Special Issue "Algebra and Number Theory"
Deadline for manuscript submissions: 31 July 2020.
Interests: Algebra; Number Theory; Information Theory; Cryptography
Interests: Lattice Packings; Number Fields; Algebraic Coding Theory; Modulation Schemes; Cryptology and Algorithmic Complexity
Interests: Mathematics; Algebra; Number Theory
Algebra and number theories have always attracted the human mind, stimulated man’s curiosity, and have significantly contributed to forging the mathematical disciplines that pervade every aspect of modern life. Although it is difficult to foresee the future domains of application of aimless pure mathematical discoveries, today’s dominating fields are information theory and cryptography.
The prophetic words of Abraham Adrian Albert, stating that “abstract cryptography is identical with abstract mathematics”, could not be truer today in view of the reliance of modern society on cryptography for connectivity and intelligent systems. The prophecy may have included fascinating branches and problems in algebra and number theory; in particular, those of a computational and combinatorial nature such as the following:
- Finite fields
- Generation of sequences with random characteristics and the study of their complexity
- The intractability of standard lattice problems, such as the shortest vector and the closest vector problems
- Non-associative algebraic structures
- The intractability of the general decoding problem for linear codes
- Pairings, isogenies, and arithmetic of elliptic curves
- Integer factoring, distribution of primes, and primality proving
Recently, applications involving many of the above branches and problems have been emerging for potential use in post-quantum cryptography. Although this trend is in line with today’s credo in applicable mathematics, the most relevant aspects of algebra and number theory are ultimately their beauty and the satisfaction of the human spirit: Fermat’s Last Theorem is likely the most eloquent example of that.
Prof. Michele Elia
Prof. J. Carmelo Interlando
Dr. Nadir Murru
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 papers will be 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 monthly 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 1200 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.
- Computational complexity
- Diophantine equations
- Elliptic curves
- Linear codes
- Pseudorandom sequences.