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In known security reductions for the Fujisaki-Okamoto transformation,decryption failures are handled via a reduction solving the rather unnaturaltask of finding failing plaintexts given the private key, resulting in a Groversearch bound. Moreover, they require an implicit rejection mechanism forinvalid ciphertexts to achieve a reasonable security bound in the QROM. Wepresent a reduction that has neither of these deficiencies: We introduce twosecurity games related to finding decryption failures, one capturing thecomputationally hard task of using the public key to find a decryption failure,and one capturing the statistically hard task of searching the random oraclefor key-independent failures like, e.g., large randomness. As a result, oursecurity bounds in the QROM are tighter than previous ones with respect to thegeneric random oracle search attacks: The attacker can only partially computethe search predicate, namely for said key-independent failures. In addition,our entire reduction works for the explicit-reject variant of thetransformation and improves significantly over all of its known reductions.Besides being the more natural variant of the transformation, security of theexplicit reject mechanism is also relevant for side channel attack resilienceof the implicit-rejection variant. Along the way, we prove several technicalresults characterizing preimage extraction and certain search tasks in the QROMthat might be of independent interest.

Failing gracefully: Decryption failures and the Fujisaki-Okamoto transform