Adaptively secure hierarchical identity-based encryption over lattice

Abstract

Quantum computer is regarded as a threat to the cryptosystem at present. Lattice with a rich mathematics structure gave a choice for building post-quantum secure hierarchical identity-based encryption (HIBE) system. But in the existing works, there are many shortcomings such as large public/private key space and weak security model. To overcome these shortcomings, a method for delegating a short lattice basis is discussed in this paper. It maintains the lattice dimension is constant. This distinct feature is used to construct the secure HIBE. The issued scheme has many advantages over the available, such as short public/private keys, achieving adaptive security. It is fair that our scheme is the first one which achieves both constant size private key space and adaptive security. In addition, we also convert our scheme from an one-bit version to an N-bit version. Based learning with errors (LWE) problem, we prove the security in the standard model.