Abstract
Because of their complex behaviour, simple mathematical and digital hardware representation, one-dimensional (1D) chaotic functions were the earliest choices of cryptologists for applying chaos theory to cryptography. It was discovered later that most of these functions suffer from orbits collapsing into a specific period, especially under finite precision realization and weakness because of their limited number of control parameter(s). This in turn exposed many security issues and was proven to be vulnerable to various types of attacks. This paper addresses the issue of limited number of control parameters by introducing a 1D chaotic function with five control parameters (in addition to the initial condition). Analysis of the function implies its chaotic properties in addition to its ability to generate a cryptographically secured random stream of numbers. To further elaborate on its robustness, a new image encryption algorithm incorporating the function as its random number generator is presented. Various analyses of the new scheme confirm it to be secure with good confusion-diffusion properties.