# How to keep phi(n) secret in RSA?

As we know, RSA cryptosystem have both private key(a,p,q) and public key(b,n), by chinese remainder theorem and fermat's little theorem, we know that the importance of keep p and q secret, and from this Why is it important that phi(n) is kept a secret, in RSA post , we know $\phi$n need kept secret, but my question is, if n is a public key as encryption needed, how we keep $\phi$n as secret?

• We don't tell people what it is? The problem of finding $\phi(n)$ given $n$ is a hard problem (if $n$ is hard to factor). So, if we give people a number that they can't factor, and we don't give them $\phi(n)$, they can't determine it on their own. – poncho Apr 11 '14 at 17:17

## 1 Answer

How do we keep $\phi(n)$ secret?

We don't tell people what it is. The problem of finding $\phi(n)$ given $n$ is a hard problem (if $n$ is hard to factor). So, if we give people a number that they can't factor, and we don't give them $\phi(n)$, they can't determine it on their own.