Subring homomorphic encryption

Abstract

In this paper, we construct subring homomorphic encryption scheme that is a homomorphic encryption scheme built on the decomposition ring, which is a subring of cyclotomic ring. In the scheme, each plaintext slot contains an integer in Z p l , rather than an element of GF(p d ) as in conventional homomorphic encryption schemes on cyclotomic rings. Our benchmark results indicate that the subring homomorphic encryption scheme is several times faster than HElib for mod-p l integer plaintexts, due to its high parallelism of mod-p l integer slot structure. We believe in that such plaintext structure composed of mod-p l integer slots will be more natural, easy to handle, and significantly more efficient for many applications such as outsourced data mining, than conventional GF(p d ) slots.