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A fully homomorphic encryption (FHE) would be the important cryptosystem as the basic scheme for the cloud computing. Since Gentry discovered in 2009 the first fully homomorphic encryption scheme, some fully homomorphic encryption schemes were proposed. In the systems proposed until now the bootstrapping process is the main bottleneck and the large complexity for computing the ciphertext is required. In 2011 Zvika Brakerski et al. proposed a *leveled* FHE without bootstrapping. But circuit of arbitrary level cannot be evaluated in their scheme while in our scheme circuit of any level can be evaluated. The existence of an efficient fully homomorphic cryptosystem would have great practical implications in the outsourcing of private computations, for instance, in the field of the cloud computing. In this paper, IND-CCA1secure FHE based on the difficulty of prime factorization is proposed which does not need the bootstrapping and it is thought that our scheme is more efficient than the previous schemes. In particular the computational overhead for homomorphic evaluation is O(1).

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.1 pp.275-282

- Publication Date
- 2021/01/01

- Publicized
- 2020/07/08

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2020EAP1057

- Type of Manuscript
- PAPER

- Category
- Cryptography and Information Security

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Masahiro YAGISAWA, "IND-CCA1 Secure FHE on Non-Associative Ring" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 1, pp. 275-282, January 2021, doi: 10.1587/transfun.2020EAP1057.

Abstract: A fully homomorphic encryption (FHE) would be the important cryptosystem as the basic scheme for the cloud computing. Since Gentry discovered in 2009 the first fully homomorphic encryption scheme, some fully homomorphic encryption schemes were proposed. In the systems proposed until now the bootstrapping process is the main bottleneck and the large complexity for computing the ciphertext is required. In 2011 Zvika Brakerski et al. proposed a *leveled* FHE without bootstrapping. But circuit of arbitrary level cannot be evaluated in their scheme while in our scheme circuit of any level can be evaluated. The existence of an efficient fully homomorphic cryptosystem would have great practical implications in the outsourcing of private computations, for instance, in the field of the cloud computing. In this paper, IND-CCA1secure FHE based on the difficulty of prime factorization is proposed which does not need the bootstrapping and it is thought that our scheme is more efficient than the previous schemes. In particular the computational overhead for homomorphic evaluation is O(1).

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020EAP1057/_p

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@ARTICLE{e104-a_1_275,

author={Masahiro YAGISAWA, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={IND-CCA1 Secure FHE on Non-Associative Ring},

year={2021},

volume={E104-A},

number={1},

pages={275-282},

abstract={A fully homomorphic encryption (FHE) would be the important cryptosystem as the basic scheme for the cloud computing. Since Gentry discovered in 2009 the first fully homomorphic encryption scheme, some fully homomorphic encryption schemes were proposed. In the systems proposed until now the bootstrapping process is the main bottleneck and the large complexity for computing the ciphertext is required. In 2011 Zvika Brakerski et al. proposed a *leveled* FHE without bootstrapping. But circuit of arbitrary level cannot be evaluated in their scheme while in our scheme circuit of any level can be evaluated. The existence of an efficient fully homomorphic cryptosystem would have great practical implications in the outsourcing of private computations, for instance, in the field of the cloud computing. In this paper, IND-CCA1secure FHE based on the difficulty of prime factorization is proposed which does not need the bootstrapping and it is thought that our scheme is more efficient than the previous schemes. In particular the computational overhead for homomorphic evaluation is O(1).},

keywords={},

doi={10.1587/transfun.2020EAP1057},

ISSN={1745-1337},

month={January},}

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TY - JOUR

TI - IND-CCA1 Secure FHE on Non-Associative Ring

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 275

EP - 282

AU - Masahiro YAGISAWA

PY - 2021

DO - 10.1587/transfun.2020EAP1057

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E104-A

IS - 1

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - January 2021

AB - A fully homomorphic encryption (FHE) would be the important cryptosystem as the basic scheme for the cloud computing. Since Gentry discovered in 2009 the first fully homomorphic encryption scheme, some fully homomorphic encryption schemes were proposed. In the systems proposed until now the bootstrapping process is the main bottleneck and the large complexity for computing the ciphertext is required. In 2011 Zvika Brakerski et al. proposed a *leveled* FHE without bootstrapping. But circuit of arbitrary level cannot be evaluated in their scheme while in our scheme circuit of any level can be evaluated. The existence of an efficient fully homomorphic cryptosystem would have great practical implications in the outsourcing of private computations, for instance, in the field of the cloud computing. In this paper, IND-CCA1secure FHE based on the difficulty of prime factorization is proposed which does not need the bootstrapping and it is thought that our scheme is more efficient than the previous schemes. In particular the computational overhead for homomorphic evaluation is O(1).

ER -