Subring Homomorphic Encryption

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 Zpl , rather than an element of GF(p) 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 integer plaintexts, due to its high parallelism of mod-p integer slot structure. We believe in that such plaintext structure composed of mod-p 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) slots.