International Association
for Cryptologic Research

Isogeny-based cryptosystems continue to show promise in post-quantum cryptography. In recent years, numerous constructions have been proposed, one of which is POKÉ, a compact and efficient public-key exchange system that uses higher-dimensional isogenies. This paper leverages a well-known adaptive attack on SIDH by Galbrath, Petit, Shani and Ti, and demonstrates a similar attack on POKÉ, when given a key exchange oracle with the same assumptions as those posed by Galbraith et al. This attack relies on the user to employ long-term static keys which is against the intent of the designers of POKÉ. Indeed, this attack provides further evidence that POKÉ should not be used with a long-term static key.