Subring Homomorphic Encryption

  • Seiko Arita
  • Sari Handa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10779)


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.


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



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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© 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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