Spring 2014

MATH 341 / LGIC 220, T Th 12-1:30, DRL 4C8

Discrete Mathematics II

Professor Andre Scedrov

Office: Room DRL 4E6
Office Hours: Mondays and Tuesdays 1:30 - 2:30 or by appointment. No office hours on Mondays February 10, February 17, March 31, and April 21. Those weeks the Tuesday office hours February 11, February 18, April 1, and April 22 will be held 1:30 - 3:30.


Further References


Algebra of sets, power set, cartesian product, binary relations, closure properties, equivalence relations, functions, Cantor Theorem, countable sets, equinumeruous sets, uncountability of the set of reals. [Grimaldi Chapters 3, 5, and 7, and Appendix 3 and Moschovakis Chapters 1 and 2].

Overview of Probability Theory: Probability Distribution, Random Variable, Conditional Probability, Bayes Theorem, Expected Value. [Grimaldi Chapter 3 and Buchmann Chapter 4].

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. [Buchmann Chapters 3 and 4].

Introduction to Number Theory: Congruences, Chinese Remainder Theorem, Fermat's Little Theorem, Euler's Theorem, Modular Exponentiation by Repeated Squaring. [Grimaldi Chapters 14 and 17 and Buchmann Chapters 1 and 2].

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 27

This is the complete set of problems for Homework #1 due in class on Thursday, February 27, 2014.

Homework #2 Due in Class on Tuesday, April 8

This is the complete set of problems for Homework #2 due in class on Tuesday, April 8, 2014.

Take-Home Final Exam Due in Hardcopy in DRL 4E6 on Friday, May 9, 2014 at 11 a.m.

This is a complete list of assignments due May 9, 2014.