Studies On The Broadcast Encryption Scheme Over Lattice

The standard public key cryptosystems, whose security is based on the NumberTheorem assumption, would be insecure under quantum attack on quantum computer.So how to achieve the quantum security of the cryptosystem has attracted more andmore attentions in cryptographic area. Fortunately, the hard problems over lattice,such as the closest vector problem and the shortest vector problem, are still hard evenon quantum computer. Hence, the lattice-based cryptography has been a typicalpost-quantum cryptography. Recently, lattice-based cryptography has been a hot topicfor public key cryptography and has achieved many breakthroughs. When we study thelattice-based cryptography, an interesting research direction is that how can we design aspecial functional cryptosystems over lattice? For example, how to build anidentity-based broadcast encryption system over lattice.This paper firstly studies the basic techniques and tools of the lattice-basedcryptography, and then discusses the notions and the security models of theidentity-based cryptography and the broadcast encryption scheme. At last, combiningthe identity-based broadcast encryption with the Bonsai trees primitive of thelattice-based cryptography, this paper proposes a new identity-based broadcastencryption scheme over lattice. The proposed scheme succeeds to avoid the decryptionfailure problem in the existing lattice-based broadcast encryption scheme. Moreover,the proposed scheme can also supports the dynamic expansion of clients and deals withthe setting of stateless receivers. Based on the hardness of the learning with errorsproblem, we prove that the proposed scheme is indistinguishable under the chosenplaintext and identity attack in the standard model. Since there is a quantum hardassumption about the LWE problem, the proposed scheme is still secure even onquantum computer.