Inner Product Encryption from Middle-Product Learning with Errors

Abstract

AbstractInner product encryption (IPE) is an essential area of research for functional encryption systems. It has extensive applications in emerging fields such as cloud computing, where it can improve users’ access control and fine-grained queries. Lattice-based inner product encryption has the advantages of resistance to quantum algorithm attack and relatively simple encryption algorithm, so it has a good application prospect. At present, the provable security of lattice-based public key cryptography algorithms is mostly based on Learning With Errors (LWE) and Polynomial Learning With Errors (PLWE) problems. However, the majority of encryption schemes based on the LWE problem have the issue of excessively large public keys and ciphertexts size. Although the encryption scheme based on the PLWE problem reduces the size even further, its hardness is limited by polynomials, and the security guarantee is diminished. Compared with LWE and PLWE problem, Middle-Product Learning With Errors (MP-LWE) problems loosen the restrictions on polynomials, and make full use of the polynomial characteristics to achieve a better balance between security and efficiency. Therefore, in this paper, we present the first MP-LWE based inner product encryption schemes with Indistinguishability against Selective Chosen Plaintext Attack secure (Sel-IND-CPA-secure), while keeping the algorithm structure simple and efficient.KeywordsMiddle-product learning with errorsInner product encryptionFunction encryption