CIAO Cryptography Isogenies and Abelian varieties Overwhelming

The aim of the CIAO 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.

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.

Tasks

• 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.
• Security of isogeny based cryptosystems: security reduction and security parameters, point counting and endomorphism rings computation, security in the wild.

Results