What cryptography is suitable to motivate High School students to learn math? [closed]

Question

A High School math teacher in the Bronx asked me if I knew of any way to use cryptography in a way that motivates students (15 to 18 years old) to learn math.

I do know that many of them want to protect (encrypt) Snapchat pictures, and understand how SSL and encryption "works".

Is anyone aware of a curriculum, or is willing to share a mental outline of an age-appropriate set of challenges that will get them thinking in the right direction? The focus is for non-math majors who need to "justify the reason" for learning math, and to gain a sense of empowerment and removing fear from the word "encryption".

One exercise could be to "use exponents to encrypt a password", or other weak crypto that can be done with a pen and paper. I also want to get students thinking about prime numbers, and why they are important, and other similar "building block" concepts.

Answer 1

15-18 is an age where kids are looking for independence and question authority of adults. Cryptography is often horribly implemented, and can serve as a teaching tool of where professionals have gone wrong.

So pick some real world blunders, and do some analysis on those blunders. There's enough cryptographic blunders that are easy enough for HS students to understand to fill an entire course with.

A good recent example is the Adobe password leak. A good writeup is available here You could very easily find the leaked data, create a small, anonymized subset of it, and repeat the same analysis done in the article on that subset.

It's a great example because it uses something kids use every day that's highly mathematical (passwords on websites), but they're unaware of. It also shows how adults screwed up, which every kid loves, but also how to do things right. The mathematics is simple enough that you don't need advanced degrees in mathematics, and you don't really need to go into depth on how the crypto works.