A Note On the Bounds for the Generalized Fibonacci-p-Sequence and its Application in Data-Hiding

TL;DR

This paper establishes bounds for the generalized Fibonacci-p-sequence and demonstrates their application in enhancing data-hiding techniques by increasing the number of bit-planes used for steganography without significant image quality loss.

Contribution

It provides new bounds for the generalized Fibonacci-p-sequence and applies these results to improve steganographic data hiding methods.

Findings

Bounds for the generalized Fibonacci-p-sequence are derived.

The ratio of consecutive terms converges to a polynomial of degree p.

Enhanced data hiding capacity with minimal image distortion.

Abstract

In this paper, we suggest a lower and an upper bound for the Generalized Fibonacci-p-Sequence, for different values of p. The Fibonacci-p-Sequence is a generalization of the Classical Fibonacci Sequence. We first show that the ratio of two consecutive terms in generalized Fibonacci sequence converges to a p-degree polynomial and then use this result to prove the bounds for generalized Fibonacci-p sequence, thereby generalizing the exponential bounds for classical Fibonacci Sequence. Then we show how these results can be used to prove efficiency for data hiding techniques using generalized Fibonacci sequence. These steganographic techniques use generalized Fibonacci-p-Sequence for increasing number available of bit-planes to hide data, so that more and more data can be hidden into the higher bit-planes of any pixel without causing much distortion of the cover image. This bound can be used as a theoretical proof for efficiency of those techniques, for instance it explains why more and more data can be hidden into the higher bit-planes of a pixel, without causing considerable decrease in PSNR.