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New probabilistic public-key encryption based on the RSA cryptosystem

New probabilistic public-key encryption based on the RSA cryptosystem Abstract 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 = p q ${n=pq}$ , 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 = p q ${n=pq}$ and the Euler function ϕ ( n ) = ( p - 1 ) ( q - 1 ) ${\varphi (n)=(p-1)(q-1)}$ . In fact, the proposed encryption does not use any extra tools or functions compared to the RSA cryptosystem. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups Complexity Cryptology de Gruyter

New probabilistic public-key encryption based on the RSA cryptosystem

Groups Complexity Cryptology , Volume 7 (2) – Nov 1, 2015

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Publisher
de Gruyter
Copyright
Copyright © 2015 by the
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/gcc-2015-0016
Publisher site
See Article on Publisher Site

Abstract

Abstract 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 = p q ${n=pq}$ , 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 = p q ${n=pq}$ and the Euler function ϕ ( n ) = ( p - 1 ) ( q - 1 ) ${\varphi (n)=(p-1)(q-1)}$ . In fact, the proposed encryption does not use any extra tools or functions compared to the RSA cryptosystem.

Journal

Groups Complexity Cryptologyde Gruyter

Published: Nov 1, 2015

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