Imagine Magazine - Johns Hopkins - November/December 2013 - (Page 16)

I have always had a fascination with numbers and patterns and how they apply in the real world. As a huge Portland Trailblazers fan, I first came to appreciate math in the form of basketball statistics. Later, as I advanced in my school math classes, I came to see how math could be applied in a wide range of fields, from finance and economics to computer science and engineering. But it was a family vacation that turned my interest in math into something more and made me want to do more than study math in a classroom. The summer before my freshman year, my family and I visited the International Spy Museum in Washington, DC. There, I learned about the intriguing concept of using mathematical techniques to communicate securely in the presence of "malicious adversaries"-and I was captivated. I told a math teacher at my school about my interest, hoping he could guide me in conducting research in the field. He was unable to teach me the cryptography and number theory I wanted to learn, but he did give me a book called A Friendly Introduction to Number Theory to help me get started. Expert Guidance & THE R SCIENCE SOCIETY FO PUBLIC 16 imagine The following summer, I sent emails to several math professors working in the field of cryptography at local colleges and universities, asking if they would be willing to help me conduct a cryptography research project. At first, no one was. But I continued to send emails and make cold calls until finally, someone responded. Dr. Neal Koblitz, a professor at the University of Washington, is a worldrenowned mathematician and the inventor of one of the world's most secure public-key cryptographic systems, elliptic curve cryptography (ECC). ECC is a highly sophisticated mathematical algorithm that uses algebraic equations called elliptic curves to encrypt sensitive information. This algorithm had caught my interest in my initial background research, so I was astonished when Dr. Koblitz was willing to meet with me and discuss research ideas. The first time I visited him in his oﬃce at UW that summer, I was hoping he would provide me with reading material to expand my knowledge and suggest cool ideas to pursue for a research project. The meeting went remarkably well: He gave me a ton of material to read about number theory, including two books that he wrote himself. Furthermore, he encouraged me to look into the computational aspects of ECC to see if there was a way to make them faster. Beginning with that very first meeting, Dr. Koblitz provided me with two essential things: direction in what I needed to learn, and answers to my questions whenever I needed them. In Search of a Problem For the rest of that summer and most of my sophomore year, I spent my free time doing research. Not only was it painstaking to learn the number theory behind elliptic curves and cryptography, but I also had to become proficient at computer programming, which I accomplished by taking a course at Portland Community College. Once I gained the necessary background, I was able to define a problem for my research: improving the speed of an operation called scalar multiplication, which refers to multiplying a point on an elliptic curve by an integer. Scalar multiplication takes up the majority of running time in cryptographic algorithms, so it's a critical problem, and one I was excited to work on. For my research project, I designed, implemented, and tested new algorithms that were much faster than those typically used for scalar multiplication. By March 2012, I had completed a research project I was extremely proud to present at the regional science fair. All the hard work of learning the background and doing the actual research had paid off with successful results, and I had high hopes that I might even make it to the International Science and Engineering Fair (ISEF). While I won first place in the math category, I was the only person competing in that category, and I didn't qualify for ISEF. Journey into Galois Fields My disappointment didn't dampen my interest, though. With Dr. Koblitz's encouragement and suggestions, I delved deeper into the arithmetic behind ECC algorithms for my next research project. More specifically, I decided to explore ways Nov/Dec 2013

Table of Contents for the Digital Edition of Imagine Magazine - Johns Hopkins - November/December 2013

In My Own Words
Interested in Econ
The World in Numbers
Reckoning with Randomness
Elliptic Curves
A League of Our Own
More Than Math
Developing Your Numbersense
Where Math Meets Imagination
Selected Opportunities & Resources
Dancing in the Footsteps of My Ancestors
Off the Shelf
Word Wise
Exploring Career Options
Planning Ahead for College
Students Review
Mark Your Calendar
Knossos Game

Imagine Magazine - Johns Hopkins - November/December 2013