to resist attacks by quantum computers, making them the most recent family of cryptosystems studied in post-quantum cryptography.
This mini-symposium brings together presentations on cryptosystems built on top of isogenies, their use in applications, and different approaches to the cryptanalysis, including quantum cryptanalysis.
(25 minutes for each presentation, including questions, followed by a 5-minute break; in case of x<4 talks, the first x slots are used unless indicated otherwise)
Post-quantum signature schemes and more from supersingular isogenies
Ward Beullens
KU Leuven
Algorithmic aspects of cryptographic invariant maps from isogenies
Florian Hess
University of Oldenburg
We discuss some algorithmic aspects of candidate cryptographic invariant maps from isogenies, in particular those presented by Boneh, Glass, Krashen, Lauter, Sharif, Silverberg, Tibouchi and Zhandry in their paper on multiparty non-interactive key exchange.
Verifiable Delay Functions from Isogenies and Pairings
Luca De Feo
Ecole Polytechnique
We present a (non-post-quantum) framework for proving statements on isogeny walks in supersingular graphs. The framework can be seen as a combination of the BLS signature scheme with the supersingular isogeny graphs popularized by the key exchange protocols SIDH and CSIDH.
An instatiation of the framework for signature and interactive identification was already suggested in a 2010 patent owned by Microsoft; however the most interesting new application we obtain is a Verifiable Delay Function, whereby an isogeny walk of "great" length between two elliptic curves is made public, and the framework produces a succinct and easily verifiable proof of isogeny evaluation (similar to a proof of work).
This is joint work with S. Masson, C. Petit and A. Sanso.
Cryptographic goals beyond key exchange and signatures
Jeff Burdges
GNUnet
We shall discuss some cryptographic problems beyond key exchange and signatures for which practical post-quantum protocols would be much appreciated. These come in two flavours depending upon motivation, protocols desired for a more ethical applications that protect metadata, and protocols used in modern consensus algorithms.