Compact (Targeted Homomorphic) Inner Product Encryption from LWE

摘要

Inner product encryption (IPE) is a public-key encryption mechanism that supports fine-grained access control. Agrawal et al. (ASI-ACRYPT 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~3 n) and O(un log~3 n), respectively. Then, Xagawa (PKC 2013) proposed the improved scheme with public parameter of size O(un~2 log~2 n) and ciphertext of size O(un log~2 n). In this paper, we construct a more compact IPE scheme under the LWE assumption, which has public parameter of size O(un~2 log n) and ciphertext of size O(un log n). Thus our scheme improves the size of Xagawa's IPE scheme by a factor of log n. Inspired by the idea of Brakerski et al. (TCC 2016), we propose a targeted homomorphic IPE (THIPE) scheme based on our IPE scheme. Compared with Brakerski et al.'s scheme, our THIPE scheme has more compact public parameters and ciphertexts. However, our scheme can only apply to the inner product case, while in their scheme the predicate f can be any efficiently computable polynomial.