Multiplexer-based double-exponentiation for normal basis of GF(2m)

In many cryptographic protocols, double-exponentiation is a key arithmetic operation. In this study, we will present a multiplexer-based algorithm for double-exponentiation in GF(2m). The proposed algorithm utilizes the concept of the modified Booth's algorithm. Multiplexers are employed for implementation of the proposed algorithm. The proposed double-exponentiation algorithm only requires m multiplications and saves about 66% time complexity while comparing with the ordinary binary method.