Efficient Noninteractive Outsourcing of Large-Scale QR and LU Factorizations

Algorithm 1

A CPA indistinguishability experiment in value.

(1)	A client C generates a random matrix and a key K with the security parameter
(2)	An adversary output and two different values
(3)	C picks randomly, replaces the element of with to get , and calculates the masked task
(4)	predicts with the access to the oracle
(5)	Return 1 if and 0 otherwise
(C)	Efficiency: it actually means that the overhead involved in using outsourcing scheme by the client should be substantially less than the overhead required for executing the computational task computation on its own.
(D)	Verifiability: it is commonly required that the proposed algorithm can verify correctness of the returned result, the correct results can pass the verification algorithm successfully, and the probability of incorrect results sent back from a malicious cloud server can pass the verification is negligible.