Paper 2020/064

Dual System in Lattice: Fully Secure ABE from LWE Assumption

Geng Wang, Ming Wan, Zhen Liu, and Dawu Gu

Abstract

Dual system encryption is an important method used in pairing-based cryptography for constructing fully secure IBE, ABE and FE schemes. A long time open question is that, whether there is an analogue of dual system method in lattice, which can be used to prove the full security of lattice-based ABE or FE schemes. We solve this problem in this paper. We do this by introducing a new primitive called approximate inner product encryption (aIPE), which is the approximate version of the well known inner product encryption. We show that a fully secure ABE supporting CNF as its access policy can be constructed from a selectively secure aIPE and the LWE assumption. We also point out that the functionality of aIPE is included in FE for arbitrary circuits, which can be constructed from LWE assumption, hence the full security of our scheme can be totally based on the hardness of LWE.