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Discrete Mathematics Seminar

Fall 2014 - Friday at 11:00 a.m. in Lytle 203

September 26 - Problem Solving Session

September 19 - Dr. Eric Landquist

"Making Cryptanalysis Less Cryptic and Fried Eggs on Friday: Cracking early versions of the UberCrypt stream cipher"

In this talk, I'll give a quick overview of last week's talk and then poke around with pseudorandom number generators as a way of practically implementing a one-time pad, the only cryptosystem with perfect security. This provides the motivation for the stream cipher UberCrypt, developed by Mr. Joe Chiarella of Colloid, LLC, based in the Harrisburg area. UberCrypt aims to create a cryptographically secure pseudorandom number generator in order to provide perfect security. I'll describe the essential components of UberCrypt and show how one can crack earlier versions of the cipher via a chosen plaintext attack. The approach uses linear algebra with slightly more sophistication than you would see in a high school algebra course. (The only difference is that all arithmetic is performed modulo 2, that is, over the binary field {0, 1}.) The current version of UberCrypt has not been cracked as of the writing of this abstract, and so remains an open problem.

September 12 - Dr. Eric Landquist

"Makinig Cryptography Less Cryptic"

 In this talk, I will give an overview of cryptography and go over enough mathematical background to help everyone follow next week's talk on how to crack a stream cipher. We'll talk about private key versus public key cryptography, but will focus on different kinds of private key cryptosystems. We'll then get into different kinds of attacks on a cryptosystem and the attributes of a secure cipher.

Spring 2014 - Friday at 11:00 a.m. in Lytle 136

April 25 - Professor John Botzum

"Don't Stand So Close to Me or: How I Learned to Stop Worrying and Love the Twin Prime Conjecture"

Number theory -- the most easily accessible, but possibly the least penetrable of branches of mathematics has intrigued professional and amateur mathematicians for centuries. In honor of the monumental paper published by Yiteng Zhang last April 17th, I will present an introduction to the Twin Prime Conjecture and discuss Zhang's work and the work of Polymath 8a, an international group of renowned mathematicians led by Terrence Tao.

April 14 - Combinatorical Problems (continued)

April 11 - Combinatorical Problems

  1. The Cable-Trench Problem
  2. Analyze the game Free Flow - For a board of a given size and a given number of dots, how many different games are there? How many give you a unique solution or no solution?

April 4 - Dr. Greg Schaper

Problem Solving Processes

The key to success isn't knowing what to think, but knowing how to think.  Dr. Schaper will give an overview of the process that he uses to solve problems and how different brances of Math, Computer Science, and other disciplines factor into this problem solving process.

March 28 - Dr. Fran Vasko

Dr. Vasko will explain how he has applied the matching problem in graph theory to the problem of determining optimal cuts of rectangular pieces of stock.  This work was successfully implemented for Bethlehem Steel and published the Journal of the Operational Research Society in 2000.

March 14 - Bitcoin Part 4

Computer Science undergraduates discuss cryptocurrency

March 7 - Bitcoin Part 3

Hacks of the Online Cryptocurrency Exchange Mt. Gox

February 28 - Bitcoin Part 2

February 19 (Wednesday) - Dr. Brian Kronenthal

"Two Perspectives on Generalized Quadrangles"

February 7 - Bitcoin

Bitcoin is a decentralized digital currency whose security relies on various cryptographic protocols and mathematically and computationally hard problems.  It is a fascinating protocol in many regards.