Data Switching and Information Leakage Hypothesis: Let $z,a$ be uniformly random elements of a field $\mathbb{F}_p$ where $p$ is a large prime number. Also, let $(-z)$ be additive inverse of $z$.



I have a fixed secret value $x$. I mask it as $I=x+z$ and send it to a semi-honest server. 

Later on, I send $w$ and $c=(-z)\cdot w+a$ to the server, and ask it to do as follows: 
$K=I\cdot w+c=(x+z)\cdot w+(-z)\cdot w+a=wx+a$.

Question: Given $I, w,c$ and $K$, can the server learn anything about $x$?



Note 1: $z,a$ are secret values, too. So if the server learns about them it may learn about $x$.

Note 2: The above scenario is a part of protocol and it may not make sense for the readers at first glance.
Server receives three messages:


$I=x+z$. This is the value $x$ encrypted with a one-time pad $z$. The server cannot find $x$ without knowing (something about) $z$.
$w$. This is (presumably) independent of anything secret.
$c=(-z)\cdot w+a$. This is the value $(-z)\cdot w$ encrypted with a one-time pad $a$. The server receives no information about $(-z)\cdot w$ and thus $z$ or $x$ without knowing something about $a$.


Therefore, assuming that $z$ and $a$ are generated randomly just for this instantiation and never reused or revealed, and that $w$ is independent of $x, z, a$, the server learns nothing about $x$.