Tutte Colloquium - David Jao

Title: The Problem Landscape of SIDH

Abstract:

The Supersingular Isogeny Diffie-Hellman protocol (SIDH) has recently been the subject of increased attention in the cryptography community. Conjecturally quantum-resistant, SIDH has the feature that it shares the same data flow as ordinary Diffie-Hellman: two parties exchange a pair of public keys, each generated from a private key, and combine them to form a shared secret. To create a potentially quantum-resistant scheme, SIDH depends on a new family of computational assumptions involving isogenies between supersingular elliptic curves which replace both the discrete logarithm problem and the computational and decisional Diffie-Hellman problems. As in the case of ordinary Diffie-Hellman, one is interested in knowing if these problems are related. In fact, more is true: there is a rich network of reductions between the isogeny problems securing the private keys of the participants in the SIDH protocol, the computational and decisional SIDH problems, and the problem of validating SIDH public keys. In this talk we explain these relationships, in the hopes of providing a clearer picture of the SIDH problem landscape to the community at large.