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Image encryption based on permutation polynomials over finite fields

Wu Jianhua, Liu Hai, Zhu Xishun

Optica Applicata

2020

Vol. 50, nr 3

357--376

In this paper, we propose an image encryption algorithm based on a permutation polynomial over finite fields proposed by the authors. The proposed image encryption process consists of four stages: i) a mapping from pixel gray-levels into finite field, ii) a pre-scrambling of pixels’ positions based on the parameterized permutation polynomial, iii) a symmetric matrix transform over finite fields which completes the operation of diffusion and, iv) a post-scrambling based on the permutation polynomial with different parameters. The parameters used for the polynomial parameterization and for constructing the symmetric matrix are used as cipher keys. Theoretical analysis and simulation demonstrate that the proposed image encryption scheme is feasible with a high efficiency and a strong ability of resisting various common attacks. In addition, there are not any round-off errors in computation over finite fields, thus guaranteeing a strictly lossless image encryption. Due to the intrinsic nonlinearity of permutation polynomials in finite fields, the proposed image encryption system is nonlinear and can resist known-plaintext and chosen-plaintext attacks.

Wielomianowe generatory kongruencyjne jako źródło silnie nieliniowych funkcji boolowskich

Janoska A., Paszkiewicz A.

Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne

2017

nr 1

13--18

W artykule zebrano podstawowe informacje o najprostszych wykorzystywanych w praktyce generatorach kongruencyjnych liczb pseudolosowych i opisano ich własności. Przedstawiono mało znane warunki na okresowość generatorów wielomianowych. Wykorzystano wielomianowe generatory kongruencyjne do znajdowania nieliniowych funkcji boolowskich zwanych s-boxami.

This paper contains basic informations concerning the simplest pseudorandom congruential generators used in practice. Not very much known conditions for periodicity of polynomial generators are given. Polynomial congruential generators are used to produce nonlinear boolean functions called s-boxes.

An Analysis of the C Class of Bent Functions

Mandal B., Gangopadhyay S., Stănică P., Pasalic E.

Fundamenta Informaticae

2016

Vol. 146, nr 3

271--292

Two (so-called C;D) classes of permutation-based bent Boolean functions were introduced by Carlet [4] two decades ago, but without specifying some explicit construction methods for their construction (apart from the subclass D0). In this article, we look in more detail at the C class, and derive some existence and nonexistence results concerning the bent functions in the C class for many of the known classes of permutations over F2n. Most importantly, the existence results induce generic methods of constructing bent functions in class C which possibly do not belong to the completed Maiorana-McFarland class. The question whether the specific permutations and related subspaces we identify in this article indeed give bent functions outside the completed Maiorana-McFarland class remains open.