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Number theory is the study of the properties and construction of numbers, particularly integers. Prime numbers are of particular interest to number theorists and consequently cryptographers as they are considered the "building blocks" of numbers and produce many interesting results which are useful in cryptography. Questions covering number theory and primes should use this tag; questions involving finite fields and groups might use this tag if relevant.

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Why $f(x)=x^e$ is a bijection i.f.f $e\in{\mathbf{Z^*_{\phi(N)}}}$?

The correct form is: The integer $a \mod Z_n$ has multiplicative inverse iff $gcd(n,a)=1$ Here, you are working on exponents, so you must consider the modulo as $\phi(n)$ not $n$. Therefore, here yo …
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