The application of modified Chebyshev polynomials in asymmetric cryptography

Lawnik, Marcin; Kapczyński, Adrian

doi:10.7494/csci.2019.20.3.3307

Cited by 11 publications

(6 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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%

“…The use of the residue number system (RNS) [19][20][21] in the implementation of cryptographic algorithms for information security based on polynomial arithmetic in the Z x ring [22,23], by analogy with the integer RNS [24,25], leads to parallelization of the computation process [26,27] and reduction of the amount of data that must be processed during cryptographic operations [28][29][30]. In turn, it reduces the implementation time and improves the efficiency of the encryption method.…”

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

View full text Add to dashboard Cite

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.

show abstract

“…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

show abstract

“…From a scientific and practical point of view, chaotic oscillations are the most interesting. They are found both in engineering (e.g., in chemical reactors [ 1 , 2 , 3 ]) and in such fields as cryptography (e.g., [ 4 ]). Research in the field of chaos covers issues such as hyperchaos and multistability [ 5 , 6 ], Lyapunov exponents [ 7 ], or systems with lags [ 8 ].…”

Section: Introductionmentioning

confidence: 99%

Hidden Attractors in Discrete Dynamical Systems

Berezowski

Lawnik

2021

Entropy

Self Cite

View full text Add to dashboard Cite

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

show abstract

“…The ability to calculate the private key from the public is almost very difficult if not impossible. Usually, the public key encryption based on the chaotic map used the Chebyshev map due to the semigroup property of this map [19]. Prasadh et al [20] designed a public-key cryptosystem based on the Chebyshev map to encrypt the image.…”

Section: Introductionmentioning

confidence: 99%

Public key cryptosystem based on multiple chaotic maps for image encryption

S.Najaf

Mahmood

2021

IJEECS

View full text Add to dashboard Cite

Image is one of the most important forms of information. In this paper, two public key encryption systems are proposed to protect images from various attacks. Both systems depend on generating a chaotic matrix (<em>I</em>) using multiple chaotic maps. The parameters for these maps are taken from the shared secret keys generated from Chebyshev map using public keys for Alice and secret key for Bob or vice versa. The second system has the feature of deceiving the third party for searching for fake keys. Analysis and tests showed that the two proposed systems resist various attacks and have very large key space. The results are compared with other chaos based systems to show the superiority of these two proposed systems.

show abstract

The application of modified Chebyshev polynomials in asymmetric cryptography

Cited by 11 publications

References 34 publications

Symmetric Encryption Algorithms in a Polynomial Residue Number System

Symmetric Encryption Algorithms in a Polynomial Residue Number System

Hidden Attractors in Discrete Dynamical Systems

Public key cryptosystem based on multiple chaotic maps for image encryption

Contact Info

Product

Resources

About