Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems

Abstract

Traditionally, chaotic systems are built on the domain of infinite precision in mathematics. However, the quantization is inevitable for any digital devices, which causes dynamical degradation. To cope with this problem, many methods were proposed, such as perturbing chaotic states and cascading multiple chaotic systems. This paper aims at developing a novel methodology to design the higher-dimensional digital chaotic systems (HDDCS) in the domain of finite precision. The proposed system is based on the chaos generation strategy controlled by random sequences. It is proven to satisfy the Devaney's definition of chaos. Also, we calculate the Lyapunov exponents for HDDCS. The application of HDDCS in image encryption is demonstrated via FPGA platform. As each operation of HDDCS is executed in the same fixed precision, no quantization loss occurs. Therefore, it provides a perfect solution to the dynamical degradation of digital chaos.

12 pages

References in corpus (5)

• Cryptanalyzing image encryption using chaotic logistic map
• Increasing Average Period Lengths by Switching of Robust Chaos Maps in Finite Precision
• Network Analysis of the State Space of Discrete Dynamical Systems
• Theoretical design and circuit implementation of integer domain chaotic systems
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Cited by in corpus (6)

• Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks
• Cryptanalysis of a Chaotic Image Encryption Algorithm Based on Information Entropy
• Cryptanalyzing an Image-Scrambling Encryption Algorithm of Pixel Bits
• From Chaos to Pseudo-Randomness: A Case Study on the 2D Coupled Map Lattice
• Cryptanalysis of a Classical chaos-based cryptosystem with some quantum cryptography features
• Design and ARM-embedded implementation of a chaotic map-based multicast scheme for multiuser speech wireless communication