Introduction to Cryptography: 1st Edition (Hardback) book cover

Introduction to Cryptography

1st Edition

By Sahadeo Padhye, Rajeev A. Sahu, Vishal Saraswat

CRC Press

252 pages | 4 Color Illus. | 19 B/W Illus.

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Hardback: 9781138071537
pub: 2018-07-31
eBook (VitalSource) : 9781315114590
pub: 2018-09-04
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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.

Table of Contents


Overview of Cryptography


Goals of Cryptography

Classification of Cryptosystem

Practically Useful Cryptosystem


Basic Algebra





Number Theory


Prime Numbers

Cardinality of Primes

Extended Euclidean Algorithm

Primality Testing

Factorization and Algorithms for it


Quadratic Congruence

Exponentiation and Logarithm

Discrete Logarithm Problem and Algorithms for it


Probability and Perfect Secrecy

Basic Concept of Probability

Birthday Paradox

Perfect Secrecy

Vernam One Time Pad

Random Number Generation

Pseudo-random Number Generator


Complexity Theory

Running Time and Size of Input

Big-O Notation

Types of algorithm

Complexity Classes


Classical Cryptosystems

Classification of Classical Cryptosystem

Block Cipher

Stream Cipher

Cryptanalysis of Cryptosystems



Block Ciphers


Modes of Operation


Design Considerations

Data Encryption Standard

Advanced Encryption Standard


Hash Function

Compression and Hash Functions

Hash function for cryptography

Random Oracle Model

Cryptographic Hash Functions


Public Key Cryptosystem


Diffie-Hellman Key Exchange Protocol

RSA Cryptosystem

Rabin Cryptosystem

ElGamal Cryptosystem

Elliptic Curve Cryptosystem


Digital Signature

Formal Definitions

Attack Goals for Digital Signature

Digital Signature in Practice

Some Popular Digital Signatures


Research Directions in Cryptography

Pairing-Based Cryptography

Zero-knowledge Proof System

Authenticated Group Key Exchange

Attribute-Based Cryptography

Homomorphic Encryption

Secure Multi-party Computation

Secret Sharing

Post-Quantum Cryptography

Side-Channel Analysis



About the Authors


Sahadeo Padhyehas a doctorate in Cryptography, and currently working as Associate Professor at Department of Mathematics, Motilal Nehru National Institute of Technology Allahabad, India. His research interests include Public key Cryptography, Elliptic Curve Cryptography, Digital Signatures, Lattice Based Cryptography. He has published many research papers in reputed international journals and conferences in Cryptography.

Rajeev A Sahuhas a doctorate in Cryptography and currently working as a Post-Doctoral Researcher at Université Libre de Bruxelles, Belgium. He has also worked as an Assistant Professor at C.R. Rao Advanced Institute of Mathematics Statistics & Computer Science, Hyderabad, India. His research interests are Identity-Based Cryptography, Elliptic Curve Cryptography, Digital Signature, Searchable Encryption, Post-Quantum Cryptography on which he has published over two dozen research papers in reputed international journals and conferences in Computer Science and Cryptography.

Vishal Saraswat received his Ph.D. in Cryptography from University of Minnesota, Minneapolis, USA and has held regular and visiting positions at a variety of institutions, including IIT Jammu, IIT Hyderabad, ISI Kolkata, Univ. of Hyderabad and AIMSCS, Hyderabad. His research interests include anonymity and privacy, searchable encryption, postquantum crypto, and active and passive cryptanalysis, topics on which he has published several papers in reputed international journals and conferences.

Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Security / Cryptography
MATHEMATICS / Combinatorics