Scalar Multiplication Algorithms of Elliptic Curve Cryptography over GF (2m )
Praful Kumar Singh1, Mrityunjay Kumar Choudhary2
1Mrityunjay Kumar Choudhary, Master M.Tech Degree, Department of Program Information Technology, USICT, GGSIPU, India.
2Praful Kumar Singh, Master M.Tech Degree, Department of Information Technology, USICT, GGSIPU, India.
Manuscript received on 11 June 2013 | Revised Manuscript received on 17 June 2013 | Manuscript Published on 30 June 2013 | PP: 246-250 | Volume-3 Issue-1, June 2013 | Retrieval Number: A0953063113/13©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Since the inception of elliptic curve cryptography by Koblitz [1] and Miller [2] for implementing public-key protocols as the Diffie-Hellman key agreement, elliptic curve cryptography has become one of the most researched area for providing one stop reliable and secure solution in the field of cryptography. The ECC covers all relevant asymmetric cryptographic primitives like digital signature (ECDSA), key exchange and agreement protocols. Point multiplication serves as the basic building block in all ECC primitives and is the computationally most expensive operation and our analysis revolves around this concept. This paper gives an introduction to Elliptic Curve Cryptography and deals with evaluation of fast scalar multiplication with parallelization of field operation and point addition/multiplication. Elliptic curve cryptography offers best optimized solution with minimum resources like Low memory, High Throughput, low power consumption and minimum key length for the same level of security as compared to its counterpart like RSA, DSA etc. in public key cryptography domain. The work is based on the extensive research work done by Julio Lopez, Ricardo Dahab, Montgomery and other pioneer scientists and academicians in the field of elliptic curve cryptography. Given the importance of Scalar multiplication , we focused ourselves on the Fast Multiplication on Elliptic Curves over finite Binary field GF(2m ) without Pre-computation whose background is set by Julio Lopez et al. in [1], because the finite field operations can be implemented very efficiently in hardware and software.
Keywords: Elliptic Curve Cryptography, Scalar Multiplication, Encryption.
Scope of the Article: Web Algorithms