Chaos-based image encryption schemes have been extensively employed over the past few years. Many issues such as the dynamical degradation of digital chaotic systems and information security have been explored, and plenty of successful solutions have also been proposed. However, the impact of finite precision in different hardware and software setups has received little attention. In this work, we have shown that the finite precision error may produce distinct cipher-images on different devices. In order to overcome this problem, we introduce an efficient cryptosystem, in which the chaotic logistic map and the Galois field theory are applied. Our approach passes in the ENT test suite and in several cyberattacks. It also presents an astonishing key space of up to 2 4096 . Benchmark images have been effectively encrypted and decrypted using dissimilar digital devices.

Neste trabalho apresentamos técnicas recentes para o cálculo de idempotentes primitivos emálgebras de grupo ou emálgebras polinomiais. Esses idempotentes podem ser vistos como geradores de códigos cíclicos minimais. Exibiremos duas abordagens para tais cálculos: a primeira, que chamaremos abordagem polinomial,é realizada no anel das classes residuais módulo x n − 1 de um anel de polinômios, onde n denota o comprimento do código. Já a segundá e realizada no contexto deálgebras de grupo de grupos abelianos sobre corpos finitos de ordem prima. Em particular, consideramos grupos cíclicos de ordem n e apresentamos um isomorfismo entre o anel de classes residuais e aálgebra de grupo de modo que possamos trabalhar livremente nestas duas abordagens.

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In this paper we characterize the orbit codes as geometrically uniform codes. This characterization is based on the description of all isometries over a projective geometry. In addition, Abelian orbit codes are defined and a construction of Abelian non-cyclic orbit codes is presented. In order to analyze their structures, the concept of geometrically uniform partitions have to be reinterpreted. As a consequence, a substantial reduction in the number of computations needed to obtain the minimum subspace distance of these codes is achieved and established.An application of orbit codes to multishot subspace codes obtained according to a multi-level construction is provided.2010 Mathematics Subject Classification: Primary: 11T71, 94B60; Secondary: 51E99.

The use of permutation polynomials over finite fields has appeared, along with their compositional inverses, as a good choice in the implementation of cryptographic systems. As a particular case, the construction of involutions is highly desired since their compositional inverses are themselves. In this work, we present an effective way of how to construct several linear permutation polynomials over [Formula: see text] as well as their compositional inverses using a decomposition of [Formula: see text] based on its primitive idempotents. As a consequence, involutions are also constructed.