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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.39 no.1 Antofagasta feb. 2020 


A cryptography method based on hyperbolicbalancing and Lucas-balancing functions

1 Sambalpur University, School of Mathematical Sciences, Sambalpur, OR, India. e-mail:


The goal is to study a new class of hyperbolic functions that unite the characteristics of the classical hyperbolic functions and the recurring balancing and Lucas-balancing numbers. These functions are indeed the extension of Binet formulas for both balancing and Lucas-balancing numbers in continuous domain. Some identities concerning hyperbolic balancing and Lucas-balancing functions are also established. Further, a new class of square matrices, a generalization of balancing QB-matrices for continuous domain, is considered. These matrices indeed enable us to develop a cryptography method for secrecy purpose.

Keywords: Balancing numbers; Lucas-balancing numbers; Hyperbolic balancing functions; Hyperbolic Lucas-balancing functions; Cryptography

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Received: December 2018; Accepted: December 2019

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