Fractional two-dimensional discrete chaotic map and its applications to the information security with elliptic-curve public key cryptography

Abstract

A novel fractional two-dimensional triangle function combination discrete chaotic map is proposed by use of the discrete fractional calculus. The chaos behaviors are then discussed when the difference order is a fractional one. The bifurcation diagrams, the largest Lyapunov exponent and the phase portraits are displayed, especially, the elliptic curve public key cryptosystem is used in color image encryption algorithm.

Keywords

Chaos discrete fractional calculus fractional two-dimensional triangle function combination discrete chaotic map image encryption elliptic-curve in finite field

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