scholarly journals An Efficient Golden Ratio Method for Secure Cryptographic Applications

2018 ◽  
Vol 23 (4) ◽  
pp. 58 ◽  
Author(s):  
Anthony Overmars ◽  
Sitalakshmi Venkatraman
Keyword(s):  
Data Storage ◽  
Golden Ratio ◽  
Fibonacci Sequence ◽  
Ratio Method ◽  
Secure Communications ◽  
Security Attacks ◽  
Security Breaches ◽  
Elliptic Curve Cryptosystems ◽  
Electronic Transactions ◽  
Sequence Method

With the increase in the use of electronic transactions in everyday life, secure communications and data storage to withstand any kind of attack is warranted. The golden ratio, being the most irrational among irrational numbers, can be used in elliptic curve cryptosystems, power analysis security, and other applications. However, in such applications, cryptographic operations should take place very quickly before the keys are extracted or decoded by the attackers. This paper proposes an efficient method of golden ratio computation in cryptography to resist information security breaches. We compare our new golden ratio method with the well-known Fibonacci sequence method. The experimental results show that our proposed method is more efficient than the Fibonacci sequence method. Our golden ratio method with infinite precision provides reliable counter measure strategy to address the escalating security attacks.

scholarly journals The Role of Blockchain in Cyber Security

2021 ◽  
Vol 3 (1) ◽  
Author(s):  
Dylan Rafferty ◽  
Kevin Curran
Keyword(s):  
Data Storage ◽  
Cyber Security ◽  
Board Members ◽  
The Internet ◽  
Network Architectures ◽  
General Data Protection Regulation ◽  
Security Breaches ◽  
General Data ◽  
The Internet Of Things

Cyber security breaches are on the rise globally. Due to the introduction of legislation like the EU’s General Data Protection Regulation (GDPR), companies are now subject to further financial penalties if they fail to meet requirements in protecting user information.  In 2018, 75% of CEOs and board members considered cyber security and technology acquisitions among their top priorities, and blockchain based solutions were among the most considered options. Blockchain is a decentralised structure that offers multiple security benefits over traditional, centralised network architectures. These two approaches are compared in this chapter in areas such as data storage, the Internet of Things (IoT) and Domain Name System (DNS) in order to determine blockchain’s potential in the future of cyber security.

scholarly journals From Fibonacci Sequence to the Golden Ratio

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Alberto Fiorenza ◽  
Giovanni Vincenzi
Keyword(s):  
Characteristic Polynomial ◽  
Golden Ratio ◽  
Fibonacci Sequence ◽  
Maximum Modulus ◽  
Point Of View ◽  
General Point ◽  
Constant Coefficients ◽  
The Difference ◽  
New Perspective

We consider the well-known characterization of the Golden ratio as limit of the ratio of consecutive terms of the Fibonacci sequence, and we give an explanation of this property in the framework of the Difference Equations Theory. We show that the Golden ratio coincides with this limit not because it is the root with maximum modulus and multiplicity of the characteristic polynomial, but, from a more general point of view, because it is the root with maximum modulus and multiplicity of a restricted set of roots, which in this special case coincides with the two roots of the characteristic polynomial. This new perspective is the heart of the characterization of the limit of ratio of consecutive terms of all linear homogeneous recurrences with constant coefficients, without any assumption on the roots of the characteristic polynomial, which may be, in particular, also complex and not real.

scholarly journals Musica fibonacciana: Aesthetic and practical approach

New Sound ◽  
2017 ◽  
pp. 70-90
Author(s):  
Rima Povilionienè
Keyword(s):  
Music Composition ◽  
Golden Ratio ◽  
Fibonacci Numbers ◽  
Laws Of Nature ◽  
Fibonacci Sequence ◽  
Number Sequences ◽  
Music And Mathematics ◽  
To Come ◽  
Composition Structure ◽  
And Mathematics

