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Improving Efficiency of an ‘On the Fly’ Identification Scheme by Perfecting Zero-Knowledgeness

  • Bagus Santoso
  • Kazuo Ohta
  • Kazuo Sakiyama
  • Goichiro Hanaoka
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5985)

Abstract

We present a new methodology for constructing an efficient identification scheme, and based on it, we propose a lightweight identification scheme whose computational and storage costs are sufficiently low even for cheap devices such as RFID tags. First, we point out that the efficiency of a scheme with statistical zero-knowledgeness can be significantly improved by enhancing its zero-knowledgeness to perfect zero-knowledge. Then, we apply this technique to the Girault-Poupard-Stern (GPS) scheme which has been standardized by ISO/IEC.

The resulting scheme shows a perfect balance between communication cost, storage cost, and circuit size (computational cost), which are crucial factors for implementation on RFID tags. Compared to GPS, the communication and storage costs are reduced, while the computational cost is kept sufficiently low so that it is implementable on a circuit nearly as small as GPS. Under standard parameters, the prover’s response is shortened 80 bits from 275 bits to 195 bits and in application using coupons, storage for one coupon is also reduced 80 bits, whereas the circuit size is estimated to be larger by only 328 gates. Hence, we believe that the new scheme is a perfect solution for fast authentication of RFID tags.

Keywords

Identification scheme RFID zero-knowledge impersonation 

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References

  1. 1.
    Baudron, O., Boudot, F., Bourel, P., Bresson, E., Corbel, J., Frisch, L., Gilbert, H., Girault, M., Goubin, L., cois Misarsky, J.F., Nguyen, P., Patarin, J., Pointcheval, D., Poupard, G., Stern, J., Traoré, J.: GPS - an Asymmetric identification scheme for on the fly authentication of low cost smart cards Ver 2.0 (October 2001)Google Scholar
  2. 2.
    Bellare, M., Palacio, A.: GQ and Schnorr identification schemes: Proofs of security against impersonation under active and concurrent attacks. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 162–177. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  3. 3.
    Brickell, E.F., McCurley, K.S.: An interactive identification scheme based on discrete logarithms and factoring. J. Cryptology 5(1), 29–39 (1992)zbMATHCrossRefGoogle Scholar
  4. 4.
    Burmester, M., Desmedt, Y., Beth, T.: Efficient zero-knowledge identification schemes for smart cards. Comput. J. 35(1), 21–29 (1992)CrossRefGoogle Scholar
  5. 5.
    Chaum, D., Evertse, J.H., van de Graaf, J., Peralta, R.: Demonstrating possession of a discrete logarithm without revealing it. In: Odlyzko, A.M. (ed.) CRYPTO 1986. LNCS, vol. 263, pp. 200–212. Springer, Heidelberg (1987)Google Scholar
  6. 6.
    Addressing Insecurities and Violations of Privacy. In: Cole, P.H., Ranasinghe, D.C. (eds.) Networked RFID Systems and Lightweight Cryptography. Springer, Heidelberg (2008)Google Scholar
  7. 7.
    Dobkin, D.M.: The RF in RFID:physical layer operation of passive UHF tags and readers: 4. UHF RFID Protocols (July 2009), http://www.enigmatic-consulting.com/Communications_articles/RFID/RFID_protocols.html
  8. 8.
    Feldhofer, M., Dominikus, S., Wolkerstorfer, J.: Strong authentication for RFID systems using the AES algorithm. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 357–370. Springer, Heidelberg (2004)Google Scholar
  9. 9.
    Girault, M.: Self-certified public keys. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 490–497. Springer, Heidelberg (1991)Google Scholar
  10. 10.
    Girault, M., Poupard, G., Stern, J.: On the fly authentication and signature schemes based on groups of unknown order. Journal of Cryptology 19(4), 463–487 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Girault, M., Stern, J.: On the length of cryptographic hash-values used in identification schemes. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 202–215. Springer, Heidelberg (1994)Google Scholar
  12. 12.
    GNU Multiple Precision Arithmetic Library (2004), http://www.swox.com/gmp
  13. 13.
    Hitachi, Ltd. Secure RFID μ-Chip Hibiki (UHF) (March 2009), http://www.hitachi.co.jp/Prod/mu-chip/mu-chip_hibiki_secure.pdf
  14. 14.
    Hofferek, G., Wolkerstorfer, J.: Coupon recalculation for the GPS authentication scheme. In: Grimaud, G., Standaert, F.-X. (eds.) CARDIS 2008. LNCS, vol. 5189, pp. 162–175. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  15. 15.
  16. 16.
    ISO/IEC. International Standard ISO/IEC 9798 Part 5: Mechanisms Using Zero Knowledge Techniques (December 2004)Google Scholar
  17. 17.
    Lenstra, A.K., Verheul, E.R.: Selecting cryptographic key sizes. Journal of Cryptology 14(4), 255–293 (2001)zbMATHMathSciNetGoogle Scholar
  18. 18.
    McLoone, M., Robshaw, M.J.B.: New architectures for low-cost public key cryptography on RFID tags. In: ISCAS, pp. 1827–1830. IEEE, Los Alamitos (2007)Google Scholar
  19. 19.
    McLoone, M., Robshaw, M.J.B.: Public key cryptography and RFID tags. In: Abe, M. (ed.) CT-RSA 2007. LNCS, vol. 4377, pp. 372–384. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  20. 20.
    Naccache, D., M’Raïhi, D., Vaudenay, S., Raphaeli, D.: Can D.S.A. be improved? In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 77–85. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  21. 21.
    NESSIE. Final report of European project IST-1999-12324: New European Schemes for Signatures Integrity and Encryption, GPS - Public Report No. NES/DOC/RHU/WP3/004/b (February 2004)Google Scholar
  22. 22.
    Okamoto, T., Katsuno, H., Okamoto, E.: A fast signature scheme based on new on-line computation. In: Boyd, C., Mao, W. (eds.) ISC 2003. LNCS, vol. 2851, pp. 111–121. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  23. 23.
    Pointcheval, D.: The composite discrete logarithm and secure authentication. In: Imai, H., Zheng, Y. (eds.) PKC 2000. LNCS, vol. 1751, pp. 113–128. Springer, Heidelberg (2000)Google Scholar
  24. 24.
    Poupard, G., Stern, J.: Security analysis of a practical ”on the fly” authentication and signature generation. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 422–436. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  25. 25.
    Poupard, G., Stern, J.: On the fly signatures based on factoring. In: Proc. of the 6th CCS, pp. 48–57. ACM Press, New York (1999)Google Scholar
  26. 26.
    Santoso, B., Ohta, K.: A new ’on the fly’ identification scheme: an asymptoticity trade-off between ZK and correctness. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E92.A (1), 122–136 (2009)CrossRefGoogle Scholar
  27. 27.
    Schnorr, C.P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1990)Google Scholar
  28. 28.
    SkyeTek, Inc. SkyeModule M7: compact 900 MHz UHF RFID reader/writer, http://www.skyetek.com/Portals/0/Documents/Products/SkyeModule_M7_DataSheet.pdf

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Bagus Santoso
    • 1
  • Kazuo Ohta
    • 2
  • Kazuo Sakiyama
    • 2
  • Goichiro Hanaoka
    • 1
  1. 1.National Institute of Advanced Industrial Science and Technology (AIST)TokyoJapan
  2. 2.The University of Electro-CommunicationsTokyoJapan

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