In CRYPTO 2010,Wee proposed the notion of “extractable hash proof systems” (XHPS), and its richer version, “all-but-one XHPS” (ABO-XHPS), and showed that chosen ciphertext secure (CCA secure) key encapsulation mechanisms (KEM) can be constructed from them. This elegantly explains several recently proposed practical KEMs constructed based on the “all-but-one” simulation paradigm in a unified framework. Somewhat frustratingly, however, there still exist popular KEMs whose construction and security proofs are not captured by this framework. In this paper, we revisit the framework of the ABOXHPS- based KEM. Firstly, we show that to prove CCA security of the ABOXHPS- based KEM, some requirements can be relaxed. This relaxation widens the applicability of the original framework, and explains why many known practical KEMs can be proved CCA secure. Moreover, we introduce new properties for ABO-XHPS, and show how one of the properties leads to KEMs that achieve “constrained” CCA security, which is a useful security notion of KEMs for obtaining CCA secure public key encryption via hybrid encryption. Thirdly, we investigate the relationships among computational properties that we introduce in this paper, and derive a useful theorem that enables us to understand the structure of KEMs of a certain type in a modular manner. Finally, we show that the ABO-XHPS-based KEM can be extended to efficient multi-recipient KEMs. Our results significantly extend the framework for constructing a KEM from ABOXHPS, enables us to capture and explain more existing practical CCA secure schemes (most notably those based on the decisional Diffie-Hellman assumption) in the framework, and leads to a number of new instantiations of (singleand multi-recipient) KEMs.
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