Fully Homomorphic Encryption Scheme Based on Decomposition Ring

Seiko ARITA; Sari HANDA

doi:10.1587/transfun.2019CIP0027

IEICE TRANSACTIONS on Fundamentals

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Fully Homomorphic Encryption Scheme Based on Decomposition Ring

Seiko ARITA, Sari HANDA

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In this paper, we propose the decomposition ring homomorphic encryption scheme, that is a homomorphic encryption scheme built on the decomposition ring, which is a subring of cyclotomic ring. By using the decomposition ring the structure of plaintext slot becomes ℤ_p^l, instead of GF(p^d) in conventional schemes on the cyclotomic ring. For homomorphic multiplication of integers, one can use the full of ℤ_p^l slots using the proposed scheme, although in conventional schemes one can use only one-dimensional subspace GF(p) in each GF(p^d) slot. This allows us to realize fast and compact homomorphic encryption for integer plaintexts. In fact, our benchmark results indicate that our decomposition ring homomorphic encryption schemes are several times faster than HElib for integer plaintexts due to its higher parallel computation.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E103-A No.1 pp.195-211

Publication Date: 2020/01/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.2019CIP0027

Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)

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Authors

Seiko ARITA
Institute of Information Security
Sari HANDA
Institute of Information Security

Keyword

fully homomorphic encryption, ring-LWE, cyclotomic ring, decomposition ring, plaintext slots

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Seiko ARITA, Sari HANDA, "Fully Homomorphic Encryption Scheme Based on Decomposition Ring" in IEICE TRANSACTIONS on Fundamentals, vol. E103-A, no. 1, pp. 195-211, January 2020, doi: 10.1587/transfun.2019CIP0027.
Abstract: In this paper, we propose the decomposition ring homomorphic encryption scheme, that is a homomorphic encryption scheme built on the decomposition ring, which is a subring of cyclotomic ring. By using the decomposition ring the structure of plaintext slot becomes ℤ_p^l, instead of GF(p^d) in conventional schemes on the cyclotomic ring. For homomorphic multiplication of integers, one can use the full of ℤ_p^l slots using the proposed scheme, although in conventional schemes one can use only one-dimensional subspace GF(p) in each GF(p^d) slot. This allows us to realize fast and compact homomorphic encryption for integer plaintexts. In fact, our benchmark results indicate that our decomposition ring homomorphic encryption schemes are several times faster than HElib for integer plaintexts due to its higher parallel computation.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019CIP0027/_p

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@ARTICLE{e103-a_1_195,
author={Seiko ARITA, Sari HANDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Fully Homomorphic Encryption Scheme Based on Decomposition Ring},
year={2020},
volume={E103-A},
number={1},
pages={195-211},
abstract={In this paper, we propose the decomposition ring homomorphic encryption scheme, that is a homomorphic encryption scheme built on the decomposition ring, which is a subring of cyclotomic ring. By using the decomposition ring the structure of plaintext slot becomes ℤ_p^l, instead of GF(p^d) in conventional schemes on the cyclotomic ring. For homomorphic multiplication of integers, one can use the full of ℤ_p^l slots using the proposed scheme, although in conventional schemes one can use only one-dimensional subspace GF(p) in each GF(p^d) slot. This allows us to realize fast and compact homomorphic encryption for integer plaintexts. In fact, our benchmark results indicate that our decomposition ring homomorphic encryption schemes are several times faster than HElib for integer plaintexts due to its higher parallel computation.},
keywords={},
doi={10.1587/transfun.2019CIP0027},
ISSN={1745-1337},
month={January},}

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TY - JOUR
TI - Fully Homomorphic Encryption Scheme Based on Decomposition Ring
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 195
EP - 211
AU - Seiko ARITA
AU - Sari HANDA
PY - 2020
DO - 10.1587/transfun.2019CIP0027
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2020
AB - In this paper, we propose the decomposition ring homomorphic encryption scheme, that is a homomorphic encryption scheme built on the decomposition ring, which is a subring of cyclotomic ring. By using the decomposition ring the structure of plaintext slot becomes ℤ_p^l, instead of GF(p^d) in conventional schemes on the cyclotomic ring. For homomorphic multiplication of integers, one can use the full of ℤ_p^l slots using the proposed scheme, although in conventional schemes one can use only one-dimensional subspace GF(p) in each GF(p^d) slot. This allows us to realize fast and compact homomorphic encryption for integer plaintexts. In fact, our benchmark results indicate that our decomposition ring homomorphic encryption schemes are several times faster than HElib for integer plaintexts due to its higher parallel computation.
ER -

IEICE TRANSACTIONS on Fundamentals