Balancing and Lucas-Balancing Numbers and their Application to Cryptography

Sujata Swain (Department of Computer Science, DAV Unit-8, Bhubaneswar)
Chidananda Pratihary (Department of Mathematics, National Institute of Technology, Rourkela)
Prasanta Kumar Ray (Department of Mathematics, VSS University of Technology, Burla)

ComEngApp : Computer Engineering and Applications Journal
Vol 5 No 1 (2016)

It is well known that, a recursive relation for the sequence  is an equation that relates  to certain of its preceding terms . Initial conditions for the sequence  are explicitly given values for a finite number of the terms of the sequence. The recurrence relation is useful in certain counting problems like Fibonacci numbers, Lucas numbers, balancing numbers, Lucas-balancing numbers etc. In this study, we use the recurrence relations for both balancing and Lucas-balancing numbers and examine their application to cryptography.