Enhanced digital chaotic maps based on bit reversal with applications in random bit generators

• Published in: Information sciences 2020-02, Vol.512, p.1155-1169
• Main Authors: Alawida, Moatsum, Samsudin, Azman, Teh, Je Sen
• Format: Article
• Language: English
• Subjects: Chaotification; Digital chaotic map; Fixed point arithmetic; Henon map; Logistic map; Pseudorandom bit generator
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2019.10.055

•A mathematical proof showcases the capability of the proposed bit reversal method.•1D & 2D maps have improved chaotic properties when modified by the proposed method.•The modified maps outperform their classical maps and other chaotification methods.•The proposed bit generator depicts sufficient randomness with no statistical bias. Digital chaotic maps are becoming increasingly popular in the area of cryptography due to commonalities but have drawbacks which adversely effect security strength. Thus, enhancing digital chaotic maps in terms of their chaoticity and statistical properties contributes towards the improvement of chaos-based cryptography. This paper proposes a bit reversal approach to address these issues. The proposed method modifies chaotic state values (represented as fixed point numbers) by reversing the order of their fractional bits. Experimental verification indicates that chaotic maps modified by the proposed approach depict better chaotic performance, have higher complexity and larger chaotic parameter range. These results exceed those of existing digital chaotic maps and other chaotification methods. The simplicity of the proposed bit reversal approach and the use of fixed point representation makes it easy to implement on any computing platform. This approach is also highly flexible as it does not require any external inputs, making it a universal method for enhancing any digital chaotic map. As a proof-of-concept, a pseudorandom bit generator (PRBG) was designed based on cascading chaotic maps modified by the proposed method. Simulation and security analysis indicate that the proposed PRBG is statistically random, has a uniform data distribution and high key sensitivity.