Fast Algorithm in ECC for Wireless Sensor Network Xu Huang, Pritam Shah, and Dharmendra Sharma Abstract—Elliptic curve cryptography (ECC) has been attractive to the people who are working in the field of the network security due to its good potential for wireless sensor network security due to its smaller key size and its high strength of security. But there is a room to reduce the key calculation time to meet the potential applications, in particular for wireless sensor networks (WSN). It is well known that scalar multiplication is the operation in elliptical curve cryptography which takes 80% of key calculation time on wireless sensor network motes. In this paper, the research proposes algorithm based on 1’s complement subtraction to represent scalar in scalar multiplication which offer less Hamming weight and will remarkably improve the computational efficiency of scalar multiplication. Index Terms—Elliptic curve cryptography, Scalar multiplication, Non-adjacent form, Hamming weight, one’s complement subtraction, ROM, wireless sensor networks I. INTRODUCTION Rapid growth in the very large scale integrated (VLSI) technology, embedded systems and micro electro mechanical systems (MEMS) has enabled production of less expensive sensor nodes which can communicate information shorter distances with efficient use of power [1]. Sensor node detects information, processes it with the help of an in-built microcontroller and communicates results to the ‘sink or base station’. The base station is a more powerful node linked with central station via satellite or internet communication. Wireless sensor networks can be deployed in various applications namely environmental monitoring e.g. volcano detection [2,3], distributed control system [4] , detection of radioactive sources [5], agricultural and farm management [6, 17], and computing platform for tomorrows’ internet[7] . II CHALLENGES IN DEVELOPING SECURED PROTOCOLS FOR WIRELESS SENSOR NETWORKS Compared to traditional networks, a wireless sensor network has many resource constraints [4]. The MICA2 mote consists of an 8 bit ATMega 128L microcontroller working on 7.3 MHz. As a result nodes of WSN have limited computational power. Normally, radio transceiver of MICA motes can achieve maximum data rate of 250 Kbits/sec which puts a limitation on the communication resources. The flash memory which is available on the MICA mote is only 512 Kbyte. Apart from these the battery which is available on the board is of 3.3.V with 2A-Hr capacity. Due to the above boundaries the current state of art protocols and algorithms are expensive for sensor networks due to their high communication overheads. III ELLIPTIC CURVE CRYPTOGRAPHY PRELIMINARIES Elliptic Curve Cryptography was introduced by Victor Miller [9] and Neal Koblitz [10] independently in the early eighties. The advantage of ECC over other public key cryptography techniques such as RSA, Diffie-Hellman is that the best known algorithm for solving ECDLP the underlying hard mathematical problem in ECC takes the fully exponential time. On the other hand the best algorithm for solving RSA and Diffie-Hellman takes sub exponential time [11]. To sum up the problem of ECC can be solved only in exponential time and so far there is a lack of sub exponential attack on ECC. An elliptic curve E over GF(p) can be defined by where a, b ∈ GF(p) and b ax x y + + = 3 2 in the GF(p) (1) 0 27 4 2 3 ≠ + b a The point (x, y) on the curve satisfies above equation and the point at infinity denoted by ∞ is said to be on the curve. Let’s have examples: 5 2 3 2 + + = x x y (2) (3) 1 2 3 2 + − = x x y Fig. 1 Elliptic curve equation (2) Fig. 2 Elliptic curve equation (3) Proceedings of the International MultiConference of Engineers and Computer Scientists 2010 Vol II, IMECS 2010, March 17 - 19, 2010, Hong Kong ISBN: 978-988-18210-4-1 ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online) IMECS 2010