Spring 2020

MATH 341 / LGIC 220 online

Discrete Mathematics II

Professor Andre Scedrov


Professor Scedrov's Office Hours: Online Tuesdays 10:30 a.m. - 11:50 a.m. EDT and Fridays 7:30 p.m. - 9 p.m. EDT, or by appointment.
TA Office Hours: Mr. Logan Crew will also hold office hours online by appointment.


Suggested Text


Further References


Topics Covered So Far

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. Finite Fields. Splitting Fields. Quadratic Residues. Legendre Symbol. Jacobi Symbol. Law of Quadratic Reciprocity.

Public-Key Cryptosystems: Diffie-Hellman Key Exchange, Person-in-the Middle Attack. Discrete Logarithm. RSA Public-Key Cryptosystem.


Topics Still To Be Covered

Attacks on RSA. ElGamal 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.


Take-Home Midterm #1 due in class Tuesday, February 18

This is the complete set of problems for Take-Home Midterm #1 due in class on Tuesday, February 18, 2020.


Take-Home Midterm #2 due in pdf by email on or before Thursday, April 2, 12 noon EDT

This is the complete set of problems for the Take-Home Midterm due as a pdf file by email on or before Thursday, April 2, 2020, 12 noon EDT.

Please note: Also due with Midterm #2 is your choice of a topic of your 5-page report for the final exam. This is only the choice of the topic; the report itself will be due together with the final exam.