Suppose Alice would like to obtain the product of two $m\times m$ matrices i.e. $A$ and $B.$ Alice has $A,$ whereas Bob has $B.$
Since Alice does not want to reveal $A$ to Bob, she chooses a $m\times m$ random invertible matrix $R.$ She sends $RA$ to Bob over a secure channel.
Bob obtains $RA,$ and calculates $RAB,$ and sends it to Alice over a secure channel.
Alice obtains $AB$ by inverting $R$ i.e. $R^{-1}RAB$.
$R$ is only utilized once.
Any ideas on how to proceed with the security analysis of the above protocol?
Specifically is H(A|RA) = H(A) ?