Compact (Targeted Homomorphic) Inner Product Encryption from LWE

Abstract

Inner product encryption (IPE) is a public-key encryption mechanism that supports fine-grained access control. Agrawal et al. (ASIACRYPT 2011) proposed the first IPE scheme from the Learning With Errors (LWE) problem. In their scheme, the public parameter size and ciphertext size are \(O(un^2\log ^3n)\) and \(O(un\log ^3n)\), respectively. Then, Xagawa (PKC 2013) proposed the improved scheme with public parameter of size \(O(un^2\log ^2n)\) and ciphertext of size \(O(un\log ^2n)\).