Contents

## DEVELOPMENT OF AN IMPROVED PLAYFAIR CRYPTOSYSTEM USING RHOTRIX

**CHAPTER ONE**

**INTRODUCTION**

**1.1 Background of the Study**

The security of data transmission is an important problem in communication networks. A communication system is reliable as long as it maintains the integrity, availability, and privacy of data. Data integrity is the protection of data from unauthorized modification, resistance to penetration and undetected modification. Therefore, it is important to secure cryptosystem which provides encryption and decryption to the data. To achieve a secure cryptosystem, Cryptology is essential. Cryptology is the study of cryptography and cryptanalysis.

Cryptography is the study of information hiding and verification. It includes the protocols, algorithms and strategies to securely and consistently prevent or delay unauthorized access to sensitive information and enable verifiability of every component in a communication (Saini and Mandal, 2015).

Cryptanalysis is the art of ‘attacking’ cryptosystems in order to ‘crack’ them or at least discover their weaknesses (Stallings, 2011). When cryptanalysis reveals weaknesses in cryptosystems, cryptographers create more secure cryptosystems. Conversely, as cryptosystems become stronger, cryptanalysts try to discover more powerful methods of attacking them. Thus, cryptography and cryptanalysis are complementary.

Cryptography is divided into three main branches (Chirstof and Pelzi 2010) which are:

**a. Symmetric Algorithms:** it refers to encryption and decryption methods in which both the sender and receiver share a secret key. All cryptography from ancient times until 1976 was exclusively based on symmetric methods. Symmetric ciphers are still in widespread use, especially for data encryption and integrity check of messages.

**b. Asymmetric (or Public-Key) Algorithms:** In public-key cryptography, a user possesses a secret key as in symmetric cryptography and a public key that may be freely distributed. Asymmetric algorithms can be used for applications such as digital signatures and key establishment, and also for classical data encryption.

**c. Cryptographic Protocols:** crypto protocols deal with the application of cryptographic algorithms. Symmetric and asymmetric algorithms can be viewed as building blocks with which applications such as secure Internet communication can be realized. The Transport Layer Security (TLS) scheme,

which is used in every Web browser, is an example of a cryptographic protocol. Symmetric cryptography addresses the problem of secrecy protection by using the shared secret key to transform the message in such a way that it cannot be recovered anymore without this key. This process is called symmetric encryption. Based on the paradigm used to process the message, these ciphers are typically categorized into one of two classes: block ciphers and stream ciphers. The security of symmetric encryption algorithms can in general not be proved (the notable exception being the one-time pad). Instead, the trust in a cipher is merely based on the fact that no weaknesses have been found after a long and thorough evaluation phase (Canniere, 2007). Two types of ciphers are used in Symmetric Key **Cryptography:** Transposition cipher and Substitution cipher (Stallings, 2006).

In transposition cipher the characters in the plaintext are swapped to get the cipher text i.e. the characters retain their plaintext form but their position is changed. The plaintext is organized into two dimensional table and columns are interchanged according to a predefined key. In substitution cipher one symbol of the plaintext is replaced by another symbol. Substitution ciphers has further two types. Mono-alphabetic substitution cipher and poly alphabetic substitution cipher.

Mono-alphabetic substitution cipher, is when a character in the plaintext is always changed to the same character in the cipher text. The well-known example of Mono alphabetic substitution cipher is the CAESAR cipher.

The Poly-alphabetic substitution cipher a single character in the plaintext is changed to many characters in the cipher text. The well-known example of poly alphabetic substitution cipher is VIGENERE cipher which changes a single character in the plaintext into many characters in the cipher text by considering the position of character in the plaintext.

This research work focuses on Playfair cipher which is a type of block cipher and also a substitution cipher, the Scheme was invented by British scientist Sir Charles Wheatstone in 1854, but was named after Lord Playfair who promoted the use of the cipher and hence it is called Playfair Cipher (Iqbal et al., 2014). It was used by the British in the first and Second World War. It was also used by the Australians and Germans during World War II. Playfair is reasonably easy to use and was used to handle important but non-critical secrets. By the time the enemy cryptanalysts could break the message, the information would be useless to them. Between February 1941 and September 1945 the Government of New Zealand used it for communication between New Zealand, the Chatham Islands and the Pacific Islands. The technique encrypts pairs of letter, instead of single letters as in the simple substitution cipher. It was the first practical digraph substitution cipher, in which the cipher-text character replaces a particular plaintext character in the encryption which depend on an adjacent character in the plaintext. If the plaintext is viewed as a sequence of bits, then substitution involves replacing plaintext bit patterns with cipher-text bit patterns (Stallings, 2011). The Playfair algorithm is based on the use of a 5 × 5 matrix on the 26-letter characters of the English language constructed from the encryption key, with 2 of the 26 characters occupying a single position in the array .These two characters are i and j. Usually it is easy to distinguish from the context which of these two letters was intended in the plaintext. The encryption key for a Playfair cipher is a word, i.e., a finite sequence of characters taken from the set of plaintext characters. This keyword will determine the positioning of the characters in the encryption arrays.

