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 \(\mathbb {Z}_{p^l}\), rather than an element of \(\mathrm {GF}(p^d)\) 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 \(\mathrm {GF}(p^d)\) slots.