My understanding is that, simply put, a stream cipher is just a CSPRNG such that $R(i,k)$ will produce a deterministic but statistically random sequence, where $i$ is an IV, and $k$ is the session key. The resultant key-stream $K$ is then combined with plaintext (i.e. $C = K \oplus M$).

Now, if we take two messages $m_1$ and $m_2$, and assume $\mathcal{E}(x)$ and $\mathcal{D}(x)$ are functions that encrypt and decrypt a message as described above, surely the following is a partially homomorphic cryptosystem?

$\mathcal{D}(\mathcal{E}(m_1) \oplus m_2) = m_1 \oplus m_2$

This seems a really simple and fundamental way to perform unauthenticated homomorphic cryptography, yet the Wikipedia article doesn't mention it at all.

Am I incorrect in saying that this process demonstrates homomorphism?

My understanding is that, simply put, a stream cipher is just a CSPRNG such that $R(i,k)$ will produce a deterministic but statistically random sequence, where $i$ is an IV, and $k$ is the session key. The resultant key-stream $K$ is then combined with plaintext (i.e. $C = K \oplus M$).

Now, if we take two messages $m_1$ and $m_2$, and assume $\mathcal{E}(x)$ and $\mathcal{D}(x)$ are functions that encrypt and decrypt a message as described above, surely the following is a partially homomorphic cryptosystem?

$$\mathcal{D}(\mathcal{E}(m_1) \oplus m_2) = m_1 \oplus m_2$$

This seems a really simple and fundamental way to perform unauthenticated homomorphic cryptography, yet the Wikipedia article doesn't mention it at all.

Am I incorrect in saying that this process demonstrates homomorphism?