Abstract
Due to the influence of finite calculation accuracy and binary quantization method, the performance of chaotic binary sequences has been degraded in varying degrees, and some sequences emerge as multi-period phenomena. Aiming at the problem that it is difficult to accurately detect this phenomenon, this paper proposes a multi-period positioning algorithm (MPPA), which can accurately detect and locate the accurate period and local period phenomena contained in chaotic binary sequences. In order to test the effectiveness and correctness of the algorithm, the multi-period characteristics of logistic binary sequences with different calculation accuracy are analyzed. MPPA evaluates the randomness of binary sequences from a new perspective, which provides a new idea for the analysis of cryptographic security of chaotic sequences.
Highlights
In order to compensate for the shortcomings of the aforementioned method, we designed a multi-period positioning algorithm (MPPA) based on the periodic detection matrix and monotonic stack technology
Entropy 2022, 24, 331 a weak randomness problem will appear in the local range of the chaotic binary sequence (Figure 1), which is called the local periodicity of the binary sequence in this paper
To solve the problem of the difficult detection of locally weak randomness of chaotic To solve the problem of the difficult detection of locally weak randomness of chaotic binary sequences, a multi-period positioning algorithm is designed based on the periodic binary sequences, a multi-period positioning algorithm is designed based on the periodic detection matrix and monotone stack technology
Summary
At present, related scholars generally use common detection methods for performance analysis of chaotic binary sequences, such as autocorrelation detection, discrete Fourier transform, linear complexity [11,12], entropy theory [13–15], frequency test, etc. From the perspective of encryption, the appearance of this phenomenon is bound to affect the security and anti-attack ability of chaotic sequence ciphers This phenomenon is difficult to locate and evaluate accurately by employing commonly used detection methods such as frequency detection, autocorrelation, poker detection, approximate entropy, overlapping subsequence, and binary derivation. In order to compensate for the shortcomings of the aforementioned method, we designed a multi-period positioning algorithm (MPPA) based on the periodic detection matrix and monotonic stack technology This algorithm can precisely locate the accurate period and local period phenomena contained in the chaotic binary sequence. MPPA enriches the set of randomness detection methods for chaotic binary sequences and provides a new idea for the analysis of the security of chaotic stream ciphers
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