Paper 2017/1005

Tightly-Secure Key-Encapsulation Mechanism in the Quantum Random Oracle Model

Tsunekazu Saito, Keita Xagawa, and Takashi Yamakawa

Abstract

Key-encapsulation mechanisms secure against chosen ciphertext attacks (IND-CCA-secure KEMs) in the quantum random oracle model have been proposed by Boneh, Dagdelen, Fischlin, Lehmann, Schafner, and Zhandry (CRYPTO 2012), Targhi and Unruh (TCC 2016-B), and Hofheinz, Hövelmanns, and Kiltz (TCC 2017). However, all are non-tight and, in particular, security levels of the schemes obtained by these constructions are less than half of original security levels of their building blocks. In this paper, we give a conversion that tightly converts a weakly secure public-key encryption scheme into an IND-CCA-secure KEM in the quantum random oracle model. More precisely, we define a new security notion for deterministic public key encryption (DPKE) called the disjoint simulatability, and we propose a way to convert a disjoint simulatable DPKE scheme into an IND-CCA-secure key-encapsulation mechanism scheme without incurring a significant security degradation. In addition, we give DPKE schemes whose disjoint simulatability is tightly reduced to post-quantum assumptions. As a result, we obtain IND-CCA-secure KEMs tightly reduced to various post-quantum assumptions in the quantum random oracle model.

Note: * add a new conversion KC that converts a perfectly-correct OW-CPA-secure DPKE scheme into a perfectly-correct disjoint-simulatable DPKE scheme with a quadratic loss in the QROM. In the ROM, the security proof is tight. * update implementation results of NTRU-HRSS-SXY with AVX2. * 2021: Correct lemmas and adjust constants.