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Evaluating 16-Bit Processors for Elliptic Curve Cryptography

  • Erich Wenger
  • Mario Werner
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7079)

Abstract

In a world in which every processing cycle is proportional to used energy and the amount of available energy is limited, it is especially important to optimize source code in order to achieve the best possible runtime. In this paper, we present a side-channel secure C framework performing elliptic curve cryptography and improve its runtime on three 16-bit microprocessors: the MSP430, the PIC24, and the dsPIC. To the best of our knowledge we are the first to present results for the PIC24 and the dsPIC. By evaluating different multi-precision and field-multiplication methods, and hand-crafting the performance critical code in Assembler, we improve the runtime of a point multiplication by a factor of up to 5.41 and the secp160r1 field-multiplication by 6.36, and the corresponding multi-precision multiplication by 7.91 (compared to a speed-optimized C-implementation). Additionally, we present and compare results for four different standardized elliptic curves making our data applicable for real-world applications. Most spectacular are the performance results on the dsPIC processor, being able to calculate a point multiplication within 1.7 – 4.9 MCycles.

Keywords

Elliptic Curve Cryptography ECC Prime Field MSP430 PIC24 dsPIC Assembler Optimization 

References

  1. 1.
    American National Standards Institute (ANSI). AMERICAN NATIONAL STANDARD X9.62-2005. Public Key Cryptography for the Financial Services Industry, The Elliptic Curve Digital Signature Algorithm, ECDSA (2005)Google Scholar
  2. 2.
    Atmel Corporation. 8-bit AVR Microcontroller with 128K Bytes In-System Programmable Flash (August 2007), http://www.atmel.com/dyn/resources/prod_documents/doc2467.pdf
  3. 3.
    Bernstein, D., Lange, T.: Explicit-formulas database, http://www.hyperelliptic.org/EFD
  4. 4.
    Certicom Research. Standards for Efficient Cryptography, SEC 2: Recommended Elliptic Curve Domain Parameters, Version 1.0 (September 2000), http://www.secg.org/
  5. 5.
    Certicom Research. Standards for Efficient Cryptography, SEC 2: Recommended Elliptic Curve Domain Parameters, Version 2.0 (January 2010), http://www.secg.org/
  6. 6.
    Comba, P.: Exponentiation cryptosystems on the IBM PC. IBM Systems Journal 29(4), 526–538 (1990)CrossRefGoogle Scholar
  7. 7.
    Coron, J.-S.: Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems. In: Koç, Ç.K., Paar, C. (eds.) CHES 1999. LNCS, vol. 1717, pp. 292–302. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  8. 8.
    Crossbow Technology, Inc. MICAz Wireless Measurement System, http://www.xbow.com/Products/Product_pdf_files/Wireless_pdf/MICAz_Datasheet.pdf
  9. 9.
    Ebeid, N., Lambert, R.: Securing the Elliptic Curve Montgomery Ladder Against Fault Attacks. In: Proceedings of Workshop on Fault Diagnosis and Tolerance in Cryptography - FDTC 2009, Lausanne, Switzerland, pp. 46–50 (September 2009)Google Scholar
  10. 10.
    Fan, J., Guo, X., Mulder, E.D., Schaumont, P., Preneel, B., Verbauwhede, I.: State-of-the-Art of Secure ECC Implementations: A Survey on known Side-Channel Attacks and Countermeasures. In: Proceedings of 3rd IEEE International Symposium Hardware-Oriented Security and Trust - HOST 2010, California, USA, June 13-14, pp. 76–87. IEEE (2010)Google Scholar
  11. 11.
    Großmann, M.: Optimize Elliptic Curve Cryptography for MSP430 Processor. Bachelor Thesis at Graz University of Technology (May 2011)Google Scholar
  12. 12.
    Großschädl, J., Savaş, E.: Instruction Set Extensions for Fast Arithmetic in Finite Fields GF(p) and GF(2m). In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 133–147. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  13. 13.
    Gura, N., Patel, A., Wander, A., Eberle, H., Shantz, S.C.: 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
  14. 14.
    Hankerson, D., Menezes, A.J., Vanstone, S.: Guide to Elliptic Curve Cryptography. Springer, Heidelberg (2004)zbMATHGoogle Scholar
  15. 15.
