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The Eigenvalue Complexity of Sequences in the Real Domain

1
School of Software, Nanchang University, Nanchang 330031, China
2
School of Automation, Huazhong University of Science & Technique, Wuhan 430074, China
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(12), 1194; https://doi.org/10.3390/e21121194
Received: 5 November 2019 / Revised: 27 November 2019 / Accepted: 3 December 2019 / Published: 5 December 2019
(This article belongs to the Section Complexity)
The eigenvalue is one of the important cryptographic complexity measures for sequences. However, the eigenvalue can only evaluate sequences with finite symbols—it is not applicable for real number sequences. Recently, chaos-based cryptography has received widespread attention for its perfect dynamical characteristics. However, dynamical complexity does not completely equate to cryptographic complexity. The security of the chaos-based cryptographic algorithm is not fully guaranteed unless it can be proven or measured by cryptographic standards. Therefore, in this paper, we extended the eigenvalue complexity measure from the finite field to the real number field to make it applicable for the complexity measurement of real number sequences. The probability distribution, expectation, and variance of the eigenvalue of real number sequences are discussed both theoretically and experimentally. With the extension of eigenvalue, we can evaluate the cryptographic complexity of real number sequences, which have a great advantage for cryptographic usage, especially for chaos-based cryptography. View Full-Text
Keywords: eigenvalue; real number sequences; complexity eigenvalue; real number sequences; complexity
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Liu, L.; Xiang, H.; Li, R.; Hu, H. The Eigenvalue Complexity of Sequences in the Real Domain. Entropy 2019, 21, 1194.

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