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Mathematics
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Advances in Mathematics Cryptography and Information Security
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Advances in Mathematics Cryptography and Information Security

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

Deadline for manuscript submissions: 30 June 2026 | Viewed by 1012

Special Issue Editor

Prof. Dr. Ferucio Laurentiu Tiplea

E-Mail Website
Guest Editor
Department of Computer Science, Alexandru Ioan Cuza University of Iasi, 700506 Iasi, Romania
Interests: higher-order residuosity in cryptography; cryptographic protocols; cryptographic multi-linear maps; code-based cryptography
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Over the last decade, we have witnessed an extraordinary expansion of cryptography across nearly all sectors of daily life. Many of the scenarios once envisioned by cryptographers—such as elliptic-curve cryptography, zero-knowledge proofs, oblivious RAM, attribute-based encryption, searchable encryption, secure computation with encrypted data, and post-quantum cryptography—have already been implemented or are on the verge of large-scale deployment in a wide range of applications. Indeed, we are currently experiencing a true golden age of cryptography.

This rapid development has been made possible by solid mathematical foundations, including computational number theory, algebraic structures, linear algebra, probability and statistics, discrete mathematics, and algebraic geometry. In most cases, a deep mathematical investigation has been essential for the construction of viable cryptographic primitives.

This Special Issue—the first in a planned series dedicated to the interplay between mathematics and cryptography—aims to attract research articles that propose or analyze cryptographic constructions with well-defined and rigorously justified mathematical underpinning. While we do not restrict the thematic scope, we particularly encourage submissions in the following areas:

  • Classical cryptography;
  • Elliptic-curve cryptography;
  • Residuosity-based cryptography;
  • Code-based cryptography;
  • Lattice-based cryptography;
  • Cryptographic protocols;
  • Security and privacy models.

Papers on quantum cryptography or quantum algorithms related to mathematical structures underlying cryptographic primitives will also be considered.

Prof. Dr. Ferucio Laurentiu Tiplea
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

  • classical cryptography
  • elliptic-curve cryptography
  • residuosity-based cryptography
  • code-based cryptography
  • lattice-based cryptography
  • cryptographic protocols
  • security
  • privacy

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Published Papers (2 papers)

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Research

21 pages, 379 KB  
Article
On the Structural Solvability of MLWE with Rank-Deficient Public Matrices
by Nor Siti Khadijah Arunah, Amir Hamzah Abd Ghafar, Muhammad Asyraf Asbullah and Muhammad Rezal Kamel Ariffin
Mathematics 2026, 14(10), 1749; https://doi.org/10.3390/math14101749 - 19 May 2026
Viewed by 62
Abstract
The security of Module Learning With Errors (MLWE) relies on the assumption that the public matrix is sampled uniformly and forms a full-rank operator. In this work, we examine the structural consequences of relaxing this assumption by considering public matrices that demonstrate slot-wise [...] Read more.
The security of Module Learning With Errors (MLWE) relies on the assumption that the public matrix is sampled uniformly and forms a full-rank operator. In this work, we examine the structural consequences of relaxing this assumption by considering public matrices that demonstrate slot-wise rank deficiency under the Number Theoretic Transform (NTT). Focusing on the case where each NTT slot matrix has rank 1, we show that this leads to enlarged left nullspace, which allows the elimination of the secret component s1, reducing the original relation to a linear system consisting only of s2. Given partial knowledge of s2, this projected system admits a unique solution once a sufficient number of independent constraints is available. After recovering s2, the problem of determining s1 reduces to solving a bounded linear system, which can be viewed as a structured instance of the Short Integer Solution (SIS) problem. These results provide a dimension-based characterization of solvability under slot-wise rank-deficient public matrices. Using ML-DSA as a concrete instantiation, we illustrate how such structural deviations affect the behavior of the system and discuss simple safeguards, such as rank verification during key generation, to mitigate these issues. Full article
(This article belongs to the Special Issue Advances in Mathematics Cryptography and Information Security)
20 pages, 326 KB  
Article
The Jacobi Symbol Problem for Quadratic Congruences and Applications to Cryptography
by Ferucio Laurenţiu Ţiplea
Mathematics 2026, 14(3), 465; https://doi.org/10.3390/math14030465 - 29 Jan 2026
Viewed by 542
Abstract
Modern security models for public-key cryptography, such as one-way encryption under chosen plaintext attack (OWE-CPA) or indistinguishability under chosen plaintext attack (IND-CPA), rely on reductions between the security of cryptographic schemes and well-studied hard problems, such as integer factorization, discrete logarithm, quadratic residuosity, [...] Read more.
Modern security models for public-key cryptography, such as one-way encryption under chosen plaintext attack (OWE-CPA) or indistinguishability under chosen plaintext attack (IND-CPA), rely on reductions between the security of cryptographic schemes and well-studied hard problems, such as integer factorization, discrete logarithm, quadratic residuosity, or learning with errors. The reduction can go from the hard problem to the security property under study, or vice versa, or in both directions (in which case we say there is an equivalence). Equivalences fundamentally tie the security property to the hard problem, thus offering multiple benefits. But obtaining an equivalence between a security property and a computational hard problem can be challenging, as is the case with the equivalence between the OWE-CPA security of the textbook RSA cryptosystem and the integer factorization problem. In this paper, we introduce a new computational problem, namely, distinguishing the Jacobi symbols of the solutions of a quadratic congruence modulo an RSA modulus (JSP(QC)). We show that this problem is at least as hard as the quadratic residuosity problem. Then, we show that the IND-CPA security of two public-key encryption schemes due to Cocks is equivalent to JSP(QC). We then specialize JSP(QC) to roots of quadratic residues and establish several computational indistinguishability results. Full article
(This article belongs to the Special Issue Advances in Mathematics Cryptography and Information Security)
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