(2026-06) Adaptive attacks on FESTA variants with masked-degree isogenies
2026-06-11
FESTA is an isogeny-based trapdoor function proposed as a high-performance alternative in isogeny-based cryptography. Its core design principles have inspired a number of related constructions, collectively referred to as FESTA variants.
The MOXZ attack is an adaptive attack that exploits malicious ciphertexts together with access to a checking oracle, aiming to compromise FESTA and its variants. This attack applies to FESTA variants whose secret keys are derived from isogenies of known degree; however, it does not extend to variants employing masked-degree isogenies.
In this work, we present a novel adaptive attack that generalizes the MOXZ attack. Our attack successfully targets several FESTA variants even when their secret keys are isogenies of masked degree. We also identify POKE-4D as an exception for which our attack does not appear to be applicable.