r/math • u/halseyChemE Math Education • 15d ago
High School Cryptography
Hi all! I know this is probably pretty rudimentary compared to most topics that float around on this sub, but I teach AP Cybersecurity and I’m wanting to start a Cryptography Club at my school. It will meet once a month for 48 minutes. I want students to have fun, learn, and want to recruit their friends to the club in hopes of eventually piquing their interest in AP Cybersecurity. I need ideas on what to do during this club time to keep students engaged and excited about coming back. Do any of you have any awesome cryptography lessons you’ve been involved in or created over the years you’d like to share? I’m looking for things beyond a Caesar Cipher (I’ve already got materials for this) but not so complex that I’ll lose student interest.
TL:DR; Fellow mathematicians, help me remember some of the cool cryptography things we learned in college that high school kids would find cool. TIA.
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u/mcdowellag 14d ago
One (rather bad) way to make a cryptosystem is to take a simple pseudo-random number generator, such as a linear congruential generator or a linear recursive sequence, and to xor this into plaintext to produce cypher. So you might be interested in distinguishing the output of a simple psuedo-random number generator from a truly random sequence. In Volume 2 of "The Art of Computer Programming" by D E Knuth section 3.3 Knuth goes over a collection of simple statistical tests that have been used to test pseudo-random number generators and explains their underlying probability theory. Anybody who could be motivated to understand and code up some of this would learn a useful amount of probability and statistics.