Updatable All-But-One Dual Projective Hashing and Its Applications

Dual projective hashing is an extension of Cramer-Shoup projective hashing, which implies lossy trapdoor functions (LTDFs) and deterministic PKE schemes secure with respect to hard-to-invert auxiliary input. In this paper, we introduce the notion of updatable all-but-one dual projective hashing (UDPH) based on the all-but-one variant of dual projective hashing, which allows us to investigate the continuous leakage of invisible key update in the same context. In particular, we give a general construction of leakage-resilient all-but-one LTDFs via UDPH, which yields high efficiency compared with existed direct leakage-resilient all-but-one LTDFs constructions based on MDDH and SXDH. Concretely, our generic framework can be instantiated with k-LIN, DCR, QR and LWE assumptions in the standard model.we present a modular framework for leakage-resilient deterministic PKEs with hard-to-invert auxiliary input, which is proven secure under the introduced continuous-leakage-resilient strong privacy indistinguishability-based security model of invisible key update. Compared with the known MDDH/SXDH-based schemes, our constructions can be instantiated with more widely-accepted assumptions including k-LIN, DCR, QR and LWE.