PUBLIC KEY CRYPTOGRAPHY THAT ENHANCES SECURITY OF THE DIFFIE-HELLMAN ALGORITHIM
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Course
CRYPTOGRAPHY (SMPQ)
Institution
THE TECHNICAL UNIVERSITY
Cryptographic algorithms play a vital role in providing the data security against malicious attacks. Deffie-Hellman algorithm is extensively used in the popular implementations of Public Key Infrastructures. In asymmetric key cryptography, also called Public Key cryptography, two different keys (wh...
PUBLIC KEY CRYPTOGRAPHY THAT ENHANCES SECURITY OF THE
DIFFIE-HELLMAN ALGORITHIM
PRESENTED BY
IRUNGU JULIUS GIKONYO
ON AUGUST 2018
,ABSTRACT;
Cryptographic algorithms play a vital role in providing the data security against malicious
attacks. Deffie-Hellman algorithm is extensively used in the popular implementations of
Public Key Infrastructures. In asymmetric key cryptography, also called Public Key
cryptography, two different keys (which form a key pair) are used. One key is used for
encryption and only the other corresponding key must be used for decryption. No other key
can decrypt the message – not even the original (i.e. the first) key used for encryption. Our
aim is to implement encryption technique namely; Deffie-Hellman algorithm whereby we
propose a trapdoor function to describe the algorithm for key agreement and public key
encryption using a given commutative ring of integers.
, Contents
ABSTRACT; .............................................................................................................................................................. 2
Contents ................................................................................................................................................................. 3
CHAPTER ONE ......................................................................................................................................................... 5
INTRODUCTION ...................................................................................................................................................... 5
1.1: Introduction and Background of the study ................................................................................................. 5
1.2 Statement of the problem ........................................................................................................................ 6
1.3: Objective of the study ................................................................................................................................. 6
1.4. Significance of the Study ............................................................................................................................. 6
1.5 Methodology ................................................................................................................................................ 6
1.6 LITERATURE REVIEW .................................................................................................................................... 7
CHAPTER TWO ........................................................................................................................................................ 9
2.1. BASIC DEFINITIONS ...................................................................................................................................... 9
2.1.1 MATRICES .............................................................................................................................................. 9
2.1.2 Types of matrices ................................................................................................................................ 10
2.3 MATRIX ARITHMETIC .................................................................................................................................. 11
2.3.1 Matrix addition ................................................................................................................................... 11
2.3.2 Matrix subtraction .............................................................................................................................. 11
2.3.3 Multiplication of matrix by a scalar .................................................................................................... 11
2.3.4 Matrix multiplication .......................................................................................................................... 11
2.4 Functions of a matrix .................................................................................................................................. 12
2.4.1 The transpose of a matrix ................................................................................................................... 12
2.4.2 The determinant ................................................................................................................................. 12
2.4.3 The matrix inverse .............................................................................................................................. 13
2.5 More special matrices ................................................................................................................................ 14
2.5.1Symmetric matrix ................................................................................................................................. 14
2.5.2 Circulant Matrix .................................................................................................................................. 14
2.5.3 The Greatest Common Divisor (GCD) of a circulant matrix. ............................................................... 14
2.5.4 Prime circulant matrix ......................................................................................................................... 14
2.5.5 Doubly circulant coefficient matrix ............................................................................................... 15
Lemma 1 ...................................................................................................................................................... 15
Lemma 2 ...................................................................................................................................................... 16
2.6.0 Eigen values and Eigen vectors ............................................................................................................... 16
CHAPTER THREE .................................................................................................................................................... 17
3.1.1: Definitions .................................................................................................................................................. 17
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