Paper 2021/196

QCCA-Secure Generic Key Encapsulation Mechanism with Tighter Security in the Quantum Random Oracle Model

Xu Liu and Mingqiang Wang

Abstract

Xagawa and Yamakawa (PQCrypto 2019) proved the transformation SXY can tightly turn DS secure PKEs into IND-qCCA secure KEMs in the quantum random oracle model (QROM). But transformations such as KC, TPunc that turn PKEs with standard security (OW-CPA or IND-CPA) into DS secure PKEs still suffer from quadratic security loss in the QROM. In this paper, we give a tighter security reduction for the transformation KC that turns OW-CPA secure deterministic PKEs into modified DS secure PKEs in the QROM. We use the Measure-Rewind-Measure One-Way to Hiding Lemma recently introduced by Kuchta et al. (EUROCRYPT 2020) to avoid the square-root advantage loss. Moreover, we extend it to the case that underlying PKEs are not perfectly correct. Combining with other transformations, we finally obtain a generic KEM from any IND-CPA secure PKE. Our security reduction has roughly the same tightness as the result of Kuchta et al. without any other assumptions and we achieve the stronger IND-qCCA security. We also give a similar result for another KEM transformation achieving the same security notion from any OW-CPA secure deterministic PKE.