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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?

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    $\begingroup$ 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. $\endgroup$ – poncho Apr 11 '14 at 17:17
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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.

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