The Handling of Noise and Security of Two Fully Homomorphic Encryption Schemes

Abstract

Noise is introduced as a means to ensure security of encryption schemes in general, and fully homomorphic encryption schemes in particular. Strategies to control the growth of this and thereby guarantee correct decryption are presented. These strategies are then applied in two similar fully homomorphic encryption schemes, and the requirements of sufficient and successful noise reductions are discussed in both. It is shown that this forces the parameters of either scheme to satisfy certain bounds, which compromises the security of one scheme, whilst it is of no great consequence with regards to security of the other.