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Fibonacci shift operation on Fibonacci numbers of order m

Prasad B.

Control and Cybernetics

2016

Vol. 45, no. 2

259--266

Fibonacci codes of diﬀerent orders are of variable length. They are used for encoding of numbers and ﬁnd applications in information and coding theory. The Fibonacci binary encoding and computation of its values are closely associated with Fibonacci shift operations. Walder et al. (2012) established a relation for kth Fibonacci left shift for Fibonacci numbers of order m = 2,3. In this paper, we establish a relation for kth Fibonacci left shift for Fibonacci numbers of order m = 4 and we generalize the formula for kth Fibonacci left shift for the Fibonacci numbers of all orders.

Multivariable extension of m sequences for Fibonacci numbers in cryptography

Prasad B.

Control and Cybernetics

2015

Vol. 44, no. 4

519--526

In this paper, we introduce multivariable extension of m sequences of the Fibonacci number polynomials of order m and a new Sn matrix of order m. Consequently, we discuss various properties of the Sn matrix. The polynomial, derived therefrom, hj, contains m multiple variables which improves the cryptography protection and security, and complexity increases as m increases.