A Fast Parallel Modular Exponentiation Algorithm

Modular exponentiation is a fundamental and most time-consuming operation in several public-key cryptosystems such as the RSA cryptosystem. In this paper, we propose two new parallel algorithms. The first one is a fast parallel algorithm to multiply n numbers of a large number of bits. Then we use it to design a fast parallel algorithm for the modular exponentiation. We implement the parallel modular exponentiation algorithm on Google cloud system using a machine with 32 processors. We measured the performance of the proposed algorithm on data size from $$2^{12}$$212 to $$2^{20}$$220 bits. The results show that our work has a fast running time and more scalable than previous works.

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