Advancement Through Research
This paper presents a novel parallel reduction algorithm specifically designed for handling multiple-precision integers within the finite field GF(2n). We begin by thoroughly analyzing the data dependencies inherent in the traditional sequential reduction algorithm. This analysis is critical as it informs the design of our parallel algorithm, allowing for optimized performance while reducing computational bottlenecks. To measure the efficiency of both algorithms, we define a single clock cycle as the basic unit of computation time. We then calculate the time complexities associated with the parallel and sequential algorithms, allowing for a direct comparison of their performance. The results of our evaluation show that the parallel algorithm achieves a remarkable speedup over its sequential counterpart. This significant improvement highlights the effectiveness and efficiency of the proposed parallel reduction algorithm, making it a valuable contribution to the field of computational mathematics and cryptography, particularly in applications where large integers must be processed rapidly.
Multiple Precision; Parallel Algorithm; Finite Field GF(2n); Reduction
