Soft Computing

, Volume 21, Issue 19, pp 5665–5673 | Cite as

Secure and efficient ECC speeding up algorithms for wireless sensor networks

  • Yunqi Dou
  • Jiang Weng
  • Chuangui Ma
  • Fushan Wei
Methodologies and Application


Wireless sensor networks have been widely used in several applications ranging from environmental and health-care monitoring to military uses. Since sensor networks are typically deployed in hostile environments, broadcast authentication is a fundamental security service in wireless sensor networks. The slow signature verification in existing schemes always causes high energy consumption and long verification delay for broadcast authentication. In this paper, we study the secure and efficient ECC speeding up algorithms for fast authentication in wireless sensor networks. We propose two fast algorithms based on constrained triple base number system to improve the efficiency for situations with and without precomputations. These new algorithms combine the sparsity of constrained TBNS with Yao algorithm to reduce the cost of scalar multiplication. Several experiments have been conducted using Magma software to assess the performance of the proposed algorithms. Our experiments show that the two algorithms are more efficient than existing algorithms. Furthermore, the improvement of efficiency will reduce the energy consumption and thus prolong the network lifetime due to the decrease of computation overhead in signature verification.


Elliptic curve Scalar multiplication Constrained triple-base number system Greedy algorithm Wireless sensor network Authentication Security 



This work was supported by the National Natural Science Foundation of China (No. 61309016, 61379150, 61201220), the Funding of Science and Technology on Information Assurance Laboratory (No. KJ1302) and Key Scientific and Technological Project of Henan Province (No. 122102210126, 092101210502).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical standards

This manuscript describes original work, and neither the entire nor any part of its content has been published previously or has been accepted by any journal. All authors have read the manuscript and approved submission to your journal. This article does not contain any studies with human participants or animals performed by any of the authors.


