Adaptively Secure Puncturable Pseudorandom Functions via Puncturable Identity-Based KEMs

Abstract

In this paper, we are interested in constructing Puncturable Pseudorandom Functions (PPRFs), a special class of constrained PRFs. While selectively secure PPRFs can be constructed from GGM tree-based PRFs, the adaptive counterpart is tricky to deal with. Inspired by previous works, we investigate on the possibility of directly obtaining adaptively-secure PPRF from Puncturable Identity-based Key Encapsulation Mechanism (PIB-KEM). Our contributions can be summarized as follows: (i) we show that one could derive adaptively-secure PPRFs very naturally originating from PIB-KEM satisfying two necessary conditions. (ii) we define t-puncturable IB-KEM (t-PIBKEM) and show its existence by an efficient conversion basing on Hierarchical IB-KEM (HIB-KEM). Furthermore, we demonstrate its application to constructing t-puncturable PRFs, a generalized notion of PPRFs.