International Association for Cryptologic Research

International Association
for Cryptologic Research


Kathrin Hövelmanns


Generic Authenticated Key Exchange in the Quantum Random Oracle Model 📺
We propose $$mathsf {FO_mathsf {AKE}}$$ , a generic construction of two-message authenticated key exchange (AKE) from any passively secure public key encryption (PKE) in the quantum random oracle model (QROM). Whereas previous AKE constructions relied on a Diffie-Hellman key exchange or required the underlying PKE scheme to be perfectly correct, our transformation allows arbitrary PKE schemes with non-perfect correctness. Dealing with imperfect schemes is one of the major difficulties in a setting involving active attacks. Our direct construction, when applied to schemes such as the submissions to the recent NIST post-quantum competition, is more natural than previous AKE transformations. Furthermore, we avoid the use of (quantum-secure) digital signature schemes which are considerably less efficient than their PKE counterparts. As a consequence, we can instantiate our AKE transformation with any of the submissions to the recent NIST competition, e.g., ones based on codes and lattices. $$mathsf {FO_mathsf {AKE}}$$ can be seen as a generalisation of the well known Fujisaki-Okamoto transformation (for building actively secure PKE from passively secure PKE) to the AKE setting. As a helper result, we also provide a security proof for the Fujisaki-Okamoto transformation in the QROM for PKE with non-perfect correctness which is tighter and tolerates a larger correctness error than previous proofs.
Tighter Proofs of CCA Security in the Quantum Random Oracle Model
We revisit the construction of IND-CCA secure key encapsulation mechanisms (KEM) from public-key encryption schemes (PKE). We give new, tighter security reductions for several constructions. Our main result is an improved reduction for the security of the $$U^{\not \bot }$$ -transform of Hofheinz, Hövelmanns, and Kiltz (TCC’17) which turns OW-CPA secure deterministic PKEs into IND-CCA secure KEMs. This result is enabled by a new one-way to hiding (O2H) lemma which gives a tighter bound than previous O2H lemmas in certain settings and might be of independent interest. We extend this result also to the case of PKEs with non-zero decryption failure probability and non-deterministic PKEs. However, we assume that the derandomized PKE is injective with overwhelming probability.In addition, we analyze the impact of different variations of the $$U^{\not \bot }$$ -transform discussed in the literature on the security of the final scheme. We consider the difference between explicit ( $$U^{\bot }$$ ) and implicit ( $$U^{\not \bot }$$ ) rejection, proving that security of the former implies security of the latter. We show that the opposite direction holds if the scheme with explicit rejection also uses key confirmation. Finally, we prove that (at least from a theoretic point of view) security is independent of whether the session keys are derived from message and ciphertext ( $$U^{\not \bot }$$ ) or just from the message ( $$U^{\not \bot }_m$$ ).