New Diffie Hellman key exchange primitive based upon binary field

One of the earliest public-key algorithm is Diffie Hellman key exchange algorithm.The Diffie Hellman key exchange allows two parties that have no prior knowledge of each other to jointly establish a shared secret key over an insecure communications channel.However, one drawback of this algorithm is the inherently expensive exponential calculation that provides the needed one-way trapdoor mechanism.Hence, an alternative approach is proposed whereby the key exchange will no longer depend on the prime field instead the newly proposed algorithm will now depend on the binary field as it is known that binary field operations are inexpensive and provides notably faster computations.The result evidently shows that the binary field Diffie Hellman performs almost twice as fast as the prime field Diffie Hellman.In general, this result serves as an example in which the binary field can benefit the mainstream cryptography.