Abstract: Homomorphic encryption allows evaluation on encrypted data, and it is an important encryption technique to realize data privacy security in cloud computing, big data and machine learning. Constructions of fully homomorphic encryption employ a “bootstrapping” technique, which enforces the public key of the scheme to grow linearly with the maximal depth of evaluated circuits. This is a major bottleneck with regards to the usability and the eciency of the scheme. However, the size of the public key can be made independent of the circuit depth if the somewhat homomorphic scheme can securely encrypt its own secret key. Achieving circular secure somewhat homomorphic encryption has been an interesting problem which is worth studying. This paper presents a circular secure public key homomorphic encryption scheme using noise flooding technique, and gives the security proof and parameter setting; furthermore, by introducing the refuse sampling technique, an optimized circular secure public key homomorphic encryption scheme is given, and the system parameters are reduced from the super polynomial level to the polynomial level, which greatly reduces the public key and ciphertext size. And then the computational complexity of ciphertext evaluation can be effectively improved and the performance of homomorphic encryption scheme be improved.

Key words: homomorphic encryption, circular secure, learning with errors problem, noise flooding technique, reject sampling