RSA parameter generator algorithm

i'm studying for my basic crypto class and I'm trying to formalize the algorithm for the parameter generation of RSA, unfortunately, I cannot find any algorithm, just plain text.

Can someone tell me if this algorithm could be accepted? Please focus more on the public exponent $$e$$

1. KeyGen()

1. Let $$p,q$$ be two random prime numbers
2. $$N\leftarrow pq$$
3. $$\phi(N)=(p-1)(q-1)$$
4. $$e\xleftarrow{R}\{x|\;0< x < \phi(N) \land x\in \mathbb{N} \land gcd(x,\phi(N))=1 \}$$ // $$\xleftarrow{R}$$ means that the element is chosen randomly
5. calculate $$d$$ such that $$ed\equiv 1 \pmod{\phi(N)}$$
6. $$PK\leftarrow (N,e)$$
7. $$SK\leftarrow (N,d)$$
8. return $$(pk,sk)$$
• Ideally the $e$ is selected on advance, when $\gcd(e,\phi(n))\neq 1$ we select new randoms. The key-gen should take a security parameter like $1^{2048}$ to determine the modulus size... Dec 12 '21 at 17:27
• yup i got it but i would like to avoid the while loop as hell, just to make the code clean. Said that the definition of the set Is correct? Dec 12 '21 at 17:30
• What about the Wikipedia's RSA Key-gen?. Yours almost sound like it! And, could be accepted for what? Dec 12 '21 at 17:31
• omg thank you, i don't know how but I missed it. By accepted I mean that could be okay to write that code in a basic crypto class exam (of course followed by a more verbal explanation) Dec 12 '21 at 17:32
• Interesting that a crypto class doesn't mention this properly. Edit your question so that we can review it. Dec 12 '21 at 17:47