Abstract:

The paper constructs a fully homomorphic encryption method based on Binary LWE with a shorter secret key and smaller cipher text. The main obstacle when doing implementation of the fully homomorphic encryption method is that the size of secret key and the scale of the cipher text are too big and that its efficiency is too low. This article improved the key technology of the basic encrypting method. In the previous methods, some collections chosen uniformly and randomly are added to LWE’s random samples. However, the method this article proposes will add some Gausian Error to the LWE samples chosen from Gausian Distribution. This will decrease the sample size of LWE from 2nlogq to n+1. And the private key of this method will be chosen directly from the set {0,1}ⁿ instead of the Binary decomposition algorithm. This method will adopt the key conversion technology to avoid the rapid expansion of the scale of the cipher text after tensor multiplication, and meanwhile get a smaller size of secret key. In the end, the article will attribute the security of the method to the assumptions of difficult problems when searching Binary LWE and then give a security proof.

Key words: fully homomorphic encryption, Binary LWE, size of secret keys, scale of cipher text