number sequences such communications system applications include a random number generation application an error coding application an encryption application a modulation application and the like in encryption applications the combining process is performed for masking an input data stream by some invertible operation using a number stream produced to deny determination of its generating characteristics the term u201c invertible u201d as used herein refers to the existence of a method for undoing the masking operation and obtaining the original data stream it is also desirable to have an efficient means of combining two 2 independent randomly generated number streams this combining process can provide a non linear random number stream non linearly generated random number streams make it very difficult to identify generating structures as such some embodiments of the present invention provide a method and apparatus for efficiently combining two 2 inputs via multiplication in a galois extension field such an embodiment satisfies efficiency in both time and hardware design such an embodiment further provides a simple nearly symmetric inverse operator other embodiments of the present invention provide a method for efficiently masking data in digital hardware while making unintended decoding difficult in this regard it should be appreciated that such a method can be used in a variety of communications system applications such a method can be combined with other nonlinear or mixed radix processing techniques to induce chosen statistical.