Cryptography and Network Security

Overview

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Instructor: Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur.

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 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 trapdoor 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.

Syllabus

Introduction.
Overview on Modern Cryptography.
Introduction to Number Theory.
Probability and Information Theory.
Classical Cryptosystems.
Cryptanalysis of Classical Ciphers.
Shannons Theory.
Shannons Theory (Contd...1).
Shannons Theory (Contd...2).
Symmetric Key Ciphers.
Block Cipher Standards (DES).
Block Cipher Standards (AES).
Block Cipher Standards (AES) (Contd.).
Linear Cryptanalysis.
Differential Cryptanalysis.
Few other Cryptanalytic Techniques.
Overview on S-Box Design Principles.
Modes of Operation of Block Ciphers.
Stream Ciphers.
Stream Ciphers (Contd...1).
Stream Ciphers (Contd...2).
Pseudorandomness.
Cryptographic Hash Functions.
Cryptographic Hash Functions (Contd...1).
Cryptographic Hash Functions (Contd...2).
Message Authentication Codes.
More Number Theoretic Results.
The RSA Cryptosystem.
Primality Testing.
Factoring Algorithms.
Some Comments on the Security of RSA.
Discrete Logarithm Problem (DLP).
The Diffie-Hellman Problem and Security of ElGamal Systems.
An Introduction to Elliptic Curve Cryptography.
Application of Elliptic Curves to Cryptography.
Implementation of Elliptic Curve Cryptography.
Secret Sharing Schemes.
A Tutorial on Network Protocols.
System Security.
Firewalls and Intrusion Detection Systems.
Side Channel Analysis of Cryptographic Implementations.