Parallelized Montgomery Exponentiation in GF(2^k) for Diffie-Hellman Key Exchange Protocol

Finite field arithmetic is commonly used in cryptographic applications such as establishing secure connections between systems. Recent standards have expanded the necessary key lengths, potentially increasing the time connections might take. This paper offers performance tests of highly efficient optimization structure for modular exponentiation based on parallelizing Montgomery exponentiation in GF 2 k. The paper also describes the algorithms necessary for an implementation of the optimization structure in question and performance tests for a Diffie–Hellman Key Exchange system utilizing the structure. The resulting efficiency improvements of nearly 45% over standard modular exponentiation can potentially be applied to any algorithm that relies on such operations.