Leakage-Resilient Inner-Product Functional Encryption in the Bounded-Retrieval Model

We propose a leakage-resilient inner-product functional encryption scheme (IPFE) in the bounded-retrieval model (BRM). This is the first leakage-resilient functional encryption scheme in the BRM. In our leakage model, an adversary is allowed to obtain at most l-bit knowledge from each secret key. And our scheme can flexibly tolerate arbitrarily leakage bound l, by only increasing the size of secret keys, while keeping all other parts small and independent of l. Technically, we develop a new notion: Inner-product hash proof system (IP-HPS). IP-HPS is a variant of traditional hash proof systems. Its output of decapsulation is an inner-product value, instead of the encapsulated key. We propose an IP-HPS scheme under DDH-assumption. Then we show how to make an IP-HPS scheme to tolerate l′-bit leakage, and we can achieve arbitrary large l′ by only increasing the size of secret keys. Finally, we show how to build a leakage-resilient IPFE in the BRM with leakage bound l = l ′ n from our IP-HPS scheme.