Leakage Resilient Fully Homomorphic Encryption

We construct the first leakage resilient variants of fully homomorphic encryption (FHE) schemes. Our leakage model is bounded adaptive leakage resilience. We first construct a leakageresilient leveled FHE scheme, meaning the scheme is both leakage resilient and homomorphic for all circuits of depth less than some pre-established maximum set at the time of key generation. We do so by applying ideas from recent works analyzing the leakage resilience of public key encryption schemes based on the decision learning with errors (DLWE ) assumption to the Gentry, Sahai and Waters ([17]) leveled FHE scheme. We then move beyond simply leveled FHE, removing the need for an a priori maximum circuit depth, by presenting a novel way to combine schemes. We show that by combining leakage resilient leveled FHE with multi-key FHE, it is possible to create a leakage resilient scheme capable of homomorphically evaluating circuits of arbitrary depth, with a bounded number of distinct input ciphertexts. ∗[email protected] †[email protected] (Most of the work was completed while author was a graduate student at Brown University.)