RSA Cryptosytsem, choosing $e$

Question

I am using the RSA crytposytem. I have $p$, $q$ and hence $n$ and $\phi$ however I don't understand how to get $e$ such that $gcd(e,\phi)=1$

Many thanks

@fgrieu Should we hit the close button? – Maarten Bodewes Dec 01 '14 at 11:52 — Maarten Bodewes, Dec 01 '14 at 11:52

score 1 · Answer 1 · answered Dec 01 '14 at 07:23

You need to choose e such that it is co-prime relative to PHY(n). Since you do not want to get involved in factorization of PHY(n), the best way is to choose e randomly, and better let it be a non even prime. Common values are 2^16+1, 3, etc. Most of the primes you choose will have GCD(e,PHY(n))=1.

RSA Cryptosytsem, choosing $e$

1 Answers1