Algebra and Number Theory
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Algebra, Geometry and Topology".
Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 19634
Special Issue Editors
Interests: algebra; number theory; information theory; cryptography
Interests: Lattice Packings; Number Fields; Algebraic Coding Theory; Modulation Schemes; Cryptology and Algorithmic Complexity
Special Issue Information
Dear Colleagues,
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. Dr. Michele Elia
Prof. Dr. J. Carmelo Interlando
Dr. Nadir Murru
Guest Editors
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Keywords
- Computational complexity
- Cryptography
- Diophantine equations
- Elliptic curves
- Lattices
- Linear codes
- Pseudorandom sequences.
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