Suppose Alice would like to obtain the product of two mXm 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 mXm random invertable matrix R. She sends R*A to Bob over a secure channel.
Bob obtains R*A, and calculates R*A*B, and sends it to Alice over a secure channel.
Alice obtains A*B by inverting R i.e. (R^-1)*R*A*B.
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)