Parallelization of modular exponentiations of polynomials

Modular exponentiations are very important in many fields of computer science, including network security protocols. Modular exponentiations of polynomials are a type of modular exponentiations, where the base and modulus are polynomials. In this paper, a parallel modular exponentiation algorithm, which was proposed by Lara et al., is extended to solve modular exponentiations of polynomials in parallel, and further compared to two other proposed parallel algorithms. Essentially those algorithms differ only in their load-balancing methods. The result is, for exponents of length up to 2048 bits, the implementation of Lara et al.'s algorithm results in 28.01% faster running time compared to the implementation of the sequential algorithm. The result also shows that this algorithm is more efficient than the two other proposed algorithms.