Why are stream ciphers not PRPs? In a stream cipher like RC4, a message is xored with a random stream of bits, hence a n bits message will result in a n bits random-like ciphertext.

So it's a bijection, it's invertible, the output looks like a random element in {0,1}^n...

Why are stream ciphers not considered as PRPs?
I assume that for a fixed key $K$, you are asking why $f(m) \overset{\underset{\mathrm{def}}{}}{=} &lt;STREAM&gt; \oplus\ m $ is not a PRP, where $&lt;STREAM&gt;$ is the stream that is generated from the key $K$. $f$ verifies at least two properties that PRP in general do not verify:


$f(m_1) \oplus f(m_2) = m_1 \oplus m_2$
$f(f(m_1)) = m_1$