A Two-Dimensional Map Derived From An Ordinary Difference Equation of mKdV and Its Properties

Abstract

The discrete modified Korteweg–de Vries (mKdV) is a class of discrete integrable systems that may be distinguished as integrable partial difference equations (PΔE) and integrable ordinary difference equations (OΔE). By considering traveling wave solutions, the OΔE mKdV can be obtained from PΔE mKdV. Meanwhile, a mapping can be constructed from an OΔE mKdV. In this paper, we will focus on producing a new map using a process (replacement), the interchange of a single parameter, and an integral and investigate its properties.

A Two-Dimensional mKdV Linear Map and Its Application in Digital Image Cryptography

“…In [11], the authors proposed an algorithm that involves scrambling pixel positions and changing the intensities of the pixels (see [12] for a different method in hiding an image using reference point coding to embed data in the spatial domain). In this article, a two-dimensional linear map derived from a partial discrete equation (partial discrete mKdV equation) with Consistency Around the Cube (CAC) properties will be discussed (see [13,14] for the construction of a generalized mKdV map and the investigation of its properties) and applied in cryptographic encoding algorithms for digital image data (see [15] for digital text data). This article consists of four Sections.…”