Generation of Cryptographic Keys With Algorithm of Polygon Triangulation and Catalan Numbers

Saračević, Muzafer; Selimi, Aybeyan; Selimović, Faruk

doi:10.7494/csci.2018.19.3.2749

Cited by 16 publications

(6 citation statements)

References 8 publications

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“…[34] Dyck paths have been used for generating pseudo-random numbers, identifying sequential algorithms etc., and hence, are used in stenography, cryptography, to name a few. [34][35][36] On the other hand, in Fig. 2 the n th Catalan number gives the number of all the possible structures of a rooted full binary trees (FBTs) with 2n + 1 vertices (represented by circles).…”

Section: Xx:3mentioning

confidence: 99%

Revisiting Catalan Numbers: An AB2 Polymerization Perspective

Khewle

Dayal

Misra

et al. 2022

Preprint

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Number sequences, like Fibonacci, Fermat, Markov, Euler, Bernoulli, etc., have been popular in exemplifying a variety of scientific phenomena. Here, we explore the Catalan numbers in the context of ABm step polymerisation and develop a framework to derive its alternative closed form expression. Our approach harnesses the concepts of combinatorics and graph theory, in conjunction with kinetics of AB2 polymerisation to obtain the chain length distribution that directly gives the closed-form expression of Catalan number expressed as a bivariate distribution function. Furthermore, we validate our expression by comparing first 5000 Catalan numbers obtained from its traditional closed-form. As an offshoot, we discuss “pathwidth”, a construct used in graph theory, as a better metrics for describing topology of polymer chains. The framework developed in this work can be extended to ABm step polymerisation and thus, facilitates topological characterisation of hyperbranched polymers (HPs) that ultimately, dictates their structure-property relationships.

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Section: Xx:3mentioning

confidence: 99%

Revisiting Catalan Numbers: An AB2 Polymerization Perspective

Khewle

Dayal

Misra

et al. 2022

Preprint

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“…Digital ethics and privacy, privacy enhancement technologies, self-adaptive security, zero-trust security, endto-end security, DevSecOps, and blockchain are new developments. They should balance the focus of cyber security with transparency and privacy (Saračević et al, 2018).…”

Section: Top 10 Industry 40 Trends In 2021 Cyber Security Transparenc...mentioning

confidence: 99%

Systematic Review of Big Data, Digital Transformation Areas and Industry

Selim¹

2021

ivisum

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Industrial development has been going on for several hundred years. In the XX century, three great industrial revolutions occurred in human life. Today we can discuss the fourth industrial revolution, called Industry 4.0. Industry 4.0 takes overproduction with robots that can communicate, detect the environment with sensors and realize the needs by analyzing data. This industry aims to produce better quality, cheaper, faster, and less wasteful. In addition, Industry 4.0 allows objects to communicate with each other and with people by monitoring cyber-physical systems and physical processes in modular smart factories, enabling decentralized collaborative decisions. Applying Industry 4.0 to protect and sustain their existence is inevitable in a competitive environment for businesses and organizations. It is necessary to know the industry 4.0 concept and its fundamental paradigms. Therefore, in this paper, we explained Industry 4.0 and studied his applications areas in 2021. Our study shows that Industry 4.0 is not present, and the technologies are much less current in industrial production in North Macedonia. The key term of the Fourth Industrial Revolution is poorly understood; the presence of Industry 4.0 in the media is deficient.

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“…The importance of the Catalan numbers and combinatorics in cryptography is clearly stated in [11, 12]. Our previous research [13] presented a procedure for the application of one computational geometry algorithm in the process of generating hidden cryptographic keys (Catalan objects) from one segment of the 3D image. Also, Catalan numbers play an important role in steganography (data hiding).…”

Section: Related Workmentioning

confidence: 99%

Cryptographic keys exchange model for smart city applications

Saračević

Adamović

Maček

et al. 2020

IET Intelligent Trans Sys

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This study presents a secret key sharing protocol that establishes cryptographically secured communication between two entities. A new symmetric key exchange scenario for smart city applications is presented in this research. The protocol is based on the specific properties of the Fuss‐Catalan numbers and the Lattice Path combinatorics. The proposed scenario consists of three phases: generating a Fuss‐Catalan object based on the grid dimension, defining the movement in the Lattice Path Grid and defining the key equalisation rules. In the experimental part, the authors present the security analysis of the protocol as well as its test. Also, they examine the equivalence of the proposed with Maurer's satellite scenario and suggest a new scenario that implements an information‐theoretical protocol for the public key distribution. Additionally, a comparison with related studies and methods is provided, as well as a comparison with satellite scenario, which proves the advantages of solution presented by the authors. Finally, they propose further research directions regarding key management in smart city applications.

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Generation of Cryptographic Keys With Algorithm of Polygon Triangulation and Catalan Numbers

Cited by 16 publications

References 8 publications

Revisiting Catalan Numbers: An AB2 Polymerization Perspective

Revisiting Catalan Numbers: An AB2 Polymerization Perspective

Systematic Review of Big Data, Digital Transformation Areas and Industry

Cryptographic keys exchange model for smart city applications

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