Fair point! I think that quote should read "a random coprime to [...] to ϕ(n)". Then it makes sense.

There's a lot of math behind RSA computation and we were trying to distill as much as we could, but it's not perfect. We have added a simple example to tie everything together, but it just means that you might have to plow thru the heavy bits first.

Now, the totient it needed to compute your encryption and decryption values. You start with getting 2 primes:

  n = p * q

then you compute the totient:

  ϕ(n) = (p-1)(q-1)

then you compute your encryption and decryption values:

  e x d = 1 mod ϕ(n)

Then your private key will be be a pair (d, n) and public key will be (e, n).

Then, given that m is message and c is cipher:

  Encryption

  F(m,e) = m^e mod n = c

  Decryption

  F(c,d) = c^d mod n = m