    Hutter, M., Feldhofer, M., Plos, T.: An ECDSA Processor for RFID Authentication. In: Ors Yalcin, S.B. (ed.) RFIDSec 2010. LNCS, vol. 6370, pp. 189–202. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Hutter, M., Joye, M., Sierra, Y.: Memory-Constrained Implementations of Elliptic Curve Cryptography in Co-Z Coordinate Representation. In: Nitaj, A., Pointcheval, D. (eds.) AFRICACRYPT 2011. LNCS, vol. 6737, pp. 170–187. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  17. 17.
    IAR Systems. IAR Embedded Workbench (2011), http://www.iar.com/
  18. 18.
    Kern, T., Feldhofer, M.: Low-Resource ECDSA Implementation for Passive RFID Tags. In: Proceedings of 17th IEEE International Conference on Electronics, Circuits and Systems (ICECS 2010), Athens, Greece, December 12-15, pp. 1236–1239. IEEE (2010)Google Scholar
  19. 19.
    Koç, Ç.K., Acar, T., Kaliski Jr., B.S.: Analyzing and Comparing Montgomery Multiplication Algorithms. IEEE Micro 16(3), 26–33 (1996)CrossRefGoogle Scholar
  20. 20.
    Liu, A., Ning, P.: TinyECC: A Configurable Library for Elliptic Curve Cryptography in Wireless Sensor Networks. In: Proceedings of International Conference on Information Processing in Sensor Networks - IPSN 2008, St. Louis, Missouri, USA, April 22-24, pp. 245–256 (2008)Google Scholar
  21. 21.
    Liu, Z., Großschädl, J., Kizhvatov, I.: Efficient and Side-Channel Resistant RSA Implementation for 8-bit AVR Microcontrollers. In: Proceedings of 1st International Workshop on the Security of the Internet of Things - SOCIOT 2010, Tokyo, Japan, November 29. IEEE Computer Society (2010)Google Scholar
  22. 22.
    Microchip. PIC24FJ128GA010 Family Data Sheet. DS39747E (October 2009), http://www.microchip.com
  23. 23.
    Microchip. dsPIC30F6010A/6015 Data Sheet. DS70150E (March 2011), http://www.microchip.com
  24. 24.
    Microchip. MPLAB Integrated Development Environment (2011), http://www.microchip.com
  25. 25.
    Montgomery, P.L.: Modular Multiplication without Trial Division. Mathematics of Computation 44, 519–521 (1985)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Moteiv. The Moteiv Wireless Sensor Networks Website, http://www.moteiv.com/
  27. 27.
    National Institute of Standards and Technology (NIST). FIPS-186-3: Digital Signature Standard, DSS (2009), http://www.itl.nist.gov/fipspubs/
  28. 28.
    National Institute of Standards and Technology (NIST). SP800-57 Part 1: DRAFT Recommendation for Key Management: Part 1: General (May 2011), http://csrc.nist.gov/publications/drafts/800-57/Draft_SP800-57-Part1-Rev3_May2011.pdf
  29. 29.
    Scott, M., Szczechowiak, P.: Optimizing Multiprecision Multiplication for Public Key Cryptography. Cryptology ePrint Archive, Report 2007/299 (2007), http://eprint.iacr.org/
  30. 30.
    Shamus Software. Multiprecision Integer and Rational Arithmetic C/C++ Library (2011), http://www.shamus.ie/
  31. 31.
    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
  32. 32.
    Texas Instruments. MSP430C11x1 - Mixed Signal Microcontroller (2008), http://focus.ti.com
  33. 33.
    Uhsadel, L., Poschmann, A., Paar, C.: Enabling Full-Size Public-Key Algorithms on 8-Bit Sensor Nodes. In: Stajano, F., Meadows, C., Capkun, S., Moore, T. (eds.) ESAS 2007. LNCS, vol. 4572, pp. 73–86. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  34. 34.
    Walter, C.D.: Simple Power Analysis of Unified Code for ECC Double and Add. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 191–204. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  35. 35.
    Wenger, E., Feldhofer, M., Felber, N.: Low-Resource Hardware Design of an Elliptic Curve Processor for Contactless Devices. In: Chung, Y., Yung, M. (eds.) WISA 2010. LNCS, vol. 6513, pp. 92–106. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  36. 36.
    Yan, H., Shi, Z.J., Fei, Y.: Efficient Implementation of Elliptic Curve Cryptography on DSP for Underwater Sensor Networks. In: 7th Workshop on Optimizations for DSP and Embedded Systems (ODES- 7), pp. 7–15 (March 2009)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2011

Authors and Affiliations

  • Erich Wenger
    • 1
  • Mario Werner
    • 1
  1. 1.Institute for Applied Information Processing and Communications (IAIK)Graz University of TechnologyGrazAustria

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