In the sphere of musical research, the intersection of two seemingly very different subject areas-music and mathematics is in essence related to one of the trends of music-attributing the theory of music to science, to the sphere of mathematica. It is regarded the longest-lasting interdisciplinary dialogue. The implication of numerical proportions and number sequences in the music composition of different epochs is closely related to this sphere. A significant role in creating music was attributed to the so-called infinite Fibonacci sequence. Perhaps the most important feature of the Fibonacci numbers, which attracted the attention of thinkers and creators of different epochs, is the fact that by means of the ratio between them it is possible to come maximally close to the Golden Ratio formula, which expresses the laws of nature. On a practical plane, often the climax, the most important part of any composition, matches the point of the Golden Ratio; groups of notes, rhythm, choice of tone pitches, a grouping of measures, time signature, as well as proportions between a musical composition's parts may be regulated according to Fibonacci principles. The article presents three analytical cases-Chopin's piano prelude, Bourgeois' composition for organ, and Reich's minimalistic piece, attempting to render music composition structure to the logic of Fibonacci numbers.

scholarly journals METHODOLOGICAL APPROACH TO ASSESSING THE COMPETITIVENESS OF INSTITUTIONS OF HIGHER EDUCATION

Management ◽  
2021 ◽  
Vol 32 (2) ◽  
pp. 9-24
Author(s):  
Svitlana Breus ◽  
Yevheniia Khaustova ◽  
Mykola Denysenko ◽  
Svitlana Bondarenko ◽  
Nataliia Kyrylko
Keyword(s):  
Higher Education ◽  
Economic Development ◽  
Factor Analysis ◽  
Methodological Approach ◽  
Golden Ratio ◽  
Ratio Method ◽  
Institutions Of Higher Education ◽  
Strategic Development ◽  
Knowledge Based ◽  
Socio Economic Development

Background and objectives. The problem of competitiveness of institutions of higher education (IHE) is one of the key tasks, the solution of which will help increase the socio-economic development of the country. In the context of Ukraine's European integration interests, competition between Ukrainian and foreign IHEs is intensifying, which encourages the former to find ways of their own competitiveness (which is largely determined by the competitiveness of its graduates and the ability to generate knowledge-based innovations) as a result of using appropriate factors that are directly dependent on increasing competitiveness in the context of its management.Methods. Methods of profiles and ratings using separate methods of comparative, statistical and economic-mathematical analysis (factor analysis), with the formation of an appropriate system of indicators.Findings. The results of assessing the competitiveness of KNUTD indicate a decrease in the level of competitiveness of IHEs. It has been estimated that during 2017–2019 it was at a low level (0.542, 0.541 and 0.466, respectively), which according to the proposed scale for determining the level of competitiveness of IHEs (developed using the golden ratio method) is in the range of 0.383–0.618. Conclusion. Based on studying and assessing the competitiveness of IHEs to improve it in the context of its management and ensure the strategic development of IHEs within the implementation of relevant strategic alternatives and proposed generalized areas, as well as certain factors of competitiveness, it has been determined appropriate to forecast the indicators underlying the calculation of the KNUTD competitiveness, using an improved methodological approach to the main proposed measures.

scholarly journals Balancing on the edge, the golden ratio, the Fibonacci sequence and their generalization

2018 ◽  
Vol 39 (6) ◽  
pp. 065805
Author(s):  
Gautam Dutta ◽  
Mitaxi Mehta ◽  
Praveen Pathak
Keyword(s):  
Golden Ratio ◽  
Fibonacci Sequence

On a probabilistic analogue of the Fibonacci sequence

1980 ◽  
Vol 17 (04) ◽  
pp. 1079-1082 ◽  
Author(s):  
C. C. Heyde
Keyword(s):  
Golden Ratio ◽  
Fibonacci Sequence ◽  
Population Models ◽  
Stochastic Version

One of the earliest population models to be studied gives rise to the Fibonacci sequence and has a history dating back more than 750 years. A stochastic version of the model is discussed in this paper, its basic defining property being E(Xn | Xn −1, · ··, X 0) = Xn −1 + Xn −2 a.s. The process {Xn } mimics many of the standard properties of the Fibonacci sequence. In particular, under mild additional conditions, a.s. as n → where α is the ‘golden ratio'

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