Generation of Addition Chain using Deterministic Division Based Method

Efficiency of a cryptosystem depends not only on the security it provides, but also it increases the operational speed thereby it reduces the time taken for encryption and decryption. In most numbertheoretic cryptographic algorithms like RSA, ElGamal, Massey-Omura etc., the encryption and decryption functions often involve raising large elements (x mod n) of group fields GF(2) or large powers (exponents). If they are not properly implemented, they increase the operational time which ultimately lead to customer dissatisfaction. Thus, group exponentiation has received much attention by the researchers in recent times owing to their central role in modern cryptography and it is effectively computed using the concept of addition chain. Several deterministic and stochastic algorithms have been proposed in literature to generate the shortest addition chains. Normally, stochastic algorithms produce the optimal addition chains but it is not obtained from the single run which is a time consuming process. Thus, a deterministic algorithm has been proposed which is simply based on division in this paper and it is compared with other deterministic and stochastic algorithms.