Paper 2025/1519

Does the UC-Security Notion for PAKE Imply Game-Based Security?

Abstract

A Password-Authenticated Key Exchange (PAKE) protocol allows two parties to jointly establish a cryptographically strong key, in the setting where the only information shared in advance is a low-entropy "password". The two standard security definitions for PAKE are the game-based one by Bellare, Pointcheval and Rogaway (BPR-security, EUROCRYPT 2000) and the Universally Composable (UC) one by Canetti et al. (EUROCRYPT 2005). It is well-known that UC-security implies BPR-security; however, there are a large number of variants of both definitions, and the relation between them is not entirely clear. In this work, we thoroughly study a variant of BPR-security by Katz, Ostrovsky and Yung (KOY-security, JACM 2009): 1. We show, via a counterexample, that UC-security does \emph{not} imply KOY-security; 2. We then prove that a variant of UC-security, called implicit-only UC-security (Dupont et al., EUROCRYPT 2018), implies KOY-security. Interestingly, we make the observation that KOY- and implicit-only UC-security essentially strengthen their standard counterparts in the same manner. We also present detailed explanations of all four security notions.