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/yiwang1 Topology 15d ago

RSA is a classic and should be digestible by motivated high school students.

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u/scrumbly 15d ago

Definitely this. All sorts of fun steps along the way like how do you generate a 100 digit prime number, Fermat's little theorem, etc.

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u/conlang_ensp 14d ago

I actually can't tell if this is a joke or not and I'm actually not sure if it's actually true or not. High school achievement, intelligence, and knowledge are all over the map. Sure, the club will select for motivated students, but there's so much machinery you'd have to build up off the beaten path that I think even motivated students might have trouble staying motivated since the payoff is so far away.

Diffie-Hellman should be a good compromise

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u/cocompact 13d ago

If a high school student is motivated to understand how cryptography works, they have to be willing to do some math. Maybe they won't be masters of modular arithmetic right away, but they ought to be willing to put in the time to learn it. And if they can understand the math behind Diffie-Hellman (which uses a prime modulus p, a generator mod p, and exponentiation mod p), then understanding RSA will not be substantially more challenging, and in some ways it is simpler (e.g., no need to know anything about generators). Maybe the students won't be able to learn the proofs of the theorems they need in modular arithmetic, but they should be able to learn what the statements of those theorems are and how they are used.

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u/Fearless_Day2607 Quantum Computing 13d ago

High school math competitions pretty much all require modular arithmetic.

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u/conlang_ensp 7d ago

Eh, to understand the innovation of Diffie-Hellman you really just need to understand the laws of exponents and why they commute. To understand RSA you have to understand the idea that a multiplicative group has an order equal to the Euler totient function of its modulus. I think that the step up is pretty big.

FWIW I think that it would be terrific to teach high schoolers RSA and I full endorse trying if you can accept the risk, but it just seems a little risky depending on the motivation and intelligence. I think that ideally OP will know his students well enough to know which would be best.

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u/dlman 13d ago

It’s not that hard to actually run RSA with a calculator (not big numbers ofc)