Math 361, Spring 2020, Assignment 5

Read:

1. Section 20.

Carefully define the following terms, then give one example and one non-example of each:

1. Euler totient function (or Euler $\phi$-function).
2. Symmetric cryptosystem.
3. Asymmetric cryptosystem.

Carefully state the following theorems (you do not need to prove them):

1. Formula for $\phi(p^n)$ when $p$ is prime.
2. Formula for $\phi(ab)$ when $\mathrm{gcd}(a,b)=1$.
3. Euler's Theorem.
4. Fermat's Little Theorem.

Solve the following problems:

1. Section 20, problems 1, 5, 6, 7, 10, 19, 27, and 28.

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