Leakage-resilient functional encryption from simple assumptions

Abstract

I study several problems around leakage-resilient functional encryption schemes from simple assumptions. Roughly speaking, functional encryption was intro- duced to handle the “decryption reveals all-or-nothing” problems in tradi- tional public key encryption, which means that the decryption algorithm of a functional encryption scheme only reveals and outputs a function value of the plaintext. Also, leakage-resilient cryptography was proposed to o↵er formal security guarantees when the adversary can learn some knowledge from the secret values of a cryptographic system. While there are many works on leakage-resilient PKE, IBE and ABE, designing leakage-resilient functional encryption schemes is not easy. I first focus on leakage-resilient inner-product functional encryption (IPFE), and propose a leakage-resilient IPFE scheme in the bounded-retrieval model (BRM) from hash proof system. Then, I consider an important extension of IPFE by enhancing IPFE with identity-based access control such that only users with a pre-defined identity are allowed to do the decryption, and call it identity- based inner-product functional encryption (IBIPFE). I propose an adaptive- secure IBIPFE scheme and extend it into a leakage-resilient IBIPFE scheme in the BRM. The next step after considering inner-product functions (can be viewed as linear functions) is to move to quadratic functions and even higher degree polynomials. I propose a generic adaptive-secure FE scheme for quadratic functions, and then show a transformation method which can obtain a FE scheme for degree-(m + 1) polynomials from a FE scheme for degree-m polynomials.