mathematics Article Some Notes on a Formal Algebraic Structure of Cryptology Vicente Jara-Vera * and 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;
[email protected] * Correspondence:
[email protected]; Tel.: +34–686–615–535 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 MSC: 14G50; 94A60 Citation: Jara-Vera, V.; Sánchez-Ávila, C. Some Notes on a Formal Algebraic Structure of 1. Introduction Cryptology. Mathematics 2021, 9, 2183. https://doi.org/10.3390/math9182183 Cryptology is a science that is usually explained based on its historical development.