The course deals with the underlying principles of cryptography and network security. It
develops the mathematical tools required to understand the topic of cryptography.

Starting
from the classical ciphers to modern day ciphers, the course provides an extensive coverage
of the techniques and methods needed for the proper functioning of the ciphers.

The course
deals with the construction and cryptanalysis of block ciphers, stream ciphers and hash
functions.

The course defines one way functions and trap-door functions and presents the
construction and cryptanalysis of public key ciphers, namely RSA.

The key exchange
problem and solutions using the Diffie-Hellman algorithm are discussed. Message
Authentication Codes (MAC) and signature schemes are also detailed.

The course deals
with modern trends in asymmetric key cryptography, namely using Elliptic Curves. The
course concludes with the design rationale of network protocols for key exchange and
attacks on such protocols.

A video course shall consist of 40 or more lectures with 1 hour duration per lecture.

Module

Topics

Introduction and Mathematical Foundations

Introduction

Overview on Modern Cryptography

Number Theory

Probability and Information Theory

Classical Cryptosystems

Classical Cryptosystems

Cryptanalysis of Classical Cryptosystems

Shannon’s Theory: I

Shannon’s Theory: II

Shannon’s Theory: III

Symmetric Key Ciphers

Symmetric Key Ciphers

Modern Block Ciphers (DES)

Modern Block Cipher (AES)

Modern Block Cipher (AES) contd.

Cryptanalysis of Symmetric Key Ciphers

Linear Cryptanalysis

Differential Cryptanalysis

Other Cryptanalytic Techniques

Overview on S-Box Design Principles

Modes of operation of Block Ciphers

Stream Ciphers and Pseudorandomness

Stream Ciphers

Pseudorandom functions

Hash Functions and MACs

Hash functions: The Merkle Damgard Construction

Message Authentication Codes (MACs)

Asymmetric Key Ciphers: Construction and Cryptanalysis

More Number Theoretic Results

The RSA Cryptosystem

Primality Testing

Factoring Algorithms

Other attacks on RSA and Semantic Security of RSA

The Discrete Logarithm Problem (DLP) and the Diffie Hellman Key Exchange algorithm

The ElGamal Encryption Algorithm

Cryptanalysis of DLP

Digital Signatures

Signature schemes: I

Signature schemes: II

Modern Trends in Asymmetric Key Cryptography

Elliptic curve based cryptography: I

Elliptic curve based cryptography: II

Network Security

Secret Sharing Schemes

A Tutorial on Network Protocols, Kerberos

Pretty Good Privacy (PGP)

Secure Socket Layer (SSL)

Intruders and Viruses

Firewalls

Discrete Structures, Algorithms.

Douglas Stinson, "Cryptography Theory and Practice", 2^{nd} Edition, Chapman &
Hall/CRC.

B. A. Forouzan, "Cryptography & Network Security", Tata Mc Graw Hill.

W. Stallings, "Cryptography and Network Security", Pearson Education.

Wenbo Mao, "Modern Cryptography,
Theory & Practice", Pearson Education.

Hoffstein, Pipher, Silvermman, "An
Introduction to Mathematical
Cryptography", Springer.

J. Daemen, V. Rijmen, "The Design of
Rijndael", Springer.

A. Joux,"Algorithmic Cryptanalysis",
CRC Press.

S. G. Telang, "Number Theory", Tata
Mc Graw Hill.

C. Boyd, A. Mathuria, "Protocols for
Authentication and Key Establishment",
Springer.

Matt Bishop, "Computer Security",
Pearson Education.

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