Updatable Lossy Trapdoor Functions Under Consecutive Leakage

摘要

Lossy trapdoor functions (LTFs), introduced by Peikert and Waters (STOC'08), have already been found to be a very useful tool in constructing complex cryptographic primitives in a black-box manner, such as one-way trapdoor functions, deterministic public-key encryption, CCA-secure public-key encryption, etc. Due to the existence of the side-channel attack, the leakage of trapdoor information in lossy trapdoor function systems can lead to the impossibility of provable security. Recently, Zhang et al. introduced a model of consecutive and continual leakage-resilient and updatable lossy trapdoor functions (ULTFs) and provided a concrete construction to achieve the security. Meanwhile, they proposed a consecutive and continual leakage-resilient public-key encryption scheme. However, in this paper, we demonstrate that the correctness of injective function can not be satisfied. Furthermore, the attacker can easily distinguish the evaluation key of ULTFs generated by the challenger according to the security model. Finally, we show two new constructions based on the continual leakage-resilient public-key encryption scheme of Brakerski et al. (FOCS 2010) and demonstrate the security of our scheme in the consecutive and continual leakage model.