# Thread: RSA and number of decryption exponents

1. ## RSA and number of decryption exponents

We must prove that in the RSA cryptographic system for the primes $p, q$ and the encryption exponent $e\bot\phi(pq)$ in set $\{0,\dots,\phi(pq)-1\}$ is exactly $gcd(p-1,q-1)$ elements that
you can use as the decryption exponent $d$.
(That is for every $M\in\{0,\dots,pq-1\}$, after encryption $M$ using encryption exponent $e$, and then by using the decryption exponent $d$ we get back the $M$).

2. I forgot to say that what $\phi$ means.
$\phi(n)=|\{1\leq k\leq n : k\bot n \}|$
In this situation ( $p,q$-primes) we have:
$\phi(pq)=(p-1)(q-1)$