Fully Homomorphic Encryption Scheme Based on Decomposition Ring

Abstract

In this paper, we propose the decomposition ring homomorphic encryption scheme, that is a homomorphic encryption scheme built on the decomposition ring, which is a subring of cyclotomic ring. By using the decomposition ring the structure of plaintext slot becomes ℤ_p^l, instead of GF(p^d) in conventional schemes on the cyclotomic ring. For homomorphic multiplication of integers, one can use the full of ℤ_p^l slots using the proposed scheme, although in conventional schemes one can use only one-dimensional subspace GF(p) in each GF(p^d) slot. This allows us to realize fast and compact homomorphic encryption for integer plaintexts. In fact, our benchmark results indicate that our decomposition ring homomorphic encryption schemes are several times faster than HElib for integer plaintexts due to its higher parallel computation.