Identity-Based Matrix (Level) Fully Homomorphic Encryption Scheme

Abstract

With the development of quantum theory, traditional encryption algorithms are facing enormous challenges. Once quantum computers are available, existing encryption systems will no longer be secure. The lattice cipher is proven by theory to be a new type of encryption scheme, which can resist quantum algorithm. It has the property of fast computing speed and small space occupation, hence, it has become a hot issue in today??s research. The identity-based encryption scheme can improve the utilization of storage space and facilitate user public key management. Consequently, this paper based on the hard problem of learning with errors (LWE), constructs an identity-based matrix encryption scheme at first, then applies the improved key switching technology to reduce the dimension of homomorphic ciphertext to normal, and uses the mode conversion technique to reduce noise, realizing matrix homo-morphic operation, and getting an identity-based matrix (level) fully homomorphic encryption scheme. The scheme uses matrices as the storage structure, which has greatly improved the processing capability compared to other single-bit schemes. The scheme not only satisfies the addition and Hadamard product of the matrix, but also supports matrix dot multiplication. The experimental results show that compared with other methods, the improved key switching technology in this paper inputs less noise. Through the difficulty of the LWE problem, it is proven that the scheme satisfies IND-sID-CPA (indistinguishability-selective identity-chosen plaintext attack).

Keywords

• lattice cipher
• learning with errors (lwe)
• identity-based encryption
• fully homomorphic encryption