Introduction to Cryptography

Electronic communication and financial transactions have assumed massive proportions today. But they come with high risks. Achieving cyber security has become a top priority, and has become one of the most crucial areas of study and research in IT. This book introduces readers to perhaps the most effective tool in achieving a secure environment, i.e. cryptography. This book offers more solved examples than most books on the subject, it includes state of the art topics and discusses the scope of future research. Foreword......Page 3 Preface......Page 5 Contents......Page 7 Overview of Cryptography......Page 14 Introduction......Page 15 Goals of Cryptography......Page 16 Classification of Cryptosystem......Page 17 Practically Useful Cryptosystem......Page 18 Cryptanalysis......Page 20 Basic Algebra......Page 24 Group......Page 25 Ring......Page 28 Field......Page 29 Exercises......Page 36 Number Theory......Page 38 Prime Numbers......Page 39 Cardinality of Primes......Page 40 Extended Euclidean Algorithm......Page 42 Congruences......Page 45 Integer Factorization Problem......Page 48 Primality Testing......Page 54 Quadratic Congruence......Page 58 Exponentiation and Logarithm......Page 63 Discrete Logarithm Problem......Page 64 Exercises......Page 72 Probability & Perfect Secrecy......Page 74 Basic Concept of Probability......Page 75 Birthday Paradox......Page 77 Perfect Secrecy......Page 79 Vernam One-Time Pad......Page 81 Pseudo-random Number Generator......Page 82 Exercises......Page 83 Complexity Theory......Page 85 Running Time and Size of Input......Page 86 Notation......Page 87 Types of Algorithm......Page 90 Complexity Classes......Page 91 Exercises......Page 94 Classical Cryptosystems......Page 96 Classification of Classical Cryptosystem......Page 97 Block Cipher......Page 98 Stream Cipher......Page 107 Cryptanalysis of Cryptosystems......Page 112 Exercises......Page 123 Block Ciphers......Page 125 Introduction......Page 126 Modes of Operation......Page 127 Padding......Page 136 Design Considerations......Page 138 Data Encryption Standard (DES)......Page 140 Advanced Encryption Standard (AES)......Page 145 Exercises......Page 151 Hash Function......Page 153 Compression and Hash Functions......Page 154 Hash Function for Cryptography......Page 156 Cryptographic Hash Functions......Page 162 Exercises......Page 173 Public Key Cryptosystem......Page 174 Introduction......Page 176 Diffie-Hellman Key Exchange Protocol......Page 178 RSA Cryptosystem......Page 182 Rabin Cryptosystem......Page 195 ElGamal Cryptosystem......Page 198 Elliptic Curve Cryptosystem......Page 201 Exercises......Page 210 Digital Signature......Page 213 Formal Definitions......Page 214 Attack Goals of an Adversary of a Digital Signa- ture......Page 216 Digital Signature in Practice......Page 217 Some Popular Digital Signatures......Page 229 Exercises......Page 230 Research Directions in Cryptography......Page 231 Pairing-based Cryptography......Page 232 Zero-knowledge Proof System......Page 233 Authenticated Group Key Exchange......Page 234 Attribute-based Cryptography......Page 235 Homomorphic Encryption......Page 236 Secret Sharing......Page 237 Post-Quantum Cryptography......Page 238 Side-Channel Analysis......Page 239 Refs......Page 240 Index......Page 254