The Dynamic Analysis of a Novel Reconfigurable Cubic Chaotic Map and Its Application in Finite Field

Abstract

Dynamic degradation occurs when chaotic systems are implemented on digital devices, which seriously threatens the security of chaos-based pseudorandom sequence generators. The chaotic degradation shows complex periodic behavior, which is often ignored by designers and seldom analyzed in theory. Not knowing the exact period of the output sequence is the key problem that affects the application of chaos-based pseudorandom sequence generators. In this paper, two cubic chaotic maps are combined, which have symmetry and reconfigurable form in the digital circuit. The dynamic behavior of the cubic chaotic map and the corresponding digital cubic chaotic map are analyzed respectively, and the reasons for the complex period and weak randomness of output sequences are studied. On this basis, the digital cubic chaotic map is optimized, and the complex periodic behavior is improved. In addition, a reconfigurable pseudorandom sequence generator based on the digital cubic chaotic map is constructed from the point of saving consumption of logical resources. Through theoretical and numerical analysis, the pseudorandom sequence generator solves the complex period and weak randomness of the cubic chaotic map after digitization and makes the output sequence have better performance and less resource consumption, which lays the foundation for applying it to the field of secure communication.

Adaptive Aquila Optimizer Combining Niche Thought with Dispersed Chaotic Swarm

“…The logistic mapping [ 32 ], cubic mapping [ 33 ], tent mapping [ 34 ] and DLCS mapping were used to generate sequences of a length of 1000 each on initial values with small differences and normalized to form a two-dimensional planar distribution in the interval [0, 1] for 30 uniformity comparison experiments; the metrics that constitute the chaotic model are shown in Table 2 . When the ratio of both adjacent statistical values of a chaotic distribution graph is closer to 1, the uniformity of the chaotic system is higher.…”

WAM 3D Discrete Chaotic Map for Secure Communication Applications

“…Whether the chaotic system is based on discrete or continuous time parameters, the multidimensional system has stronger randomness, more chaotic attractors, better confidentiality, larger secret key space, and higher efficiency in securing communications and data [29]. In this article, a multidimensional discrete chaotic system is proposed to be used in constructing chaotic sequence and chaotic encryption.…”

Symmetric Oscillator: Special Features, Realization, and Combination Synchronization

“…Several studies have provided important results on chaos [1][2][3]. Chaos was observed in a memristive system [4], glucose-insulin regulatory system [5], financial system [6], and modified logistic map [7], etc.…”