matrix addition

So the time complexity of Add([C.sub.1],[C.sub.2]) is mainly dominated by the matrix addition. The time complexity of matrix addition is O([N.sup.2]) under the serial computing, so we can optimize it by the parallel computing.

According to the parallel computing theory, the matrix addition can also be optimized by the computer cluster of 2-dimensional grid, which consists of p x p computers.

It is obvious that the time complexity of matrix addition is O(1) under the parallel computing because all the computations work at the same time.

From the above we know, both PFlatten() and PBitDecomp() have constant time complexity, so the main overhead of the encryption model is the product of R * A, the product of u * [I.sub.N] and the matrix addition. Because the matrix multiplication and the matrix addition have been optimized under the parallel computing, and their time complexity are O(N) and O(1) respectively.