Residue Number System Asymmetric Cryptoalgorithms

Nykolaychuk, Yaroslav; Yakymenko, Igor; Vozna, Nataliіa; Kasianchuk, Mykhailo

doi:10.1007/s10559-022-00494-7

Cited by 4 publications

(3 citation statements)

References 25 publications

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“…Below is an example of calculating the number of irreducible polynomials for n = 32 in GF p , where p = 3, 5, 7,11,13,17,19,23,29,31,37,43:…”

Section: Resultsmentioning

confidence: 99%

“…Recently, with the growth of confidential information and the spread of computer systems, the task of ensuring information security has become increasingly important [1][2][3]. To minimize the risks of unauthorized access, cryptographic methods of information protection are widely used [4,5], which are divided into symmetric and asymmetric [6,7]. In practice, symmetric cryptographic transformations are more common for encrypting large amounts of information, as asymmetric ones are quite laborious [8,9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Symmetric Encryption Algorithms in a Polynomial Residue Number System

Yakymenko,

Karpinski,

Shevchuk

et al. 2024

Journal of Applied Mathematics

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In this paper, we develop the theoretical provisions of symmetric cryptographic algorithms based on the polynomial residue number system for the first time. The main feature of the proposed approach is that when reconstructing the polynomial based on the method of undetermined coefficients, multiplication is performed not on the found base numbers but on arbitrarily selected polynomials. The latter, together with pairwise coprime residues of the residue class system, serve as the keys of the cryptographic algorithm. Schemes and examples of the implementation of the developed polynomial symmetric encryption algorithm are presented. The analytical expressions of the cryptographic strength estimation are constructed, and their graphical dependence on the number of modules and polynomial powers is presented. Our studies show that the cryptanalysis of the proposed algorithm requires combinatorial complexity, which leads to an NP-complete problem.

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“…Below is an example of calculating the number of irreducible polynomials for n = 32 in GF p , where p = 3, 5, 7,11,13,17,19,23,29,31,37,43:…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symmetric Encryption Algorithms in a Polynomial Residue Number System

Yakymenko,

Karpinski,

Shevchuk

et al. 2024

Journal of Applied Mathematics

View full text Add to dashboard Cite

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“…With the help of RNS, a reduction in the approximation error is achieved, which makes it possible to increase the efficiency of the circuit calculation. In work [53], the authors propose RNS as the basis of a new asymmetric cryptalgorithm. RNS modules are proposed to be used as secret keys.…”

Section: Introductionmentioning

confidence: 99%

Fast Operation of Determining the Sign of a Number in RNS Using the Akushsky Core Function

et al. 2023

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This article presents a study related to increasing the performance of distributed computing systems. The essence of fog computing lies in the use of so-called edge devices. These devices are low-power, so they are extremely sensitive to the computational complexity of the methods used. This article is aimed at improving the efficiency of calculations while maintaining an appropriate level of reliability by applying the methods of the Residue Number System (RNS). We are investigating methods for determining the sign of a number in the RNS based on the core function in order to develop a new, fast method. As a result, a fast method for determining the sign of a number based on the Akushsky core function, using approximate calculations, is obtained. Thus, in the course of this article, a study of methods for ensuring reliability in distributed computing is conducted. A fast method for determining the sign of a number in the RNS based on the core function using approximate calculations is also proposed. This result is interesting from the point of view of nebulous calculations, since it allows maintaining high reliability of a distributed system of edge devices with a slight increase in the computational complexity of non-modular operations.

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