RSA is a common algorithm used to generate Asymmetric keys. Lets look at an example using two small prime numbers.

Let p = 3 (The 1st prime number)

Let q = 11 (The 2nd prime number)

Now compute N = p X q = 33

Compute z = (p -1)(q-1) = (3 1)(11 1) = 20

Now pick a number e such that 1 < e < z (e has to be prime)

Pick E = 7

Now compute (D x E) mod Z ) = 1 (Pick some number d). An example for d = 3

(3 x 7) mod 20 = 1 (Satisfies the equation)

The keys are:

(D, N)

(E, N)

And in our case

Encryption Key = (3, 33)

Decryption Key = (7, 33)

Now for this discussion, you are going to use two prime number p and q and find the following

1. N

2. Z

3. D

4. Now PICK E