On the arithmetic of the endomorphisms ring End(Zp×Zp2)

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Title: On the arithmetic of the endomorphisms ring End(Zp×Zp2)
Authors: Climent, Joan-Josep | Navarro, Pedro R. | Tortosa, Leandro
Research Group/s: Grupo de Álgebra y Geometría (GAG) | Criptología y Seguridad Computacional
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: Endomorphism | Isomorphism | Noncommutative ring | Additive order | Invertible element | Key exchange protocol
Knowledge Area: Álgebra | Ciencia de la Computación e Inteligencia Artificial
Issue Date: 12-Feb-2011
Publisher: Springer
Citation: Applicable Algebra in Engineering, Communication and Computing. 2011, 22(2): 91-108. doi:10.1007/s00200-011-0138-4
Abstract: For a prime number p, Bergman (Israel J Math 18:257–277, 1974) established that End(Zp×Zp2) is a semilocal ring with p 5 elements that cannot be embedded in matrices over any commutative ring. We identify the elements of End(Zp×Zp2) with elements in a new set, denoted by E p , of matrices of size 2 × 2, whose elements in the first row belong to Zp and the elements in the second row belong to Zp2 ; also, using the arithmetic in Zp and Zp2 , we introduce the arithmetic in that ring and prove that the ring End(Zp×Zp2) is isomorphic to the ring E p . Finally, we present a Diffie-Hellman key interchange protocol using some polynomial functions over E p defined by polynomials in Z[X].
URI: http://hdl.handle.net/10045/34676
ISSN: 0938-1279 (Print) | 1432-0622 (Online)
DOI: 10.1007/s00200-011-0138-4
Language: eng
Type: info:eu-repo/semantics/article
Peer Review: si
Publisher version: http://dx.doi.org/10.1007/s00200-011-0138-4
Appears in Collections:INV - CSC - Artículos de Revistas
INV - GAG - Artículos de Revistas
INV - ANVIDA - Artículos de Revistas

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