%0 Journal Article %1 ravikishorekodali2013optimized %A Ravi Kishore Kodali, Harpreet Singh Budwal %A Prof. Narasimha Sarma, N.V.S. %D 2013 %E Hope, Dr.Martin %J Int. J. on Recent Trends in Engineering and Technology, %K coordinate forward secrecy systems %N 1 %P 7 %T Optimized Software Implementation of ECC over 192-bit NIST Curve %U http://searchdl.org/public/journals/2013/IJRTET/9/1/524.pdf %V 9 %X RSA is the most widely used public key cryptosystem, serving the purpose of key exchange for symmetric key cryptography and authentication. Improved network security demands forward secrecy, which RSA is unable to provide. Also the lower per bit security of the RSA technique, makes it difficult to be implemented in resource constrained devices. The protocols including Elliptic curve Diffie-Hellman Ephemeral (ECDHE) as the key exchange mechanism and RSA for authentication, overcomes the drawback incurred by the RSA alone and provides forward secrecy. The advantage of forward secrecy in a network is accompanied with higher complexity and computational cost. This paper describes the complete optimized software implementation of elliptic curve over the NIST prime field. The arithmetic operations over the prime are discussed. Different coordinate systems for elliptic curve point representation like affine, projective, Jacobian projective, and mixed coordinate systems are elaborated. Various techniques for scalar multiplication like Binary, NAF, sliding window, fixed based window, comb method, are given. Scalar multiplication is the most dominating operation in Elliptic curve cryptography (ECC) which consumes 85% of the execution time. A controller based on the fuzzy logic is presented for an optimum selection of window width, w, in the scalar multiplication methods. A comparison of various techniques and combinations of different techniques to perform complete ECDHE operation are provided along with the implementation timings.

@article{ravikishorekodali2013optimized, abstract = {RSA is the most widely used public key cryptosystem, serving the purpose of key exchange for symmetric key cryptography and authentication. Improved network security demands forward secrecy, which RSA is unable to provide. Also the lower per bit security of the RSA technique, makes it difficult to be implemented in resource constrained devices. The protocols including Elliptic curve Diffie-Hellman Ephemeral (ECDHE) as the key exchange mechanism and RSA for authentication, overcomes the drawback incurred by the RSA alone and provides forward secrecy. The advantage of forward secrecy in a network is accompanied with higher complexity and computational cost. This paper describes the complete optimized software implementation of elliptic curve over the NIST prime field. The arithmetic operations over the prime are discussed. Different coordinate systems for elliptic curve point representation like affine, projective, Jacobian projective, and mixed coordinate systems are elaborated. Various techniques for scalar multiplication like Binary, NAF, sliding window, fixed based window, comb method, are given. Scalar multiplication is the most dominating operation in Elliptic curve cryptography (ECC) which consumes 85% of the execution time. A controller based on the fuzzy logic is presented for an optimum selection of window width, w, in the scalar multiplication methods. A comparison of various techniques and combinations of different techniques to perform complete ECDHE operation are provided along with the implementation timings.}, added-at = {2014-02-03T06:24:20.000+0100}, author = {Ravi Kishore Kodali, Harpreet Singh Budwal and Prof. Narasimha Sarma, N.V.S.}, biburl = {https://www.bibsonomy.org/bibtex/2b223666d055cd825d50782da7e69ca79/idescitation}, editor = {Hope, Dr.Martin}, interhash = {5ed0678271a3cc7074f30930f002f394}, intrahash = {b223666d055cd825d50782da7e69ca79}, journal = {Int. J. on Recent Trends in Engineering and Technology,}, keywords = {coordinate forward secrecy systems}, month = {July}, number = 1, pages = 7, timestamp = {2014-02-03T06:24:20.000+0100}, title = {Optimized Software Implementation of ECC over 192-bit NIST Curve}, url = {http://searchdl.org/public/journals/2013/IJRTET/9/1/524.pdf}, volume = 9, year = 2013 }