Beyond the SIDH Countermeasures

During summer 2022, a series of three cryptanalysis papers lead to a
polynomial time attack on SIKE, which was in the fourth round of the NIST
standardisation process. In a recent work, we explored countermeasures
avenue to the SIDH attacks, M-SIDH and MD-SIDH.
These countermeasures, despite being slow and less compact (when compared
to SIDH and other post-quantum schemes), come with new insights that may be
of independent interest. In this talk, we will discuss an on-going work in
which we use M-SIDH together with the SIDH attacks to design a trapdoor one
way function. This trapdoor one way function can be leveraged to obtain a
public key encryption scheme, most importantly, it can be used to design an
Identity Based Encryption scheme. The main drawback is that the design is
purely theoretical at the moment, since inverting the one way function
requires computing isogenies in higher dimension of prime degree up to
5000 or even higher.