Fall 2002

Math 340, MWF 12-1

Advanced Mathematical Methods in Computer Science

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, Schroeder-Bernstein Theorem, countable sets, equinumeruous sets, Cantor space, uncountability of the set of reals, algebraic numbers, existence of transcendental numbers.

Recurrences, sums, and integer functions: Towers of Hanoi, Quicksort recurrence, floor and ceiling functions.

Basic Concepts of Cryptology, Substitution Ciphers, Permutation Ciphers, Vigenere Cipher, Rotor Machines, Attack Models. Overview of Probability Theory: Probability Distribution, Random Variable, Conditional Probability, Bayes Theorem, Expected Value. 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. Public-Key Cryptography Overview. Introduction to Number Theory: Congruences, Chinese Remainder Theorem, Fermat's Little Theorem, Euler's Theorem, Modular Exponentiation by Repeated Squaring. 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.

Counting, Permutations, and Combinations, Binomial Theorem, Multinomial Theorem, Combinations with Repetition.

Asymptotic functions, Stirling's Approximation Formula, Wallis's Formula.

Take-Home Midterm Due in Class on Monday, November 4

This is a complete list of assignments due November 4, 2002.

Take-Home Final Exam Due in DRL 4E6 on at 12 noon on Monday, December 16

This is a complete list of assignments due December 16, 2002.