Gautam Kumar Dept. of Information Technology AIET, Alwar, India gautam21ujrb@gmail.com Pratap Singh Patwal Yogesh Chand Gupta Computer Science & Engg. Computer Science & Engg. AIET AIET Alwar, India Alwar, India pratappatwal@gmail.com yogeshsofttester@gmail.com — ! " " # $ % &%’ ( ( ( )" *$ ! ( ! " ! ! ( ! + % $ ( ( + $ # ! ( $ ( ! ! $ ( " ! ! ! $ !, ! ! " -$ .#)*/#. %lliptic Curve Cryptography (ECC) was proposed in 1985 by Neal Koblitz and Victor Miller. It is an alternative to the established cryptosystems like RSA, DSA. It guarantees all the security services with the shorter keys. The use of shorter length implies less space for key storage, less arithmetic cost and time saving when keys are transmitted [1]. These characteristics make ECC the best choice to provide security in smart cards, mobile phones, online banking, network devices, controllers like routers, bridges, laser printers, applications in robotics, automotive, consumer electronics and many more. ECC has increased as evidenced by its inclusion in standards by in credited standards organizations such as American National Standards Institute (ANSI), Institute of Electrical and Electronic Engineers (IEEE), International Standards Organization (ISO), and National Institute of Standards and Technology (NIST). The security of ECC is based on the discrete logarithm problem over the points on an elliptic curve. But, it is more difficult problem than the prime number problem of RSA algorithm [2]. These two problems are closely related to the key length of cryptosystems. If the security problem is more difficult, then smaller key length can be used with sufficient security. This smaller key length makes ECC suitable for practical applications such as embedded systems and wireless applications [4]. A cryptographic algorithm running on a general: purpose has only limited physical security on most operating system. Thus, hardware encryption devices are used. These devices provide high security performance and high speeds [17]. Nowadays, mobile devices are used in global communication world. These devices are interacting with other devices to perform a task and they are forming ad:hoc networks. The two key aspects of these devices are security and interoperability in the heterogeneous inter:network environment. But due to scarce resources of mobile devices, exhaustive use of cryptographic is infeasible and therefore ECC is used [12]. ECC has received the maximum attention from the research community from the last decades and dominating RSA/DSA systems today. Koblitz curve is an extension of ECC that are dedicated to reach to the better performance used in the cryptosystem because of special kind of functionalities, an improved versions of algorithm and specialized curves [1], [7]. It offers much faster computation and requirements of less memory. The requirements of code size and memory size execution are smaller. Due to special kind of functionalities involved in the Koblitz curve which emphasizes not to go for individual operation to store at some point, the meaning is that it keeps the full power computation without effectively storing all of the precomputed values. A vast amount of research has published to offer an interesting alternative to standard prime: field:based cryptosystems because, for the same security level, they are much faster and require less memory. The scalar multiplication is evaluated on the elliptic curve by given a International Journal of Advances in Engineering Sciences Vol.1, Issue 1, Jan, 2011 18