Spring 2019

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: Right after class, Wednesdays 1-2, or by appointment.

Suggested Text

Further References


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 Thursday, February 7

This is the complete set of problems for Homework #1 due in class on Thursday, February 7, 2019.

Take-Home Midterm Due in Class on Thursday, March 21

This is the complete set of problems for the Take-Home Midterm due in class on Thursday, March 21, 2019.

ElGamal Public-Key Cryptosystem.

Take-Home Final Due in DRL 4E6 on or before Friday, May 10, 2019 at 12 noon

This is a complete list of problems for the Take-Home Final Exam due in DRL 4E6 on or before Friday, May 10, 2019 at 12 noon. Please slide your hardcopy exam under the door of DRL 4E6.