# Digital signing

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### Abstract

Digital signing is a mechanism for certifying the origin and the integrity of electronically transmitted information. In the process of digitally signing, additional information – called a digital signature – is added to the given document, calculated using the contents of the document and some private key. At a later stage, this information can be used to check the origin of the signed document. The mathematical base of the digital signing of documents is public key cryptography. This work presents the theory behind digital signatures, signature schemes and attacks on signatures and provides a survey of application areas of the digital signing technology. Moreover, there are lab exercises developed in Mathlab, to reinforce the understanding of this technology.

### 1. Introduction

The Concise Oxford Dictionary (2006) defines cryptography as the art of writing or solving codes, however modern cryptography does not met this definition. Therefore, this work starts with a literature review defining some key concepts, like what cryptography and cryptographic system are and the different types of cryptographic system are presented. The other interesting and preliminary concept is the notion of cryptosystem functions which are also discussed in the introductory section. Furthermore, it is stated that public-key encryption represents a revolution in the field of cryptography, and this work poses some basic definitions on this topic trying to explain the theory behind. The rest of the literature review is concentrated on public key cryptography and it focuses on the theory behind digital signatures, signature schemes and attacks on signatures. And finally, the literature review presents a survey of application areas on digital signatures. One part of the contribution of this work, is an overview of the secure hash standard (SHS) and implementation of the secure hash algorithm (SHA-1), required for use with digital signature algorithms. The main part though, is the implementation of AES and RSA by utilizing Mathlab. The code of all these implementations is thoroughly discussed and explained in this work. Moreover, a comparison is also presented subsequently.

### 2. Cryptography

The Greek words “krypt´os” standing for “hidden” and the word “l´ogos” that means “word”, are in essence the base from where the word cryptology was derived. As these words denote, cryptology can be best explained by the meaning “hidden word”. In this context, the original purpose behind cryptology is hiding the meaning of some specific combination of words which in turn would insure secrecy and confidentiality. This is a very limited viewpoint in today’s perspective and a wide range of security applications and issues now come under the term of cryptology (rest of the portion of this section will clarify this point of view). As field of mathematical science, Cryptology includes the study of both cryptanalysis as well as cryptography. On one hand, cryptography is a very broad term and represents any process used for data protection. On the other hand, the study of security related issues and the probabilities of breaking the cryptographic systems and a technique is known as cryptanalysis.