Some Notes on a Formal Algebraic Structure of Cryptology

Vicente Jara-Vera and Carmen Sánchez-Ávila
Additional contact information
Vicente Jara-Vera: Departamento de Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones (Escuela Técnica Superior de Ingenieros de Telecomunicación), Universidad Politécnica de Madrid, Avenida Complutense 30, 28040 Madrid, Spain
Carmen Sánchez-Ávila: Departamento de Matemática Aplicada a las Tecnologías de la Información y las Comunicaciones (Escuela Técnica Superior de Ingenieros de Telecomunicación), Universidad Politécnica de Madrid, Avenida Complutense 30, 28040 Madrid, Spain

Mathematics, 2021, vol. 9, issue 18, 1-28

Abstract: Cryptology, since its advent as an art, art of secret writing, has slowly evolved and changed, above all since the middle of the last century. It has gone on to obtain a more solid rank as an applied mathematical science. We want to propose some annotations in this regard in this paper. To do this, and after reviewing the broad spectrum of methods and systems throughout history, and from the traditional classification, we offer a reordering in a more compact and complete way by placing the cryptographic diversity from the algebraic binary relations. This foundation of cryptological operations from the principles of algebra is enriched by adding what we call pre-cryptological operations which we show as a necessary complement to the entire structure of cryptology. From this framework, we believe that it is improved the diversity of questions related to the meaning, the fundamentals, the statute itself, and the possibilities of cryptological science.

Keywords: algebra; cryptography; cryptology (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/18/2183/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/18/2183/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:9:y:2021:i:18:p:2183-:d:630506

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().