Bijective S-boxes of different sizes obtained from quasi-cyclic codes

Bikov, Dusan; Bouyukliev, Iliya; Bouyuklieva, Stefka

doi:10.13069/jacodesmath.617232

Cited by 3 publications

(4 citation statements)

References 12 publications

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“…there are 256 rows, 256 columns and one frame. Table 2 outlines secret [19] encryption keys that are preliminary values of the three chaotic maps engaged. The input image and its histogram are presented in fig.…”

Section: Resultsmentioning

confidence: 99%

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A novel symmetric image cryptosystem resistant to noise perturbation based on S8 elliptic curve S-boxes and chaotic maps

et al. 2020

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The recent decade has seen a tremendous escalation of multimedia and its applications. These modern applications demand diverse security requirements and innovative security platforms. In this manuscript, we proposed an algorithm for image encryption applications. The core structure of this algorithm relies on confusion and diffusion operations. The confusion is mainly done through the application of the elliptic curve and S8 symmetric group. The proposed work incorporates three distinct chaotic maps. A detailed investigation is presented to analyze the behavior of chaos for secure communication. The chaotic sequences are then accordingly applied to the proposed algorithm. The modular approach followed in the design framework and integration of chaotic maps into the system makes the algorithm viable for a variety of image encryption applications. The resiliency of the algorithm can further be enhanced by increasing the number of rounds and S-boxes deployed. The statistical findings and simulation results imply that the algorithm is resistant to various attacks. Moreover, the algorithm satisfies all major performance and quality metrics. The encryption scheme can also resist channel noise as well as noise-induced by a malicious user. The decryption is successfully done for noisy data with minor distortions. The overall results determine that the proposed algorithm contains good cryptographic properties and low computational complexity makes it viable to low profile applications.

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Section: Resultsmentioning

confidence: 99%

“…Ruisanchez et al [18] constructed S-boxes with high diffusion characteristics through a novel algorithm. Bikov et al [19] fabricated bijective S-boxes of varying sizes through the application of binary quasi-cyclic codes with good cryptographic properties.…”

Section: Introductionmentioning

confidence: 99%

A novel symmetric image cryptosystem resistant to noise perturbation based on S8 elliptic curve S-boxes and chaotic maps

et al. 2020

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“…For example, we used it to study bijective S-boxes with n ≤ 18 variables and good cryptographic properties which were derived from linear codes with quasi-cyclic structures in Ref. [13].…”

Section: Introductionmentioning

confidence: 99%

BooLSPLG: A Library with Parallel Algorithms for Boolean Functions and S-Boxes for GPU

2023

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In this paper, we present a library with sequential and parallel functions for computing some of the most important cryptographic characteristics of Boolean and vectorial Boolean functions. The library implements algorithms to calculate the nonlinearity, algebraic degree, autocorrelation, differential uniformity and related tables of vectorial Boolean functions. For the sake of completeness, we provide the mathematical basis of these algorithms. Furthermore, we compare the performance of the parallel functions from the developed software with the corresponding sequential functions and with analogous functions from the well-known SageMath and SET packages. Functions from BooLSPLG can be used to develop efficient algorithms for constructing Boolean and vectorial Boolean functions with good cryptographic properties. The parallel part of the library is implemented using a CUDA parallel programming model for recent NVIDIA GPU architectures. BooLSPLG is an open-source software library written in CUDA C/C++ with explicit documentation, test examples, and detailed input and output descriptions of all functions, both sequential and parallel, and it is available online.

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“…In [1], the author presents a good relation between Boolean functions and codes. Furthermore, in [2], the construction of bijective S-boxes from quasi-cyclic codes was shown. In 2005, Guillot [3] presented an extension of the Maiorana-McFarland method for building Boolean functions with good cryptographic properties.…”

Section: Introductionmentioning

confidence: 99%

Construction of Boolean Functions from Hermitian Codes

et al. 2022

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In 2005, Guillot published a method for the construction of Boolean functions using linear codes through the Maiorana–McFarland construction of Boolean functions. In this work, we present a construction using Hermitian codes, starting from the classic Maiorana–McFarland construction. This new construction describes how the set of variables is divided into two complementary subspaces, one of these subspaces being a Hermitian Code. The ideal theoretical parameters of the Hermitian code are proposed to reach desirable values of the cryptographic properties of the constructed Boolean functions such as nonlinearity, resiliency order, and order of propagation. An extension of Guillot’s work is also made regarding parameters selection using algebraic geometric tools, including explicit examples.

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Bijective S-boxes of different sizes obtained from quasi-cyclic codes

Abstract: The aim of this paper is to construct S-boxes of different sizes with good cryptographic properties. An algebraic construction for bijective S-boxes is described. It uses quasi-cyclic representations of the binary simplex code. Good S-boxes of sizes 4,

Cited by 3 publications

References 12 publications

A novel symmetric image cryptosystem resistant to noise perturbation based on S8 elliptic curve S-boxes and chaotic maps

A novel symmetric image cryptosystem resistant to noise perturbation based on S8 elliptic curve S-boxes and chaotic maps

BooLSPLG: A Library with Parallel Algorithms for Boolean Functions and S-Boxes for GPU

Construction of Boolean Functions from Hermitian Codes

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