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Mathematics
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Information Theory, Cryptography, Randomness and Statistical Modeling
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Information Theory, Cryptography, Randomness and Statistical Modeling

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (29 February 2020) | Viewed by 13795

Special Issue Editor

Prof. Dr. Boris Ryabko

E-Mail Website
Guest Editor
1. Federal Research Center for Information and Computational Technologies, 630090 Novosibirsk, Russia
2. Department of Information Technologies, Novosibirsk State University, 630090 Novosibirsk, Russia
Interests: information theory; cryptography and steganography; mathematical statistics and prediction; complexity of algorithms and mathematical biology
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Information theory, cryptography, and randomness have mutually enriched each other for decades. Among numerous examples, there is Kolmogorov’s algorithmic information theory, which emerged at the intersection of information theory and randomness, as well as an important one-time pad encryption, which is closely related to all three concepts. This Special Issue, entitled “Information Theory, Cryptography, and Randomness”, aims to develop and discuss theoretical and applied issues related to these areas.

Topics of interest include but are not limited to:

  • Random and pseudo-random generators;
  • Statistical tests for randomness;
  • Information-theoretical cryptography;
  • Cryptographical tools with proven properties;
  • Algorithmic randomness and cryptography.

Prof. Dr. Boris Ryabko
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (5 papers)

