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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Abstract

RAY, Prasanta Kumar. A cryptography method based on hyperbolicbalancing and Lucas-balancing functions. Proyecciones (Antofagasta) [online]. 2020, vol.39, n.1, pp.135-152. ISSN 0716-0917.  http://dx.doi.org/10.22199/issn.0717-6279-2020-01-0009.

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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