Fully homomorphic encryption for parallel implementation of approximate methods for solving differential equations

Artem K. Vishnevsky, Sergey F. Krendelev

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

A parallel fully homomorphic encryption for rational numbers is developed in this paper. Parallelism of processing is achieved by using methods of modular arithmetic. Encryption is constructed by mapping the field of rational numbers onto a vector space. Two operations, namely addition and multiplication, are defined. Addition and multiplication tables are constructed, which ensures that a vector space is closed under these mathematical operations. We show the implementation of protected recursive computations in rings of the form ZM, M = m1m2…mk. We give a criterion of effective use of encryption for the numerical solution of the Cauchy problem. It is proved that the efficiency of encryption increases with increasing volumes and accuracy of computations.

Original languageEnglish
Title of host publicationParallel Computational Technologies - 12th International Conference, PCT 2018, Revised Selected Papers
EditorsL Sokolinsky, M Zymbler
PublisherSpringer-Verlag GmbH and Co. KG
Pages119-134
Number of pages16
ISBN (Print)9783319996721
DOIs
Publication statusPublished - 1 Jan 2018
Event12th International Scientific Conference on Parallel Computational Technologies, PCT 2018 - Rostov-on-Don, Russian Federation
Duration: 2 Apr 20186 Apr 2018

Publication series

NameCommunications in Computer and Information Science
Volume910
ISSN (Print)1865-0929

Conference

Conference12th International Scientific Conference on Parallel Computational Technologies, PCT 2018
CountryRussian Federation
CityRostov-on-Don
Period02.04.201806.04.2018

Keywords

  • Chinese remainder theorem
  • Cloud computations
  • Differential equations
  • Fully homomorphic encryption
  • Modular arithmetic
  • Numerical methods
  • Parallel computations
  • Secure computations

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