Efficient implementation of elliptic curve Diffie-Hellman (ECDH) key distribution algorithm in pool-based cryptographic systems (PBCSs)

In Reference [1], the subject of efficient use of random numbers was studied. We gave examples for inefficient and efficient use of random numbers for the case which a random number r is generated according to the rule r < n, where r and n are k-bit integers and n is a fixed integer. In this work, we will show how to apply the 2 methods presented in [1] while implementing elliptic curve Diffie-Hellman (ECDH) algorithm in pool-based cryptographic systems (PBCSs). In this work, we also present a 3. method to use random numbers more efficiently and compare all the 3 methods. To our knowledge, this is the first work on using pool-based random numbers in the implementations of ECDH algorithm.