(Deterministic) Hierarchical Identity-based Encryption from Learning with Rounding over Small Modulus

Abstract

In this paper, we propose a hierarchical identity-based encryption (HIBE) scheme in the random oracle (RO) model based on the learning with rounding (LWR) problem over small modulus $q$. Compared with the previous HIBE schemes based on the learning with errors (LWE) problem, the ciphertext expansion ratio of our scheme can be decreased to 1/2. Then, we utilize the HIBE scheme to construct a deterministic hierarchical identity-based encryption (D-HIBE) scheme based on the LWR problem over small modulus. Finally, with the technique of binary tree encryption (BTE) we can construct HIBE and D-HIBE schemes in the standard model based on the LWR problem over small modulus.