Rhotrix is a new area of study relating to linear mathematical algebra, this concept of rhotrices was introduced by Ajibade (2003). As an extension of ideas on matrix-tertion and matrix-noitret, suggested by Atanassov and Shannon (1998). Ajibade defined rhotrix as mathematical arrays which are in some ways, between (2 x 2) and (3 x 3)-dimensional matrices. Extension in the size of R was considered possible. It is denoted by R and shown below.

### 1.2 Research Motivation

The explosive growth in computer systems and their interconnection via network has increased the dependence of both organizations and individuals on the information stored and communicated using these systems which intern has led to a heightened awareness of the need to protect data and resources from intruders. (Jitendra et al., 2013). Cryptography is the design of certain techniques for ensuring the secrecy and/or authenticity of information. The need of cryptographic algorithm is to avoid threat to integrity, confidentiality and availability. In every sector, collection of information or transfer of data with a high level of security is needed. For this reason a strong encryption technique is required. This research focuses on play fair cipher algorithm which is very strong and also requires less memory and power. Although a considerable effort has been done in analysing Playfair ciphers of various sizes, this observation motivates the study carried out in this dissertation.

The Motivation for the research is based on the existing playfair cipher and some researchers‟ concepts which address some limitation of the playfair cipher in a unique but separate ways. The initial driving force behind the conception of the work was to extend the traditional playfair cipher which was based on the 5×5 matrix and to equally use the concept of rhotrix which was introduced by Ajibade (2003) and the idea of conversion of rhotrix to a coupled matrix by Sani (2008) to obtain more security to the cipher.

### 1.3 Research Problem

Millions of monetary transactions take place per second online. Also, daily business activities nowadays depend on software and the need for strong cryptographic algorithms or concepts cannot be overemphasized. The 21st century fraudsters or hackers are sophisticated in their malicious or criminal activities and therefore software security must be far ahead of them. (Ibikun et al., 2013). As information is transferred from one user to another the information becomes highly vulnerable to all kind of threats caused by adversaries, the data communication between two entities can be secured if an encryption and decryption technique is used at two end points (Harinandan et al., 2014). Therefore achieving faster communication in most confidential data is circulated through networks as electronic data. Cryptographic ciphers have an important role for providing security to these confidential data against unauthorized attacks (Ranjeet et al., 2014). One of the well-known digraph substitution cipher is the Playfair

Cipher, which treats the plain text as single units and translates these units into cipher text. Though in the Playfair system, it is significantly hard to break with the frequency analysis used for simple monographs substitution ciphers (Safwat, 2014).

The drawback of the Playfair cipher is that the plain text consists of 25 uppercase letters only. One letter has to be omitted and cannot be reconstructed after decryption. Also lowercase letters, white space, numeric values and other printable characters cannot be handled by the traditional cipher. This means that complete sentences cannot be handled by this cipher. X is used as filler letter, and also as padding for odd numbers of letters in the message. Therefore could not cater for special characters thus limiting the possible combination for keys formation.

### 1.4 Aim and Objectives of the Study

The aim of this research is to develop a modified playfair cryptosystem using rhotrix. The objectives are to:

a. Introduce rhotrix as a coupled matrix to data structure of playfair

b. Support more characters, punctuation and some other printable characters.

c. Create more confusions to the cipher by taking advantage of a different form of matrix.

d. Implement the cryptosystem and evaluate for frequency analysis.

### 1.5 Research Methodology

The method used in this study is as follows:

a. Rhotrix is used instead of matrix, which is a new paradigm of matrix theory of rectangular arrays.

b. The size of the rhotrix is set to 6 to make it compatible with the [n×(n-1)] mode of rhotrix representation.

c. Repetitions of alphabets and strings with odd length are tackled using a filler character for efficient implementation.

d. Playfair rules for encryption and decryption was adopted.

e. Procedures from a to d are used to develop a secure cryptosystem, and would be implemented using java programming language.

### 1.6 Organization of the Dissertation

The rest of this work discusses the implementation of a modified playfair cipher using rhotrix and is organized as follows: chapter 2 presents a literature and related works. Chapter 3 analyses this work by explaining tools used in the development of this work and analysis on how it was designed. Chapter 4 shows how this work was implemented and Chapter 5 gives a general conclusion on the work done, and its importance to cryptography.