Advertisement

Abstract

Wireless ad-hoc and sensor networks play a vital role in an ever-growing number of applications ranging from environmental monitoring over vehicular communication to home automation. Security and privacy issues pose a big challenge for the widespread adoption of these networks, especially in the automotive domain. The two most essential security services needed to maintain the proper functioning of a wireless network are authentication and key establishment; both can be realized with Elliptic Curve Cryptography (ECC). In this paper, we introduce an efficient ECC implementation for resource-restricted devices such as sensor nodes. Our implementation uses a 160-bit Optimal Prime Field (OPF) over which a Gallant-Lambert-Vanstone (GLV) curve with good cryptographic properties can be defined. The combination of optimized field arithmetic with fast group arithmetic (thanks to an efficiently computable endomorphism) allows us to perform a scalar multiplication in about 5.5 ·106 clock cycles on an 8-bit ATmega128 processor, which is significantly faster than all previously-reported ECC implementations based on a 160-bit prime field.

Keywords

Ad-hoc network elliptic curve cryptography performance evaluation arithmetic in finite fields endomorphism 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Akyildiz, I.F., Su, W., Sankarasubramaniam, Y., Çayirci, E.: Wireless sensor networks: A survey. Computer Networks 38(4), 393–422 (2002)CrossRefGoogle Scholar
  2. 2.
    ASTM International: ASTM E2213-03 Standard Specification for Telecommunications and Information Exchange Between Roadside and Vehicle Systems — 5 GHz Band Dedicated Short Range Communications (DSRC) Medium Access Control (MAC) and Physical Layer (PHY) Specifications (2003)Google Scholar
  3. 3.
    Atmel Corporation: 8-bit ARV® Microcontroller with 128K Bytes In-System Programmable Flash: ATmega128, ATmega128L. Datasheet (June 2008), http://www.atmel.com/dyn/resources/prod_documents/doc2467.pdf
  4. 4.
    Crossbow Technology, Inc.: MICA2DOT Wireless Microsensor Mote. Data sheet (January 2006), http://www.xbow.com/Products/Product_pdf_files/Wireless_pdf/MICA2DOT_Datasheet.pdf
  5. 5.
    Federal Communications Commission (FCC): FCC Allocates Spectrum in 5.9 GHz Range for Intelligent Transportation Systems Uses. News release (October 1999), http://www.fcc.gov/Bureaus/Engineering_Technology/News_Releases/1999/nret9006.html
  6. 6.
    Gallant, R.P., Lambert, R.J., Vanstone, S.A.: Faster point multiplication on elliptic curves with efficient endomorphisms. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 190–200. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Großschädl, J., et al.: Optimal prime fields for use in elliptic curve cryptography (2010) (preprint, submitted for publication)Google Scholar
  8. 8.
    Großschädl, J., Tillich, S., Szekely, A.: Performance evaluation of instruction set extensions for long integer modular arithmetic on a SPARC V8 processor. In: Proceedings of the 10th Euromicro Conference on Digital System Design (DSD 2007), pp. 680–689. IEEE Computer Society Press, Los Alamitos (2007)Google Scholar
  9. 9.
    Gura, N., Patel, A., Wander, A.S., Eberle, H., Chang Shantz, S.: Comparing elliptic curve cryptography and RSA on 8-bit CPUs. In: Joye, M., Quisquater, J.J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 119–132. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Hankerson, D.R., Menezes, A.J., Vanstone, S.A.: Guide to Elliptic Curve Cryptography. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  11. 11.
    Holly, R.: A reusable Duff device. Dr. Dobb’s Journal 30(8), 73–74 (2005)Google Scholar
  12. 12.
    Hubaux, J.P., Ĉapkun, S., Luo, J.: The security and privacy of smart vehicles. IEEE Security & Privacy 2(3), 49–55 (2004)Google Scholar
  13. 13.
