RSA algorithm, relationship of the plaintext $m$ with $p$ I am studying the RSA algorithm. If for example the plaintext $m$ has some relationship with prime $p$, let's say $m$ is multiple of $p$ (where $p$ is the $p$ in $n=p \times q$). Can this give an attacker some information given we know ciphertext $y$ and public key?
So after trying a few examples with small numbers, it turns out that if message $m$ is a multiple of $p$, $m=a\times p$ then $\gcd(y,n)=p$, where y the known ciphertext. The rest is easy to compute.