On the countermeasures to the higher genus torsion point attacks on SIDH

Isogeny-based cryptography is an attractive branch of post-quantum cryptography because Isogeny-based schemes have very compact keys. Its flagship schemes are SIDH/SIKE, CSIDH and its derivatives, SQI-Sign, ... In SIDH/SIKE, some non trivial torsion point images through the secret isogeny are revealed.

In July/August 2022, SIDH and SIKE were broken in polynomial time by higher genus attacks that exploit the  torsion point information revealed in SIDH/SIKE (Castryck-Decru : eprint 2022/975, Maino-Martindale : eprint 2022/1026, and Robert : eprint 2022/1038). Two countermeasures to theses attacks have been suggested so far: one by Fouotsa (eprint 2022/1054) and another one by Moriya (eprint 2022/1019).

In this talk, we will briefly recall the principle of the attacks, describe the two countermeasures and present some advanced security analysis of these countermeasures.