Introduction to Cryptology

Cryptology is employed to communicate securely, authenticate messages and sign digitally. This four-week course “Introduction to Cryptology” is designed for both computer science and mathematics students, touching upon the most important ideas and techniques of present day cryptology. All the pre-requisite topics are revised during the lectures making this course self-contained and accessible to a wider audience. It is hoped that this course will prepare interested students for a more extensive course on Information Security.

Introduction Caeser cipher.
Modular arithmetic, shift cipher.
Affine Cipher, Vigenere Cipher.
Prefect secrecy, Application of Shift Cipher.
Problem Discussion on Affine cipher and Perfect Secrecy.
Product Cipher, Block Cipher, Modes of Operation for Block Cipher.
Substitution Permutation network, Fiestel Cipher.
S-Box Theory.
Cryptanalysis and its Variants, Linear Attack.
Problem Discussion.
Public Key Cryptology Introduction RSA Cryptosystem.
Complexity analysis of Euclidian Algorithm and RSA Cryptosystem square and multiply algorithm.
Primality testing: Miler-Rabin Algorithm, Legendre Symbol and Jacobi Symbol.
Efficien Computation of Jacobi Symbol Primality Testing:Solovay-Stassen Algorithm.
Problem Discussion on Jacobi Symbol Calculation and RSA Cryptosystem.
Cryptographic hash function: Introduction.
Random Oracle model, Security of hash functions.
Randomized Algorithm and its application on Preimage resistance and collision resistance.
Iterated Hash Functions.
Problem Discussionn.