Spring 2018

MATH 341 / LGIC 220, T Th 12-1:30, DRL 4C2

Discrete Mathematics II

Professor Andre Scedrov


Office: Please go to Room DRL 4W1 or 4W5 and the Math Department staff will conduct you to the Chair's office.
Office Hours: Mondays 10:30 - 1:30 starting January 29, or by appointment. Office hours February 12 rescheduled to Friday, February 9, 11:30 - 2:30.


Suggested Text


Further References


Topics

Overview of Probability Theory: Probability Distribution, Random Variable, Conditional Probability, Bayes Theorem, Expected Value.

Basic Concepts of Cryptology: Substitution Ciphers, Permutation Ciphers, Vigenere Cipher, Rotor Machines, Attack Models. Symmetric Ciphers, Block Ciphers, One-Time Pad, Information-Theoretic Properties of One-Time Pad, Perfect Secrecy, Misuses of One-Time Pad, Malleability. Stream Ciphers, Linear Feedback Shift Register, Golomb's Randomness Postulates, Linear Complexity, Non-linear Filters, Knapsack Keystream Generator.

Introduction to Number Theory: Congruences, Chinese Remainder Theorem, Fermat's Little Theorem, Euler's Theorem, Modular Exponentiation by Repeated Squaring.

Public-Key Cryptosystems: Diffie-Hellman Key Exchange, Person-in-the Middle Attack. Discrete Logarithm, Giant-Step Baby-Step Algorithm, Pohlig-Hellman Algorithm, ElGamal Public-Key Cryptosystem. RSA Public-Key Cryptosystem. Digital Signatures, Selective Forgery, Existential Forgery, Signature Schemes Based on RSA, Signature Schemes Based on Discrete Logarithm: ElGamal Signature Scheme.

Selected topics from modern cryptography and computer network security.


Homework #1 Due in Class on Tuesday, February 13

This is the complete set of problems for Homework #1 due in class on Tuesday, February 13, 2018.