The Fujisaki-Okamoto transform is a popular solution to design post-quantum public key encryption schemes, or key encapsulation mechanisms. In order to ensure security against chosen-ciphertext attacks, it checks the validity of ciphertexts by re-encrypting decrypted messages. This operation in turn leads to severe side-channel weaknesses, because the re-encrypted messages can be made key-dependent. Hence, distinguishing them thanks to leakage is sufficient to extract (long-term) secret key information. As a result, recent works suggested to ensure the validity of ciphertexts by other means than re-encryption. For now, the main candidate for this purpose, integrated in the Polka encryption scheme (PKC 2023) and analyzed more generically by Hövelmanns et al. (EUROCRYPT 2025), is to use continuous norm checks through the decryption process. In this paper, we evaluate the extent to which replacing the FO-transform by such norm checks helps resistance against leakage. Negatively, we exhibit new attack vectors that were not anticipated in previous (heuristic) analyzes. Positively, we observe that the removal of the FO-transform nevertheless reduces the attack surface and we identify possible tracks to further minimize it. Overall, our results therefore shed light on the challenge of designing post-quantum public-key encryption schemes, or key encapsulation mechanisms, that can be efficiently protected against side-channel attacks. We hope they can inform theory about leakage sources that could be better taken over by design, to develop new schemes allowing a scarcer use of implementation-level countermeasures.
Pay et al. (Mon,) studied this question.