Research On Lattice-Based Identity-Based Broadcast Encryption

Along with the creation and development, public key Cryptosystems has become the main technique to ensure information security. The most common Cryptosystems used at present are those systems based on Integer Factoring Problem (IFP) and Discrete Logarithm Problem (DLP). But the low efficiency resulted from the complexity of system’s operation is the main restriction in the development of public key cryptography. With the development of quantum computing, the security of these cryptosystems based on IFP and DLP will face serious challenges. The groundbreaking work of Ajtai, at1996, provides a new research direction that construction new public key cryptography based on the difficult hypothesis of lattice. Through the current research conjecture that there is no Polynomial time quantum algorithm that slove difficult problem with Polynomial time factors. And, the operation on Lattice-based cryptographic constructions is linearity because of the lattice struction, so the constructions based on lattice can be expected more efficient than others.Our research around the Cryptosystems based on the lattice, mainly analyse the difficult problems on lattice and the Cryptosystem s based on lattice problem, especially the scheme based on lattice’s LWE problem. In addition, focus on the analysis of identity based encryption (IBE) system of the idea of construction and safety proof, and connect with the broadcast encryption, then construct two based on the lattice and identity broadcast encryption (IBBE) scheme. The main research work is as follows:1. Contrstruct an IBBE scheme based on LWE problem, using trapdoor function and strongly unforgeable one-time signature algorithm. In the contruction, we use hash function to map any identity vector to matrix. Then construct a correlation matrix with the set of identity. The contruction is proved to be resisit adaptive chosen-ciphertext and chosen-identity attack (IND-ID-CCA). Proof idea comes from Agrawal:Through a series of Games between adversary and challenge to complete safety instructions. In addition, our scheme has higher efficiency compared with a bit single scheme based on LWE problem.2. Contrstruct a single bit IBBE scheme based on LWE problem, using trapdoor function. This construction use code function to map identity vector to matrix, then Construct a correlation matrix with the set of identity. In this construction, we use special ways to deal with noise vector. We also use a series of Games between adversary and challenge to complete safety instructions. The contruction is proved to be resisit selective-identity chosen-plaintext attack (IND-sID-CPA)...