A cryptography method based on hyperbolic balancing and Lucas-balancing functions
DOI:
https://doi.org/10.22199/issn.0717-6279-2020-01-0009Keywords:
Balancing numbers, Lucas-balancing numbers, Hyperbolic balancing functions, Hyperbolic Lucas-balancing functions, CryptographyAbstract
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.
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