Codification of Images Based on Deterministic Brownian Motion

Advances and developments in electronic transactions and computing have led to the need to develop new techniques to ensure information security. In this sense, cryptographic algorithms protect information from any attacks. One of the most important requirements for encryption systems is the generation of time series with strong random properties. An example of this type of behavior is Brownian motion, a dynamic behavior with random changes over time that occurs in many vital functions related to fluid environments, stock behavior, or even renewable energy generation. In this paper, we present a method for image encryption based on deterministic Brownian-like motion. By analyzing the dynamics of a fully deterministic set of differential equations reproducing Brownian-like motion, an algorithm for generating binary sequences for image encryption is proposed and the probability distribution of this system is determined. The performance of the proposed algorithm is evaluated using the security tests for cypher schemes such as entropy, pixel correlation and quality of the cypher device.