I mean, $n$ can also be easily used to find the factors $p$ and $q$ right?
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6$\begingroup$ Possible duplicate of Why is it important that phi(n) is kept a secret, in RSA? $\endgroup$ – otus Apr 26 '16 at 6:53
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No, it is not easy! RSA is based on the difficulty of factoring the product $n=pq$ of two large prime numbers. But if you know $\varphi(n)$ for plain RSA you can compute the secret exponent $d=e^{-1}\bmod \varphi(n);\;$ and you can factor $n$ from the two equations $n=pq,\;\varphi(n)=(p-1)(q-1)$.
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$\begingroup$ In general, it is easy to find the prime factors of any numbers. But here, p and q are taken so large (at least 512 bits) that it takes an veery long time. And thus we talk about the hardness of factoring the product of (very) large primes. $\endgroup$ – aguellier Apr 26 '16 at 11:17
