This year’s Awards Day Ceremony will take place on Friday April 26th at 3:30pm in Schenker Lecture Hall, followed by a talk given by Dr. Steven Miller.
The German Tank Problem: Math/Stats At War
Steven J Miller
Carnegie Mellon and Williams College
During World War II the German army used tanks to devastating advantage. The Allies needed accurate estimates of their tank production and deployment. They used two approaches to find these values: spies, and statistics. In this talk we describe the statistical approach and its generalization. Assuming the tanks are labeled consecutively starting at 1, if we observe $k$ serial numbers from an unknown number $N$ of tanks, with the maximum observed value $m$, what is the best estimate for $N$? This is now known as the German Tank Problem, and is a terrific example of the applicability of mathematics and statistics in the real world. We quickly review some needed combinatorial identities (which is why we are able to obtain clean, closed form expressions), give the proof for the standard problem, discuss the generalization, and show how if we were unable to do the algebra we could guess the formula by an application of linear regression, thus highlighting its power and applicability. Most of the talk only uses basic algebra and elementary knowledge of WWII.
Dollar signs don’t work: Some text and $e^\pi.$
Square brackets: Some text and \[e^\pi.\]
Double dollar signs: Some text and $$e^\pi.$$
Round brackets: Some text and \(e^\pi.\)
We are pleased to announce that Jill Pipher (Elisha Benjamin Andrews Professor of Mathematics at Brown University) will deliver the inaugural UConn Mathematics Distinguished Lecture on Friday, April 19th at 3:30pm in the Schenker Lecture Hall.
Mathematical ideas in public key cryptography
Elisha Benjamin Andrews Professor of Mathematics, Brown University
President, American Mathematical Society
The problem solved by public key encryption is this: how can we create secure communication over an insecure channel (like the internet) between two people who have never met or shared a secret? The model application, unknown at the time of its invention, is you and any of your online vendors.
The concept of public key encryption was introduced in the famous 1976 paper “New Directions in Cryptography” by Diffie and Hellman. At the time it was indeed a “solution in search of a problem”: the application of encryption and authentication on a mass scale had yet to emerge from the Arpanet. In that paper, Diffie and Hellman posed an extraordinarily challenging mathematical problem and laid the foundation for a new field of mathematics/computer science. Then, in 1978, Rivest, Shamir and Adelman produced the first published example of a public key cryptosystem; their RSA encryption is still widely used for secure communication.
This lecture will provide some historical background on the subject of private and public key, encryption and explain some of the ideas involved in several different encryption systems. Particular attention will be focused on lattiice-based encryption schemes such as NTRU, an efficient public key system due to Hoffstein, Pipher, and Silverman, first disseminated in1996, which continues to remain secure against the potential speed-ups of quantum computers. In the last couple of years, national agencies and large financial institutions have recognized the urgent need for post-quantum cryptography; NIST has initiated a process to solicit, evaluate, and standardize one or more quantum-resistant public-key cryptographic algorithms. We will indicate some of the applications of lattice-based cryptosystems like NTRU to post-quantum computing and to cloud computing on private data.