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Research

10 pages, 1191 KiB  
Article
Using Data-Compressors for Classification Hunting Behavioral Sequences in Rodents as “Ethological Texts”
by Jan Levenets, Anna Novikovskaya, Sofia Panteleeva, Zhanna Reznikova and Boris Ryabko
Mathematics 2020, 8(4), 579; https://doi.org/10.3390/math8040579 - 14 Apr 2020
Cited by 3 | Viewed by 2089
Abstract
One of the main problems in comparative studying animal behavior is searching for an adequate mathematical method for evaluating the similarities and differences between behavioral patterns. This study aims to propose a new tool to evaluate ethological differences between species. We developed the [...] Read more.
One of the main problems in comparative studying animal behavior is searching for an adequate mathematical method for evaluating the similarities and differences between behavioral patterns. This study aims to propose a new tool to evaluate ethological differences between species. We developed the new compression-based method for the homogeneity testing and classification to investigate hunting behavior of small mammals. A distinction of this approach is that it belongs to the framework of mathematical statistics and allows one to compare the structural characteristics of any texts in pairwise comparisons. To validate a new method, we compared the hunting behaviors of different species of small mammals as ethological “texts.” To do this, we coded behavioral elements with different letters. We then tested the hypothesis whether the behavioral sequences of different species as “texts” are generated either by a single source or by different ones. Based on association coefficients obtained from pairwise comparisons, we built a new classification of types of hunting behaviors, which brought a unique insight into how particular elements of hunting behavior in rodents changed and evolved. We suggest the compression-based method for homogeneity testing as a relevant tool for behavioral and evolutionary analysis. Full article
(This article belongs to the Special Issue Information Theory, Cryptography, Randomness and Statistical Modeling)
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13 pages, 288 KiB  
Article
Four Constructions of Asymptotically Optimal Codebooks via Additive Characters and Multiplicative Characters
by Xia Wu and Wei Lu
Mathematics 2019, 7(12), 1144; https://doi.org/10.3390/math7121144 - 23 Nov 2019
Cited by 1 | Viewed by 1745
Abstract
In this paper, we present four new constructions of complex codebooks with multiplicative characters, additive characters, and quadratic irreducible polynomials and determine the maximal cross-correlation amplitude of these codebooks. We prove that the codebooks we constructed are asymptotically optimal with respect to the [...] Read more.
In this paper, we present four new constructions of complex codebooks with multiplicative characters, additive characters, and quadratic irreducible polynomials and determine the maximal cross-correlation amplitude of these codebooks. We prove that the codebooks we constructed are asymptotically optimal with respect to the Welch bound. Moreover, we generalize the result obtained by Zhang and Feng and contain theirs as a special case. The parameters of these codebooks are new. Full article
(This article belongs to the Special Issue Information Theory, Cryptography, Randomness and Statistical Modeling)
10 pages, 275 KiB  
Article
Low-Entropy Stochastic Processes for Generating k-Distributed and Normal Sequences, and the Relationship of These Processes with Random Number Generators †
by Boris Ryabko
Mathematics 2019, 7(9), 838; https://doi.org/10.3390/math7090838 - 10 Sep 2019
Cited by 3 | Viewed by 1732
Abstract
An infinite sequence x 1 x 2 … of letters from some alphabet { 0 , 1 , … , b − 1 } , b ≥ 2 , is called k-distributed ( k ≥ 1 ) if any k-letter block [...] Read more.
An infinite sequence x 1 x 2 … of letters from some alphabet { 0 , 1 , … , b − 1 } , b ≥ 2 , is called k-distributed ( k ≥ 1 ) if any k-letter block of successive digits appears with the frequency b − k in the long run. The sequence is called normal (or ∞-distributed) if it is k-distributed for any k ≥ 1 . We describe two classes of low-entropy processes that with probability 1 generate either k-distributed sequences or ∞-distributed sequences. Then, we show how those processes can be used for building random number generators whose outputs are either k-distributed or ∞-distributed. Thus, these generators have statistical properties that are mathematically proven. Full article
(This article belongs to the Special Issue Information Theory, Cryptography, Randomness and Statistical Modeling)
19 pages, 9855 KiB  
Article
Complete Ensemble Empirical Mode Decomposition on FPGA for Condition Monitoring of Broken Bars in Induction Motors
by Martin Valtierra-Rodriguez, Juan Pablo Amezquita-Sanchez, Arturo Garcia-Perez and David Camarena-Martinez
Mathematics 2019, 7(9), 783; https://doi.org/10.3390/math7090783 - 25 Aug 2019
Cited by 12 | Viewed by 3385
Abstract
Empirical mode decomposition (EMD)-based methods are powerful digital signal processing techniques because they do not need a priori information of the target signal due to their intrinsic adaptive behavior. Moreover, they can deal with non-linear and non-stationary signals. This paper presents the field [...] Read more.
Empirical mode decomposition (EMD)-based methods are powerful digital signal processing techniques because they do not need a priori information of the target signal due to their intrinsic adaptive behavior. Moreover, they can deal with non-linear and non-stationary signals. This paper presents the field programmable gate array (FPGA) implementation for the complete ensemble empirical mode decomposition (CEEMD) method, which is applied to the condition monitoring of an induction motor. The CEEMD method is chosen since it overcomes the performance of EMD and EEMD (ensemble empirical mode decomposition) methods. As a first application of the proposed FPGA-based system, the proposal is used as a processing technique for feature extraction in order to detect and classify broken rotor bar faults in induction motors. In order to obtain a complete online monitoring system, the feature extraction and classification modules are also implemented on the FPGA. Results show that an average effectiveness of 96% is obtained during the fault detection. Full article
(This article belongs to the Special Issue Information Theory, Cryptography, Randomness and Statistical Modeling)
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19 pages, 8152 KiB  
Article
Development of Public Key Cryptographic Algorithm Using Matrix Pattern for Tele-Ultrasound Applications
by Seung-Hyeok Shin, Won-Sok Yoo and Hojong Choi
Mathematics 2019, 7(8), 752; https://doi.org/10.3390/math7080752 - 17 Aug 2019
Cited by 19 | Viewed by 4089
Abstract
A novel public key cryptographic algorithm using a matrix pattern is developed to improve encrypting strength. Compared to the Rivest–Sharmir–Adleman (RSA) and Elliptic Curve Cryptography (ECC) algorithms, our proposed algorithm has superior encrypting strength due to several unknown quantities and one additional sub-equation [...] Read more.
A novel public key cryptographic algorithm using a matrix pattern is developed to improve encrypting strength. Compared to the Rivest–Sharmir–Adleman (RSA) and Elliptic Curve Cryptography (ECC) algorithms, our proposed algorithm has superior encrypting strength due to several unknown quantities and one additional sub-equation during the encrypting process. Our proposed algorithm also provides a faster encoding/decoding speed when the patient’s images for tele-ultrasound applications are transmitted/received, compared to the RSA and ECC encrypting algorithms, because it encodes/decodes the plain memory block by simple addition and multiplication operations of n terms. However, the RSA and ECC algorithms encode/decode each memory block using complex mathematical exponentiation and congruence. To implement encrypting algorithms for tele-ultrasound applications, a streaming server was constructed to transmit the images to the systems using ultrasound machines. Using the obtained ultrasound images from a breast phantom, we compared our developed algorithm, utilizing a matrix pattern, with the RSA and ECC algorithms. The elapsed average time for our proposed algorithm is much faster than that for the RSA and ECC algorithms. Full article
(This article belongs to the Special Issue Information Theory, Cryptography, Randomness and Statistical Modeling)
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