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

Linru Zhang, Xiangning Wang, Yuechen Chen, Siu-Ming Yiu

Abstract: 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 $l=\frac{l'}{n}$ from our IP-HPS scheme.