Spring 2008

MATH 341 / LGIC 220, MWF 12-1, DRL 3C2

Discrete Mathematics II

Make-up classes on Friday, February 1, on Monday, February 4, on Friday, April 4, and on Monday, April 14

No class on Friday, February 15, nor on Monday, March 17, nor on Friday, April 25, nor on Monday, April 28

Professor Andre Scedrov

Office: Room 4E6 in David Rittenhouse Laboratory
Telephone: eight five nine eight three ( Math. Dept. Office: eight eight one seven eight )
Fax: three four zero six three
E-mail: lastname at math
Office Hours: By appointment


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.

Homework #1 Due in Class on Monday, February 18

This is the complete set of problems for Homework #1 due in class on Monday, February 18.

Take-Home Midterm Due in Class in Hardcopy on Wednesday, April 9

This is the complete set of problems for take-home midterm due in class on Wednesday, April 9, 2008. The final exam will also be take-home and it will be due in hardcopy on Monday, May 5 at 11 a.m. in Professor Scedrov's office DRL 4E6.

Take-Home Final Exam Due in Hardcopy in DRL 4E6 on Monday, May 5 at 11 a.m.

This is a complete list of assignments due May 5, 2008.