Construction of vector space and its application to facilitate bitwise XOR – Free operation to minimize the time complexity

In modern computing environments, speed of execution of any operations are gaining more attentions. The faster processing of the unit operations, opens the room for the applications such as cryptography, data communication etc. Hence, in this work a new software-oriented approach is proposed to use in the environments that requires faster executions. This proposed method speeds up the computations of the logical operations – bitwise XOR. This paper first elaborates on the procedure of how to construct the bitwise XOR vector space efficiently using recursive approach based on Pauli’s matrix. The corresponding time complexity for the construction of the bitwise XOR vector space is computed by master theorem and is O(log2(n/2n)). Later, the paper presents on the implementation of this bitwise XOR vector space constructed to facilitate the XOR – Free operations. For the evidential proof, the proposed bitwise XOR-free operations are implemented on standard key stream generation scheme, SNOW 3G. The average speed up gained by the bitwise XOR-Free operations on the SNOW 3G is 1.36x and the corresponding throughput attained is 21.85Mbps.