MAA Invited Paper Session The Non-Traditional "Traditional NSA Mathematician" Abstracts

Wednesday, August 5, 1:00 PM - 3:45 PM, Marriott Wardman Park, Delaware B

The National Security Agency's (NSA) mathematicians create breakthroughs in cryptography and communications security. It is common to associate number theory and discrete mathematics with cryptography. However, problems tackled by NSA mathematicians actually draw upon a much broader variety of fields including statistics, geometry, analysis, topology, graph theory, neuroscience, big data analytics, theoretical computer science, and computational linguistics. As a result, the research community at NSA includes experts in a wide range of mathematics and math-related subjects.

The purpose of this session is to highlight both usual and unusual problems applied to national security, with all talks being at the general non-expert level. NSA mathematicians have produced fascinating and significant results over the years, however much of the work is not published. This session is a great opportunity for the MAA community to be exposed to some of NSA's leading mathematicians and learn about the important role mathematics plays in a variety of problems.

Carla D. Martin, National Security Agency

The Coming of Enigma

1:00 PM - 1:30 PM
David Perry, National Security Agency

Prior to and during World War II the Germans used a cryptodevice called "Enigma" that was thought by everyone to provide unbreakable encryption. We will see how the device worked and why it was thought to be unbreakable by taking a whirlwind trip through the history of cryptography. Attendees will have the opportunity to see an Enigma machine in operation.

Public Key Cryptography: From Abelian Groups to Yellow Padlocks in 30 Minutes Flat

1:45 PM - 2:15 PM
Ben Benoy, National Security Agency

Modern cryptography relies on many different tools in order to achieve the interrelated goals of Confidentiality, Integrity, and Authentication. When most people think of cryptography they think of protecting data from prying eyes using a code or cipher, that is, confidentiality. However, those ciphers require that all parties to the communication share a secret: the key. How can you distribute your secret key—and keep it safe from eavesdroppers—if you don't already have a way to communicate securely? Solving that problem is the domain of Public Key Cryptography, which is largely based on the hardness of certain problems in number theory and abstract algebra. This talk will describe the problem space, and then explain how to bootstrap your way from an Abelian group all the way up to a secure communications channel.

Extending Pairwise Element Similarity to Set Similarity Efficiently

2:30 PM - 3:00 PM
Steve Knox, National Security Agency

A fundamental question in data analysis is: "how much is this like that?" Often "this" and "that" are aggregates which can be viewed as sets of atomic items. In any given context, specialist knowledge may suggest a reasonable way to measure the similarity between any pair of items. Ad hoc extension of similarity of items to similarity of sets can—and usually does—lead to measures with peculiar properties, such as sets being arbitrarily dissimilar to themselves. Such measures ought not to be used if there is a better alternative. 

This talk presents a method, called Saga, of extending any similarity measure of items to a similarity measure of sets of items. Saga set similarity has several good, provable theoretical properties and is also fast to compute. Saga is illustrated by measuring the similarity of intelligence sources based upon the similarity of intelligence reports which cite them, and other NSA mission-management applications.

Teaching Computers to See

3:15 PM - 3:45 PM
Christine Edwards, National Security Agency

The human brain is the ultimate computing machine. Its ability to identify objects and recognize events in images and videos is unparalleled by the most advanced, state-of-the-art computer vision algorithms. The field of Neurally Inspired Computing is a type of machine learning that seeks to model the human visual cortex to enable computers to not only see pixels as bits in a matrix, but to allow machines to go further and recognize objects within images and describe them in a way that is currently unique to humans. Computer vision algorithms that use the brain as a model, so-called neuro-mimetic algorithms, have been designed by mathematicians, statisticians, computer scientists, and engineers using the language of mathematics and statistics to emulate some of the brain's most fundamental processes. At their core they learn how best to represent the data, building up from low-level features to high-level concepts using numerical optimization techniques and statistical inference. In this talk I will give a brief description of some of state-of-the-art neurally inspired algorithms and show how Neurally Inspired Computing is changing the field of Computer Vision.