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Fundamentalnaya i Prikladnaya Matematika, 2015, Volume 20, Issue 1, Pages 135–143 (Mi fpm1629)  

This article is cited in 4 scientific papers (total in 4 papers)

Some homomorphic cryptosystems based on nonassociative structures

A. V. Gribov

Lomonosov Moscow State University
Full-text PDF (120 kB) Citations (4)
References:
Abstract: A homomorphic encryption allows specific types of computations on ciphertext and generates an encrypted result that matches the result of operations performed on the plaintext. Some classic cryptosystems, e.g., RSA and ElGamal, allow homomorphic computation of only one operation. In 2009, C. Gentry suggested a model of a fully homomorphic algebraic system, i.e., a cryptosystem that supports both addition and multiplication operations. This cryptosystem is based on lattices. Later M. Dijk, C. Gentry, S. Halevi, and V. Vaikuntanathan suggested a fully homomorphic system based on integers. In a 2010 paper of A. V. Gribov, P. A. Zolotykh, and A. V. Mikhalev, a cryptosystem based on a quasigroup ring was constructed, developing an approach of S. K. Rososhek, and a homomorphic property of this system was investigated. An example of a quasigroup for which this system is homomorphic is given. Also a homomorphic property of the ElGamal cryptosystem based on a medial quasigroup is shown.
English version:
Journal of Mathematical Sciences (New York), 2017, Volume 223, Issue 5, Pages 581–586
DOI: https://doi.org/10.1007/s10958-017-3367-7
Bibliographic databases:
Document Type: Article
UDC: 512.548.7+004.056.55
Language: Russian
Citation: A. V. Gribov, “Some homomorphic cryptosystems based on nonassociative structures”, Fundam. Prikl. Mat., 20:1 (2015), 135–143; J. Math. Sci., 223:5 (2017), 581–586
Citation in format AMSBIB
\Bibitem{Gri15}
\by A.~V.~Gribov
\paper Some homomorphic cryptosystems based on nonassociative structures
\jour Fundam. Prikl. Mat.
\yr 2015
\vol 20
\issue 1
\pages 135--143
\mathnet{http://mi.mathnet.ru/fpm1629}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3451667}
\elib{https://elibrary.ru/item.asp?id=25686552}
\transl
\jour J. Math. Sci.
\yr 2017
\vol 223
\issue 5
\pages 581--586
\crossref{https://doi.org/10.1007/s10958-017-3367-7}
Linking options:
  • https://www.mathnet.ru/eng/fpm1629
  • https://www.mathnet.ru/eng/fpm/v20/i1/p135
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Фундаментальная и прикладная математика
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    Abstract page:425
    Full-text PDF :189
    References:57
     
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