New Scalar Encoding Method to Accelerate Point Multiplication in Elliptic Curve Cryptography

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 202)


The security of the wireless environment, especially for those which have limited resources like in the wireless sensor network, needs lightweight algorithms. Elliptic curve cryptography (ECC) is the unique algorithm which satisfies such property. It provides the high level of security with relatively small keys; therefore, it has been the core of many standards. The efficiency of ECC is depending mostly on the implementation of the scalar multiplication which is accomplished mainly by addition and doubling operations. In the add-double method, reducing the number of ones is considered the most likely way to diminish the total number of the entirety operations. In this chapter, we present the method for recoding this scalar such that decreasing the number of addition operations. We compared our method with the one’s complement recoding method, and the simulation results showed that our proposed method produces mostly a better encoding.


Elliptic curve cryptography Encoding Scalar multiplication Hamming weight Wireless sensor network. 



This work is supported by National Science and Technology Major Project of the Ministry of Science and Technology of China (2010ZX03006-002-02), the National Natural Science Foundation of China (Grant No. 61201143), the National Science Foundation for Post-doctoral Scientists of China (Grant No. 2012M510956), the Post-doctoral Funds of Heilongjiang Province (Grant No.LBHZ11128), and the Fundamental Research Funds for the Central Universities (Grant No. HIT. NSRIF. 2010091).


  1. 1.
    Huang X, Sharma D (2010) Fuzzy controller for a dynamic window in elliptic curve cryptography wireless networks for scalar multiplication. In: Proceedings of the 16th Asia-Pacific conference communications (APCC 2010), New Zealand, pp 509–514. ISBN: 978-1-4244-8127-9Google Scholar
  2. 2.
    Huang X, Sharma D, Aseeri M, Almorqi S (2011) Secure wireless sensor networks with dynamic window for elliptic curve cryptography. In: Proceedings of the electronics, communications and photonics conference (SIECPC), Saudi Arabia, pp 1–5Google Scholar
  3. 3.
    Wang H, Sheng B, Tan CC, Li Q (2008) Comparing symmetric-key and public-key based security schemes in sensor networks: a case study of user access control. In: Proceedings of the 28th international conference on distributed computing systems, Beijing, pp 11–18Google Scholar
  4. 4.
    Katti R (2002) Speeding up elliptic cryptosystems using a new signed binary representation for integers. In: Proceedings of the euromicro Symposium on digital system design (DSD'02), Dortmund, pp 380–384Google Scholar
  5. 5.
    Reitwiesner GW (1960) The determination of carry propagation length for binary addition. IRE Trans Electron Comput EC-9(1):35–38MathSciNetCrossRefGoogle Scholar
  6. 6.
    Wang B, Zhang H, Wang Y (2007) An efficient elliptic curves scalar multiplication for wireless network. In: Proceedings of the IFIP international conference on network and parallel computing workshops, Dalian, pp 131–134Google Scholar
  7. 7.
    Mohamed MA, Md Said MR, Mohd Atan KA, Ahmad Zulkarnain Z (2010) An improved binary method for scalar multiplication in elliptic curve cryptography. J Math Stat 6(1):28–33. ISSN: 1549–3644Google Scholar
  8. 8.
    Huang X, Gajkumar Shah P, Sharma D (2010) Fast scalar multiplication for elliptic curve cryptography in sensor networks with hidden generator point. In: Proceedings of the international conference on cyber-enabled distributed computing and knowledge discovery, Huangshan, pp 243–249Google Scholar
  9. 9.
    Basu S (2011) A new parallel window-based implementation of the elliptic curve point multiplication in multi-core architectures. Int J Netw Secur 13(3):234–241Google Scholar
  10. 10.
    Certicom Research (2000) SEC 1: elliptic curve cryptography - standards for efficient cryptography. Certicom Corp.
  11. 11.
    Gura N, Pateland A, Wander A (2004) Comparing elliptic curve cryptography and RSA on 8-bit CPUs. In: Joye M, Quisquater JJ (eds) Proceedings of the 6th international workshop on cryptographic hardware and embedded systems (CHES), Lecture notes in computer science, Cambridge, MA, USA, 3156:119–132Google Scholar
  12. 12.
    Shah PG, Huang X, Sharma D (2010) Algorithm based on one’s complement for fast scalar multiplication in ECC for wireless sensor network. In: Proceedings of the IEEE 24th international conference on advanced information networking and applications workshops, Australia, pp 571–576Google Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.School of Electronics and Information TechnologyHarbin Institute of Technology HITHarbinChina

Personalised recommendations