On the arithmetic of the endomorphisms ring \(\text{End}(\mathbb Z_p\times\mathbb Z_{p^2})\).

DOI10.1007/S00200-011-0138-4zbMath1248.16024OpenAlexW1983726675MaRDI QIDQ429750

Leandro Tortosa, Joan-Josep Climent, Pedro R. Navarro

Publication date: 20 June 2012

Published in: Applicable Algebra in Engineering, Communication and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00200-011-0138-4

zbMATH Keywords

endomorphism ringsinvertible elements\(2\times 2\) matrix ringsadditive orderskey exchange protocols

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Finite rings and finite-dimensional associative algebras (16P10) Cryptography (94A60) Finite abelian groups (20K01) Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups (20K30)

Related Items (10)

Public key protocols over the ring \(E_{p}^{(m)}\) ⋮ On some class of formal matrix ring ⋮ Cryptanalysis of the CLR-cryptosystem ⋮ Formal matrices and their determinants ⋮ Key exchange protocols over noncommutative rings. The case of ⋮ On the algebraic structure of \(E_p^{(m)}\) and applications to cryptography ⋮ Cryptanalysis of a key exchange protocol based on the ring \(E_p^{(m)}\) ⋮ An extension of the noncommutative Bergman's ring with a large number of noninvertible elements ⋮ Cryptanalysis of a key exchange protocol based on the endomorphisms ring \(\mathrm{End}(\mathbb Z_p\times\mathbb Z_{p^2})\) ⋮ On the arithmetic of the endomorphism ring \(\mathrm{End}(\mathbb Z_p[x_{/\langle\overline f(x)\rangle}\times\mathbb Z_{p^2}[x]_{/\langle f(x)\rangle})\).]

Cites Work

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• Group-based cryptography
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• New approaches to designing public key cryptosystems using one-way functions and trapdoors in finite groups
• Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer

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