Leakage-Resilient Functional Encryption via Pair Encodings

Leakage-resilient cryptography is proposed to address physical attacks on real world crypto-systems. Dual system encryption methodology is developed to guide design and analysis of various functional encryption schemes (FEs) with adaptive security. Observing the compatibility of dual system methodology and leakage-resilience, Lewko et al. present constructions of a number of strong leakage-resilient functional encryptions. In particular, they present fully secure identity-based encryption (IBE), hierarchical IBE (HIBE) and attribute-based encryption (ABE) satisfying the continual memory leakage (CML) model, one of the strongest models that allows continuous leakage on both user and master secret keys. Inspired by the recent work from Attrapadung on pair encodings which greatly simplifies the design and analysis of FE, we propose a generic framework for constructing fully secure FEs in the CML model (LR-FEs). Specifically, our framework "compiles" predicate encodings into fully secure LR-FEs in a two-step process. Firstly, we propose a generic transformation of pair encoding schemes into their leakage-resilient forms. Next, we present another conversion that turns leakage-resilient pair encodings into fully secure LR-FEs. Our framework is highly compatible with Attrapadung's, meaning that it is applicable to many existing pair encoding schemes. The contribution of this paper is threefold. Firstly, our framework simplifies the design and analysis of LR-FEs into the design and analysis of predicate encodings. Secondly, our framework allows us to improve the security of some existing LR-FEs, such as LR-IBE with a tighter reduction. Thirdly, we discover new adaptively secure LR-FEs, including FE for regular languages, ABE for large universe and ABE with short ciphertext.