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Mathematics
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Advances in Mathematical Cryptography and Information Security with Applications
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Advances in Mathematical Cryptography and Information Security with Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 31 July 2026 | Viewed by 1631

Special Issue Editor

Prof. Dr. Muzafer Saracevic

E-Mail Website1 Website2
Guest Editor
Department of Computer Science, University of Novi Pazar, 36300 Novi Pazar, Serbia
Interests: cryptography; steganography; data protection; machine learning; applied mathematics

Special Issue Information

Dear Colleagues,

This Special Issue provides a platform for researchers, practitioners, and industry experts to present innovative approaches, emerging trends, and cutting-edge technologies in mathematical cryptography and information security. It encompasses the development of novel encryption techniques grounded in number theory and the mathematical foundations that underpin cryptographic protocols. The study of cryptanalysis alongside these algorithms plays a crucial role in identifying potential weaknesses strengthening security measures.

Another key area of focus is the exploration of cryptographic algorithms and their practical applications across diverse domains—ranging from securing financial transactions to safeguarding sensitive personal information. This includes research on cryptographic protocols for secure communication and data protection, as well as the integration of machine learning to enhance cryptographic methods and detect vulnerabilities in real time, paving the way for adaptive security systems.

Emerging challenges and opportunities are also being explored in quantum cryptography and blockchain security. These rapidly evolving fields are gaining prominence efforts to protect data against quantum computing threats and to establish trust in decentralized systems like blockchain. The intersection of quantum technologies with cryptographic systems offers exciting prospects for secure communication methods that are resilient against future technological advancements.

Prof. Dr. Muzafer Saracevic
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 250 words) can be sent to the Editorial Office for assessment.

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.

Keywords

  • mathematical cryptography
  • information security and public-key cryptosystems
  • post-quantum cryptography and secure communication
  • cryptographic protocols and data privacy
  • blockchain security and cybersecurity applications
  • applied cryptography

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (3 papers)

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Research

20 pages, 3073 KB  
Article
Polygon Dissections via Lucas-Inspired Encoding
by Aybeyan Selim, Muzafer Saracevic and Omer Aydin
Mathematics 2026, 14(10), 1631; https://doi.org/10.3390/math14101631 - 11 May 2026
Viewed by 3
Abstract
Classical enumeration of triangulations and angulations of convex polygons is governed by the Catalan and Fuss–Catalan families. In this paper, we introduce a Lucas-inspired symbolic encoding framework for a restricted subclass of triangulations, called Lucas-compatible triangulations. The purpose of the framework is not [...] Read more.
Classical enumeration of triangulations and angulations of convex polygons is governed by the Catalan and Fuss–Catalan families. In this paper, we introduce a Lucas-inspired symbolic encoding framework for a restricted subclass of triangulations, called Lucas-compatible triangulations. The purpose of the framework is not to replace classical Catalan enumeration, but to provide a complementary structural layer that records admissible local reductions through two canonical operations. Within this restricted setting, the geometric objects remain Catalan-based, whereas the associated encoding space satisfies a Fibonacci-type recurrence. We formalize the reduction model, define admissible Lucas words, and prove structural properties of the encoding map. We further present recursive generation algorithms, analyze their output-sensitive complexity, and compare the size of the encoding space with the size of the full triangulation space. In addition, we discuss geometric constraints, equivalence phenomena, and potential uses of the encoding in compact representation, constrained enumeration, and recursion-guided generation of polygon dissections. Computational experiments support the theoretical predictions and illustrate how the proposed encoding yields a compressed symbolic view of a restricted but mathematically meaningful class of dissections. Full article
(This article belongs to the Special Issue Advances in Mathematical Cryptography and Information Security with Applications)
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31 pages, 1339 KB  
Article
Quantum Secure Authentication and Key Exchange Protocol for UAV-Assisted VANETs
by Hyewon Park and Yohan Park
Mathematics 2026, 14(5), 820; https://doi.org/10.3390/math14050820 - 28 Feb 2026
Viewed by 459
Abstract
The integration of unmanned aerial vehicles (UAVs) into vehicular ad hoc networks (VANETs) has emerged as a promising solution to overcome the limited coverage of conventional roadside unit (RSU)-based infrastructures. However, UAVs operate in open environments and cannot be fully trusted, while the [...] Read more.
The integration of unmanned aerial vehicles (UAVs) into vehicular ad hoc networks (VANETs) has emerged as a promising solution to overcome the limited coverage of conventional roadside unit (RSU)-based infrastructures. However, UAVs operate in open environments and cannot be fully trusted, while the rapid advancement of quantum computing threatens the long-term security of classical public-key cryptographic systems. As a result, many existing UAV-based VANET authentication schemes face fundamental limitations in future deployments. Most existing schemes either lack post-quantum security or incur excessive computational and communication overhead, making them unsuitable for real-time and high-mobility vehicular environments. In addition, the common assumptions of trusted UAVs do not align with realistic threat models. To address these issues, this paper proposes a lightweight post-quantum authentication and key exchange protocol based on the module learning with errors (MLWE) problem and physically unclonable functions (PUFs). The proposed scheme treats UAVs as untrusted relay nodes and excludes them from session key generation. Its security is evaluated using informal analysis, the real-or-random (RoR) model, BAN logic, and AVISPA, while performance evaluation indicates improved efficiency compared to existing schemes. Full article
(This article belongs to the Special Issue Advances in Mathematical Cryptography and Information Security with Applications)
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19 pages, 512 KB  
Article
Limiting the Number of Possible CFG Derivative Trees During Grammar Induction with Catalan Numbers
by Aybeyan Selim, Muzafer Saracevic and Arsim Susuri
Mathematics 2026, 14(2), 249; https://doi.org/10.3390/math14020249 - 9 Jan 2026
Viewed by 773
Abstract
Grammar induction runs into a serious problem due to the exponential growth of the number of possible derivation trees as sentence length increases, which makes unsupervised parsing both computationally demanding and highly indeterminate. This paper proposes a mathematics-based approach that alleviates this combinatorial [...] Read more.
Grammar induction runs into a serious problem due to the exponential growth of the number of possible derivation trees as sentence length increases, which makes unsupervised parsing both computationally demanding and highly indeterminate. This paper proposes a mathematics-based approach that alleviates this combinatorial complexity by introducing structural constraints based on Catalan and Fuss–Catalan numbers. By limiting the depth of the tree, the degree of branching and the form of derivation, the method significantly narrows the search space, while retaining the full generative power of context-free grammars. A filtering algorithm guided by Catalan structures is developed that incorporates these combinatorial constraints directly into the execution process, with formal analysis showing that the search complexity, under realistic assumptions about depth and richness, decreases from exponential to approximately polynomial. Experimental results on synthetic and natural-language datasets show that the Catalan-constrained model reduces candidate derivation trees by approximately 60%, improves F1 accuracy over unconstrained and depth-bounded baselines, and nearly halves average parsing time. Qualitative evaluation further indicates that the induced grammars exhibit more balanced and linguistically plausible structures. These findings demonstrate that Catalan-based structural constraints provide an elegant and effective mechanism for controlling ambiguity in grammar induction, bridging formal combinatorics with practical syntactic learning. Full article
(This article belongs to the Special Issue Advances in Mathematical Cryptography and Information Security with Applications)
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