    Jiang, D., Taliwal, V., Meier, A., Holfelder, W., Herrtwich, R.G.: Design of 5.9 GHz DSRC-based vehicular safety communication. IEEE Wireless Communications 13(5), 36–43 (2006)CrossRefGoogle Scholar
  14. 14.
    Koç, Ç.K., Acar, T., Kaliski, B.S.: Analyzing and comparing Montgomery multiplication algorithms. IEEE Micro 16(3), 26–33 (1996)CrossRefGoogle Scholar
  15. 15.
    Laurendeau, C., Barbeau, M.: Threats to security in DSRC/WAVE. In: Kunz, T., Ravi, S.S. (eds.) ADHOC-NOW 2006. LNCS, vol. 4104, pp. 266–279. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Lederer, C., Mader, R., Koschuch, M., Großschädl, J., Szekely, A., Tillich, S.: Energy-efficient implementation of ECDH key exchange for wireless sensor networks. In: Markowitch, O., Bilas, A., Hoepman, J.H., Mitchell, C.J., Quisquater, J.J. (eds.) WISTP 2009. LNCS, vol. 5746, pp. 112–127. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  17. 17.
    Liu, A., Ning, P.: TinyECC: A configurable library for elliptic curve cryptography in wireless sensor networks. In: Proceedings of the 7th International Conference on Information Processing in Sensor Networks (IPSN 2008), pp. 245–256. IEEE Computer Society Press, Los Alamitos (2008)Google Scholar
  18. 18.
    Pister, K.S.: My view of sensor networks in 2010 (2010), http://robotics.eecs.berkeley.edu/~pister/SmartDust/in2010
  19. 19.
    Raya, M., Hubaux, J.P.: The security of vehicular ad hoc networks. In: Atluri, V., Ning, P., Du, W. (eds.) Proceedings of the 3rd ACM Workshop on Security of Ad Hoc and Sensor Networks (SASN 2005), pp. 11–21. ACM Press, New York (2005)CrossRefGoogle Scholar
  20. 20.
    Solinas, J.A.: Generalized Mersenne numbers. Tech. Rep. CORR-99-39, Centre for Applied Cryptographic Research (CACR), University of Waterloo, Waterloo, Canada (1999)Google Scholar
  21. 21.
    Standards for Efficient Cryptography Group (SECG): SEC 1: Elliptic Curve Cryptography. Working draft, version 1.7 (November 2006), http://www.secg.org/download/aid-631/sec1_1point7.pdf
  22. 22.
    Szczechowiak, P., Oliveira, L.B., Scott, M., Collier, M., Dahab, R.: NanoECC: Testing the limits of elliptic curve cryptography in sensor networks. In: Verdone, R. (ed.) EWSN 2008. LNCS, vol. 4913, pp. 305–320. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  23. 23.
    Ugus, O., Westhoff, D., Laue, R., Shoufan, A., Huss, S.A.: Optimized implementation of elliptic curve based additive homomorphic encryption for wireless sensor networks. In: Wolf, T., Parameswaran, S. (eds.) Proceedings of the 2nd Workshop on Embedded Systems Security (WESS 2007), pp. 11–16 (2007), http://arxiv.org/abs/0903.3900
  24. 24.
    U.S. Department of Transportation: IEEE 1609 – Family of standards for wireless access in vehicular environments (WAVE). ITS standards fact sheet (September 2009), http://www.standards.its.dot.gov/fact_sheet.asp?f=80
  25. 25.
    Wang, H., Li, Q.: Efficient implementation of public key cryptosystems on mote sensors. In: Ning, P., Qing, S., Li, N. (eds.) ICICS 2006. LNCS, vol. 4307, pp. 519–528. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  26. 26.
    Warneke, B., Last, M., Liebowitz, B., Pister, K.S.: Smart dust: Communicating with a cubic-millimeter computer. Computer 34(1), 44–51 (2001)CrossRefGoogle Scholar

Copyright information

© ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering 2012

Authors and Affiliations

  • Johann Großschädl
    • 1
  • Matthias Hudler
    • 2
  • Manuel Koschuch
    • 2
  • Michael Krüger
    • 2
  • Alexander Szekely
    • 3
  1. 1.Laboratory of Algorithmics, Cryptology and SecurityUniversity of LuxembourgLuxembourgLuxembourg
  2. 2.Competence Centre for IT-SecurityFH Campus Wien - University of Applied SciencesViennaAustria
  3. 3.Institute for Applied Information Processing and CommunicationsGraz University of TechnologyGrazAustria

Personalised recommendations