In class today we covered material corresponding to the lecture note sections
- modular arithmetic
- computing exponents moduo n (only up to the formula for computing Euler's phi function. We did not cover Euler's theorem)
We also did not have time to discuss the RSA cryptosystem. Even though it was invented in 1977 is still one of the most important and widely used cryptosystems. It's great that math of RSA can be understood using what we learned in this course.
I strongly suggest you watch the following by Eddie Wu (Australia's coolest math teacher :) )
- The RSA Encryption Algorithm (1 of 2: Computing an Example)
- The RSA Encryption Algorithm (2 of 2: Generating the Keys)
Note that it relies on exactly the material we covered in class today! The proof that the system works uses inverses in Z_n, Fermat's little theorem, and the calculation of Euler's phi function.