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Description of (Fully) Homomorphic Cryptographic Primitives Within the p-Adic Model of Encryption
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0003-1919-1495
Linnaeus University, Faculty of Technology, Department of Mathematics.ORCID iD: 0000-0002-9857-0938
2019 (English)In: Analysis, Probability, Applications, and Computation: Proceedings of the 11th ISAAC Congress, Växjö (Sweden) 2017 / [ed] Karl‐Olof Lindahl, Torsten Lindström, Luigi G. Rodino, Joachim Toft, Patrik Wahlberg, Cham: Birkhäuser Verlag, 2019, p. 241-248Conference paper, Published paper (Refereed)
Abstract [en]

In this paper we consider a description of homomorphic and fully homomorphic cryptographic primitives in the p-adic model. This model describes a wide class of ciphers (including substitution ciphers, substitution ciphers streaming, keystream ciphers in the alphabet of p elements), but certainly not all. Homomorphic and fully homomorphic ciphers are used to ensure the credibility of remote computing, including cloud technology. Within considered p-adic model we describe all homomorphic cryptographic primitives with respect to arithmetic and coordinate-wise logical operations in the ring of p-adic integers ℤ p . We show that there are no fully homomorphic cryptographic primitives for each pair of the considered set of arithmetic and coordinate-wise logical operations on ℤ p.

Place, publisher, year, edition, pages
Cham: Birkhäuser Verlag, 2019. p. 241-248
Series
Trends in Mathematics, ISSN 2297-0215, E-ISSN 2297-024X
National Category
Mathematical Analysis
Research subject
Mathematics, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-82771DOI: 10.1007/978-3-030-04459-6_23Scopus ID: 2-s2.0-85065438988ISBN: 978-3-030-04458-9 (print)ISBN: 978-3-030-04459-6 (electronic)OAI: oai:DiVA.org:lnu-82771DiVA, id: diva2:1318321
Conference
11th ISAAC Congress, Växjö, Sweden, 2017
Available from: 2019-05-27 Created: 2019-05-27 Last updated: 2019-08-29Bibliographically approved

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Yurova, EkaterinaKhrennikov, Andrei

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  • apa
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