The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Uma criptografia totalmente homomórfica (FHE) seria o criptossistema importante como esquema básico para a computação em nuvem. Desde que Gentry descobriu em 2009 o primeiro esquema de criptografia totalmente homomórfico, alguns esquemas de criptografia totalmente homomórficos foram propostos. Nos sistemas propostos até agora o processo de bootstrapping é o principal gargalo e é necessária a grande complexidade para computar o texto cifrado. Em 2011, Zvika Brakerski et al. propôs um nivelado FHE sem inicialização. Mas circuitos de nível arbitrário não podem ser avaliados em seu esquema, enquanto em nosso esquema circuitos de qualquer nível podem ser avaliados. A existência de um criptossistema eficiente e totalmente homomórfico teria grandes implicações práticas na terceirização de computações privadas, por exemplo, no campo da computação em nuvem. Neste artigo é proposto o IND-CCA1 FHE seguro baseado na dificuldade de fatoração primária que não necessita de bootstrapping e acredita-se que nosso esquema seja mais eficiente que os esquemas anteriores. Em particular, o overhead computacional para avaliação homomórfica é O(1).
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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 -