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Soft Computing

, Volume 23, Issue 5, pp 1735–1744 | Cite as

A multi-key SMC protocol and multi-key FHE based on some-are-errorless LWE

  • Huiyong Wang
  • Yong Feng
  • Yong DingEmail author
  • Shijie Tang
Methodologies and Application
  • 128 Downloads

Abstract

We study the hardness of learning with errors (LWE) problem with some equation constraints (\(\hbox {LWE}_{n,l,q,\chi }\), some-are-errorless LWE). Previously, it was proved that LWE with one equation (first-is-errorless LWE) can be made as hard as the standard \(\hbox {LWE}_{n,q,\chi }\), given a large lattice dimension n. We show that the some-are-errorless LWE problem can also be made equivalently hard as long as n is big enough and \(n \gg l\) (A similar conclusion was given using fuzzy extrators by Fuller). A second work in this paper is to construct a multi-key secure multi-party computation (SMC) protocol, whose security relies on LWE and the some-are-errorless LWE problem in semi-honest and semi-malicious environments assuming the common random string model. We study the Gentry–Sahai–Waters (GSW13) fully homomorphic encryption (FHE) scheme and its key homomorphism, which is essential for the construction of our multi-key SMC protocol. The proposed protocol naturally constitutes a multi-key FHE scheme in the same settings. Finally, we show the excellence of the proposed SMC protocol in time and space complexity by comparisons with existing relative schemes.

Keywords

LWE FHE Key homomorphism SMC 

Notes

Acknowledgements

This work is partially supported by National Natural Science Foundation of China (Grant Nos. 61772150, 61262008) and the open project of Guangxi Key Lab. of Crypto. and Info. Security (Grant Nos. GCIS201621, GCIS201622). We thank Xiaolin Qin, Jikui Wang, Jianguang Lu, Juyi Fan and Zhi Sun for helpful comments and discussions.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest with any individual or organization.

Human and animals rights

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilinPeople’s Republic of China
  2. 2.Chongqing Key Laboratory of Automated Reasoning and Cognition, Chongqing Institute of Green and Intelligent TechnologyChinese Academy of ScienceChongqingPeople’s Republic of China
  3. 3.Guangxi Key Laboratory of Cryptography and Information Security, School of Computer Science and Information SecurityGuilin University of Electronic TechnologyGuilinPeople’s Republic of China
  4. 4.Guangxi Key Laboratory of Intelligent Integrated Automation, School of Electronic Engineering and AutomationGuilin University of Electronic TechnologyGuilinPeople’s Republic of China

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