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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

Editorial Board: Ciobanu, Laura / Conder, Marston / Eick, Bettina / Elder, Murray / Fine, Benjamin / Gilman, Robert / Grigoriev, Dima / Ko, Ki Hyoung / Kreuzer, Martin / Mikhalev, Alexander V. / Myasnikov, Alexei / Perret, Ludovic / Roman'kov, Vitalii / Rosenberger, Gerhard / Sapir, Mark / Thomas, Rick / Tsaban, Boaz / Capell, Enric Ventura / Lohrey, Markus

CiteScore 2018: 0.80

SCImago Journal Rank (SJR) 2018: 0.368
Source Normalized Impact per Paper (SNIP) 2018: 1.061

Mathematical Citation Quotient (MCQ) 2017: 0.32

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New probabilistic public-key encryption based on the RSA cryptosystem

Vitalii A. Roman'kov
  • Corresponding author
  • Mathematical Department, Omsk State University n.a. F.M. Dostoevskiy, Prospekt Mira 55-A, Omsk 644077, Russia
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Published Online: 2015-10-10 | DOI: https://doi.org/10.1515/gcc-2015-0016


We propose a novel probabilistic public-key encryption, based on the RSA cryptosystem. We prove that in contrast to the (standard model) RSA cryptosystem each user can choose his own encryption exponent from a more extensive set of positive integers than it can be done by the creator of the concrete RSA cryptosystem who chooses and distributes encryption keys among all users. Moreover, we show that the proposed encryption remains secure even in the case when the adversary knows the factors of the modulus n=pq, where p and q are distinct primes. So, the security assumptions are stronger for the proposed encryption than for the RSA cryptosystem. More exactly, the adversary can break the proposed scheme if he can solve the general prime factorization problem for positive integers, in particular for the modulus n=pq and the Euler function ϕ(n)=(p-1)(q-1). In fact, the proposed encryption does not use any extra tools or functions compared to the RSA cryptosystem.

Keywords: Cryptography; public-key; RSA; semantic security

MSC: 94A60; 11T71; 68P25

About the article

Received: 2015-07-25

Published Online: 2015-10-10

Published in Print: 2015-11-01

Funding Source: RFBR

Award identifier / Grant number: 15.41.04312

Citation Information: Groups Complexity Cryptology, Volume 7, Issue 2, Pages 153–156, ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2015-0016.

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