Cryptography, Isogenies and Abelian varieties Overwhelming – CIAO

- Computational aspect of isogenies: arithmetic over finite fields, efficient isogenies, models for elliptic curves, implementation;
- Cryptographic protocols related to isogenies: key exchange and encryption, signatures and authentication, verifiable delayed functions, other cryptographic protocols;
- Higher dimensional isogenies: isogenies for abelian varieties, moduli spaces, isogeny graphs, higher dimensional supersingular isogeny Diffie-Hellman.

haltools.inria.fr/Public/afficheRequetePubli.php

Applications of this project is to improve the security of communications
in a context where the currently used cryptosystems are vulnerable to
quantum computers. Beyond post-quantum cryptography, isogeny based
cryptosystems also allow to construct new interesting cryptographic
tools, like Verifiable Delay Functions, used in block chains.

22 papers and 1 PhD.

The aim of the CIA project is to study the security and improve the
efficiency of the SIDH (supersingular isogenies Diffie Helmann) protocol,
which is one of the post-quantum cryptographic project submitted to NIST, which passed the first round selection.

The project include all aspects of SIDH, from theoretical ones (computing
the endomorphism ring of supersingular elliptic curves, generalisation of
SIDH to abelian surfaces) to more practical aspects like arithmetic
efficiency and fast implementations, and also extending SIDH to more
protocols than just key exchange.

Applications of this project is to improve the security of communications
in a context where the currently used cryptosystems are vulnerable to
quantum computers. Beyond post-quantum cryptography, isogeny based cryptosystems also allow to construct new interesting cryptographic tools, like Verifiable Delay Functions, used in block chains.