On the issues of auditing cryptographic applications and studying mono-unary algebras

Jorge Carrillo Ugalde

Doctoral thesis

Abstract:

In this thesis several applications of mono-unary algebras and a systematic approach to audit cryptographic applications were presented. This thesis is based on the observation that most of the procedures to perform IS audits utilize check-lists, which might not be applicable to all IT environments; however, by examining some applications of a simple algebraic structure, such as mono-unary algebras, a systematic methodology to execute an IS audit could be designed to improve the current IS audit approach. By defining basic components of an IS audit and simple relationships among them, one could create an efficient IS audit. It is not the aim of this thesis to provide a pure algebraic process to perform an IS audit; however, understanding several applications of mono-unary algebras can help to identify and abstract the basic elements of an IS audit. The main application of mono-unary algebras refers to the construction of the subgroupoid generated by a subset of the carrier of a finite groupoid. The aims is to extend these concepts to construct all subgrupoids of a finite groupoid, and show how some of the subalgebras of a mono-unary algebra correspond to subalgebras of a finite algebra, by replacing a finite algebra by a finite mono-unary algebra.

Abstract:

In this thesis several applications of mono-unary algebras and a systematic approach to audit cryptographic applications were presented. This thesis is based on the observation that most of the procedures to perform IS audits utilize check-lists, which might not be applicable to all IT environments; however, by examining some applications of a simple algebraic structure, such as mono-unary algebras, a systematic methodology to execute an IS audit could be designed to improve the current IS audit approach. By defining basic components of an IS audit and simple relationships among them, one could create an efficient IS audit. It is not the aim of this thesis to provide a pure algebraic process to perform an IS audit; however, understanding several applications of mono-unary algebras can help to identify and abstract the basic elements of an IS audit. The main application of mono-unary algebras refers to the construction of the subgroupoid generated by a subset of the carrier of a finite groupoid. The aims is to extend these concepts to construct all subgrupoids of a finite groupoid, and show how some of the subalgebras of a mono-unary algebra correspond to subalgebras of a finite algebra, by replacing a finite algebra by a finite mono-unary algebra.

Keywords

cryptographic applications, mono-unary algebras

Language used: English

Date on which the thesis was submitted / produced: 11. 1. 2008

Thesis defence

• Date of defence: 11. 1. 2008
• Supervisor: prof. RNDr. Jozef Gruska, DrSc.
• Reader: doc. Dr. Ing. Petr Hanáček, prof. RNDr. Václav Matyáš, M.Sc., prof. RNDr. Miroslav Novotný, DrSc.

Masaryk University

Faculty of Informatics

Doctoral programme / field:
Informatics (4-years) / Informatics