An extension of the noncommutative Bergman’s ring with a large number of noninvertible elements

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Title: An extension of the noncommutative Bergman’s ring with a large number of noninvertible elements
Authors: Climent, Joan-Josep | Navarro, Pedro R. | Tortosa, Leandro
Research Group/s: Grupo de Álgebra y Geometría (GAG) | Análisis y Visualización de Datos en Redes (ANVIDA)
Center, Department or Service: Universidad de Alicante. Departamento de Estadística e Investigación Operativa | Universidad de Alicante. Departamento de Ciencia de la Computación e Inteligencia Artificial
Keywords: Noncommutative ring | Noninvertible element | Key exchange protocol | Endomorphism | Bergman ring
Knowledge Area: Álgebra | Ciencia de la Computación e Inteligencia Artificial
Issue Date: Nov-2014
Publisher: Springer Berlin Heidelberg
Citation: Applicable Algebra in Engineering, Communication and Computing. 2014, 25(5): 347-361. doi:10.1007/s00200-014-0231-6
Abstract: For a prime number p , Bergman (Israel J Math 18:257–277, 1974) established that End(Zp×Zp2) is a semilocal ring with p5 elements that cannot be embedded in matrices over any commutative ring. In an earlier paper Climent et al. (Appl Algebra Eng Commun Comput 22(2):91–108, 2011), the authors presented an efficient implementation of this ring, and introduced a key exchange protocol based on it. This protocol was cryptanalyzed by Kamal and Youssef (Appl Algebra Eng Commun Comput 23(3–4):143–149, 2012) using the invertibility of most elements in this ring. In this paper we introduce an extension of Bergman’s ring, in which only a negligible fraction of elements are invertible, and propose to consider a key exchange protocol over this ring.
Sponsor: Partially supported by Spanish Grant MTM2011-24858 of the Ministerio de Economía y Competitividad of the Gobierno de España.
ISSN: 0938-1279 (Print) | 1432-0622 (Online)
DOI: 10.1007/s00200-014-0231-6
Language: eng
Type: info:eu-repo/semantics/article
Rights: The final publication is available at Springer via
Peer Review: si
Publisher version:
Appears in Collections:INV - ANVIDA - Artículos de Revistas
INV - GAG - Artículos de Revistas

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