Suppose I have a private matrix $A$ that I want to conceal. I do the matrix multiplication $A^\prime =AK$ and $A^\prime$ is public.
How can I quantitatively measure "how well" the matrix $A$ is concealed? To be specific, I may select different matrices $K$ and want to analyze the different protection levels provided by multiplying $K$.
I way we can think about is the probability to recover $A$ given $A^\prime$. However, even if $A$ cannot be recovered, some information (such as ratio between the entries) will be leaked. How can I quantify such information?