Inner product encryption from Middle-Product Learning With Errors

Inner product encryption (IPE) is an important research area of functional cryptosystems. It can improve user access control and fine-grained query, and has a wide range of applications in emerging fields such as cloud computing. Lattice-based inner product encryption has the advantages of resistance to quantum algorithm attacks and relatively simple encryption algorithms, and thus has good application prospects. Currently, the provable security of lattice-based public key encryption schemes is mostly based on the learning with errors (LWE) and polynomial learning with errors (PLWE) problems. However, most of the encryption schemes based on LWE problems suffer from the problem of oversized public keys and ciphers. Although encryption schemes based on the PLWE problem further reduce the size, their hardness is limited by polynomials and the security guarantees are weakened. Compared with the LWE and PLWE problems, the Middle-Product Learning With Errors (MP-LWE) problem relaxes the polynomial restriction and makes full use of the polynomial features to achieve a better balance between security and efficiency. Inspired by this, we have proposed the inner product encryption scheme of Sel-IND-CPA-secure in SocialSec 2022. In this paper, to extend the existing work and improve the functionality of IPE, we construct single-input and multi-input inner product encryption schemes of Ad-IND-CPA-secure, and also evaluate the efficiency of the schemes.