  1. Abarzúa R, Thériault N (2012) Complete atomic blocks for elliptic curves in Jacobian coordinates over prime fields. In: Hevia A, Neven G (eds) LATINCRYPT 2012, LNCS, vol 7533. Springer, Heidelberg, pp 37–55CrossRefGoogle Scholar
  2. Bellare M, Namprempre C, Neven G (2004) Security proofs for identitybased identification and signature schemes. In: Cachin C, Camenisch J (eds) EUROCRYPT 2004, LNCS, vol 3027. Springer-Verlag, Heidelberg, pp 268–286CrossRefGoogle Scholar
  3. Bernstein DJ, Lange T (2007) Faster addition and doubling on elliptic curves. In: Kurosawa K (ed) ASIACRYPT, LNCS, vol 4833. Springer, Heidelberg, pp 29–50Google Scholar
  4. Berthé V, Imbert L (2004) On converting numbers to the double-base number system. In: Luk FT (ed) Advanced signal processing algorithms, architecture and implementations XIV 2004, vol 5559. pp 70–78Google Scholar
  5. Blake IF, Seroussi G, Smart NP (eds) (2005) Advances in elliptic curve cryptography. Cambridge University Press, CambridgeGoogle Scholar
  6. Brier E, Joye M (2002) Weierstraß elliptic curves and side-channel attacks. In: Naccache D, Paillier P (eds) PKC 2002, LNCS, vol 2274. Springer, Heidelberg, pp 335–345Google Scholar
  7. Cao X, Kou W, Dang L, Zhao B (2008) IMBAS: identity-based multi-user broadcast authentication in wireless sensor networks. Comput Commun 31(4):659–667CrossRefGoogle Scholar
  8. Chevallier-Mames B, Ciet M, Joye M (2004) Low-cost solutions for preventing simple side-channel analysis: side-channel atomicity. IEEE Trans Comput 53(6):760–768CrossRefzbMATHGoogle Scholar
  9. Ciet M, Joye M (2003) (Virtually) Free randomization techniques for elliptic curve cryptography. In: Qing S, Gollmann D, Zhou J (eds) ICICS 2003, LNCS, vol 2836. Springer, Heidelberg, pp 348–359Google Scholar
  10. Coron JS (1999) Resistance against differential power analysis for elliptic curve cryptosystems. In: Koç ÇK, Paar C (eds) CHES 1999, LNCS, vol 1717. Springer, Heidelberg, pp 292–302Google Scholar
  11. Dimitrov V, Imbert L, Mishra PK (2005) Efficient and secure elliptic curve point multiplication using double-base chains. In: Roy B (ed) ASIACRYPT 2005, LNCS, vol 3788. Springer, Heidelberg, pp 59–78CrossRefGoogle Scholar
  12. Dimitrov V, Imbert L, Mishra PK (2008) The double-base number system and its application to elliptic curve cryptography. Math Comput 77(262):1075–1104MathSciNetCrossRefzbMATHGoogle Scholar
  13. Dimitrov V, Cooklev T (1995) Two algorithms for modular exponentiation using nonstandard arithmetics. IEICE Trans Fundam Electron Commun Comput Sci 78(1):82–87Google Scholar
  14. Fan X, Gong G (2012) Accelerating signature-based broadcast authentication for wireless sensor networks. Ad Hoc Netw 10:723–736CrossRefzbMATHGoogle Scholar
  15. Guo P, Wang J, Geng XH, Kim CS, Kim J-U (2014) A variable threshold-value authentication architecture for wireless mesh networks. J Internet Technol 15(6):929–936Google Scholar
  16. Hisil H, Wong K, Carter G, Dawson E (2008) An intersection form for jacobi-quartic curves. Personal communicationGoogle Scholar
  17. Joye M, Yen S-M (2003) The montgomery powering ladder. In: Kaliski BS, Koç ÇK, Paar C (eds) CHES 2002, LNCS, vol 2523. Springer, Heidelberg, pp 291–302Google Scholar
  18. Khan MK, Zhang J, Tian L (2004) Protecting biometric data for personal identification. In: Li SZ et al (eds) SINOBIOMETRICS 2004, LNCS, vol 3383. Springer, Heidelberg, pp 629–638Google Scholar
  19. Khan MK, Zhang J (2006) An efficient and practical fingerprint-based remote user authentication scheme with smart cards. In: Chen K et al (eds) ISPEC 2006, LNCS, vol 3903. Springer, Heidelberg, pp 260–268Google Scholar
  20. Khan MK, Zhang J (2008) Multimodal face and fingerprint biometrics authentication on space-limited tokens. Neurocomputing 71(13–15):3026–3031CrossRefGoogle Scholar
  21. Liu A, Ning P (2008) TinyECC: A configurable library for elliptic curve cryptography in wireless sensor networks. In: International conference on information processing in sensor networks (IPSN 2008). IEEE Computer Society Press, St. Louis, pp 245–256Google Scholar
  22. Longa P, Gebotys C (2009) Fast multibase methods and other several optimization for elliptic curve scalar multiplication. In: Jarecki S, Tsudik G (eds) PKC 2009, LNCS, vol 5443. Springer, Heidelberg, pp 443–462Google Scholar
  23. Lu CY, Jen SM, Laih CS (2013) A general framework of side-channel atomicity for elliptic curve scalar multiplication. IEEE Trans Comput 62(3):428–438MathSciNetCrossRefzbMATHGoogle Scholar
  24. Méloni N, Hasan MA (2015) Efficient double bases for scalar multiplication. IEEE Trans Comput 64(8):2204–2212MathSciNetCrossRefzbMATHGoogle Scholar
  25. Mishra D, Mukhopadhyay S, Khan MK, Chaturvedi A (2014) Security enhancement of a biometric based authentication scheme for telecare medicine information systems with nonce. J Med Syst 38(5):1–11CrossRefGoogle Scholar
  26. Mishra PK, Dimitrov V (2007) Efficient quintuple formulas for elliptic curves and efficient scalar multiplication using multibase number representation. In: Garay J et al (eds) ISC 2007, LNCS, vol 4779. Springer, Heidelberg, pp 390–406Google Scholar
  27. Perrig A, Canetti R, Tygar J, Song D (2000) Efficient authentication and signing of multicast streams over lossy channels. In: 2000 IEEE symposium on security and privacy. IEEE Computer Society Press, Berkeley, pp 56–73Google Scholar
  28. Ren K, Lou W, Zeng K, Moran PJ (2007) On broadcast authentication in wireless sensor networks. IEEE Trans Wireless Commun 6(11):4136–4144CrossRefGoogle Scholar
  29. Ren K, Yu S, Lou W, Zhang Y (2009) Multi-user broadcast authentication in wireless sensor networks. IEEE Trans Veh Technol 58(8):4554–4564CrossRefGoogle Scholar
  30. Ren Y, Shen J, Wang J, Han J, Lee S (2015) Mutual verifiable provable data auditing in public cloud storage. J Internet Technol 16(2):317–323Google Scholar
  31. Shen J, Tan H, Wang J, Wang J, Lee S (2015) A novel routing protocol providing good transmission reliability in underwater sensor networks. J Internet Technol 16(1):171–178Google Scholar
  32. Wenger E, Großschädl J (2012) An 8-bit AVR-based elliptic curve cryptographic RISC processor for the Internet of things. In: Proceedings of the 45th annual IEEE ACM international symposium on microarchitecture workshops MICROW 2012). IEEE Computer Society Press, Vancouver, pp 39–46Google Scholar
  33. Xia Z, Wang X, Sun X, Wang Q (2016) Secure and dynamic multi-keyword ranked search scheme over encrypted cloud data. IEEE Trans Parallel Distrib Syst 27(2):340–352CrossRefGoogle Scholar
  34. Xie S, Wang Y (2014) Construction of tree network with limited delivery latency in homogeneous wireless sensor networks. Wireless Pers Commun 78(1):231–246CrossRefGoogle Scholar
  35. Yao AC (1976) On the evaluation of powers. SIAM J Comput 5(1):100–103MathSciNetCrossRefzbMATHGoogle Scholar
  36. Yu W, Wang K, Li B, Tian S (2013) Triple-base number system for scalar multiplication. In: Youssef A, Nitaj A, Hassanien AE (eds) AFRICACRYPT 2013, LNCS, vol 7918. Springer, Heidelberg, pp 443–451Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Yunqi Dou
    • 1
  • Jiang Weng
    • 1
  • Chuangui Ma
    • 1
    • 2
  • Fushan Wei
    • 1
  1. 1.State key Laboratory of Mathematical Engineering and Advanced ComputingZhengzhouChina
  2. 2.Department of BasicArmy Aviation InstitutionBeijingChina

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