Fuzzy controlled scalar multiplication for ECC

Abstract

Traditionally, RSA is being used for authentication and key exchange for symmetric key cryptography (SKC). Improved network security demands forward secrecy also. Even though, RSA, a widely used key exchange approach can not provide forward secrecy, the same can be achieved by making used Elliptic Curve Diffie-Hellman Ephemeral (ECDHE) technique for SKC and RSA for the purpose of authentication. However, ECDHE_RSA based approach is more compute intensive compared to the RSA alone. The predominant operation in the ECDHE technique is Elliptic Curve (EC) based scalar multiplication. Hence, speeding up of ECDHE operation demands faster EC scalar multiplication algorithm. Binary method, Non-adjacent form (NAF) method and sliding window method are used to carry out the EC scalar point multiplication. An algorithm based on both the NAF and the sliding window techniques is considered. This technique is more efficient in terms of EC point operations. There is a trade-off between the number of EC point addition operations and the number of pre-computed values. A fuzzy based controller method is proposed to determine an optimum window width, resulting in faster scalar multiplication.