Investigating effects of co-ordinate system on execution time of elliptical curve protocol in wireless sensor networks

All standard ECC protocols like Elliptical Curve Diffie Hellman (ECDH), Elliptical Curve Digital Signature Algorithm (ECDSA) used for pair wise key establishment and authentication in WSN requires scalar multiplication operation to calculate public key. Scalar multiplication occupies 80% of the protocol execution time and depends on several factors including choice of coordinate system. One of the crucial decisions, when implementing an efficient ECC on WSN is deciding which coordinate system going to use. The coordinate system determines the efficiency of point addition and point doubling algorithms on the elliptic curve, and hence the efficiency of the basic cryptographic operation of scalar multiplication. This paper has investigated relative performance of various coordinate systems and have suggested appropriate one for WSN. The results have been validated on MIRACL crypto library with real life examples.