On the Relation Between SIM and IND-RoR Security Models for PAKEs

Password-based Authenticated Key-Exchange (PAKE) protocols allow users, who need only to share a password, to compute a high-entropy shared session key despite passwords being taken from a dictionary.
Security models for PAKE protocols aim to capture the desired security properties that such protocols must satisfy when executed in the presence of an active adversary.
They are usually classified into i) indistinguishability-based (IND-based) or ii) simulation-based (SIM-based).
The relation between these two security notions is unclear and mentioned as a gap in the literature.
In this work, we prove that SIM-BMP security from Boyko et al.~(EUROCRYPT 2000) implies IND-RoR security from Abdalla et al.~(PKC 2005) and that IND-RoR security implies a slightly modified version of SIM-BMP security. We also investigate whether IND-RoR security implies (unmodified) SIM-BMP security.