Subring Homomorphic Encryption

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10779)

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 \(\mathbb {Z}_{p^l}\), 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.

Keywords

Fully homomorphic encryption Ring-LWE Cyclotomic ring Decomposition ring Plaintext slots 

Notes

Acknowledgments

This work was supported by JST CREST Grant Number JPMJCR1503. This work is further supported by the JSPS KAKENHI Grant Number 17K05353.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Graduate School of Information SecurityInstitute of Information SecurityYokohamaJapan

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