My entry for the Breakthrough Junior Challenge.
Solution to test exercise:
p = 71, q = 89
n = 6319
phi = 6160
e = 3
d = 4107
"Go" = 715 (3320 encoded)
"Up" = 2116 (5350 encoded)
Modular Arithmetic: http://artofproblemsolving.com/wiki/index.php/Modular_arithmetic/Introduction
Euclidean Algorithm: http://artofproblemsolving.com/wiki/index.php/Euclidean_algorithm
Euler Totient Function: http://www.artofproblemsolving.com/wiki/index.php/Euler's_totient_function
Exponentiation By Squaring: https://en.wikipedia.org/wiki/Exponentiation_by_squaring
Euler’s Theorem: https://en.wikipedia.org/wiki/Euler%27s_theorem
Fermat’s Little Theorem: https://en.wikipedia.org/wiki/Fermat%27s_little_theorem
---There are many fascinating concepts and theories to choose from. Why did you pick this one?
I picked RSA encryption as my topic because it is fundamental to the security of the internet, something which most people take for granted. Everyone should know why it is safe to send messages across the internet without fear of them being stolen. Since RSA is one of the primary encryption methods used by modern computers, people should know how it works. I also felt that this topic would be something that the majority of people don't actually know, so it would be beneficial to have a video such as this that is accessible for the average person to understand. I also make it a point to add in a clear, concrete example of why RSA encryption works, so that someone who watched the video could visualize the way RSA protects our information.
---Tell us about yourself! Why do you believe that it is important to study mathematics, life sciences, or physics?
I have a lot of experience in math. Ever since I was young, math has been my favorite subject. In high school I took an accelerated math course through multi variable calculus, and I also participated in many math competitions such as USAMO. The reason that studying STEM areas is so important is because they literally represent the future progress of our society. Each discovery and breakthrough furthers our society's knowledge and gives us access to new technology to improve the quality of life of everyone on the planet. Furthermore, STEM jobs pay very nice salaries, making it very easy to have a comfortable life as a STEM worker.
---What specific area(s) of mathematics, life sciences, or physics would you like to pursue in the future and why?
Currently I am not sure exactly which areas of math I will pursue in the future, since I could see myself in either a pure or an applied field. But hey, isn't that what college is for?
---Tell us about a teacher who inspired your interest in mathematics, life sciences, or physics. What is the teacher's name? What did that teacher do to develop your passion for learning and discovery?
The teacher who inspired me the most was my math team coach, Mr. Curt Michener. He convinced me to join the math team, and eventually I caught the math bug. If it weren't for him, I would have never truly realized my love for mathematics. He also provided me many opportunities to participate in math competitions, such as AMC, Math League, and Moody's Mega Math Challenge. I couldn't have done it without Mr. Michener.
---If you win the Breakthrough Junior Challenge, your school will receive a new, cutting-edge science lab from Cold Spring Harbor. How would this lab benefit your school?
The lab would reward those who worked hard in their science classes, hopefully causing more people to fall in love with science. That would be great for my school because we always need more science majors.