Robust Metering Schemes for General Access Structures

  • Ventzislav Nikov
  • Svetla Nikova
  • Bart Preneel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3269)


In order to decide on advertisement fees for web servers, Naor and Pinkas introduced (threshold) metering schemes secure against coalitions of corrupt servers and clients. They show that one should be able to detect illegal behavior of clients, i.e., one needs to verify the shares received from clients. Most metering schemes do not offer this feature. But Ogata and Kurosawa pointed out a minor flaw in the extension protocol by Naor and Pinkas providing detection of such illegal behavior and propose a correction. In this paper we extend the linear algebra approach from Nikov et al. in order to build robust unconditionally secure general metering schemes. As a tool to achieve this goal we introduce doubly-labelled matrices and an operation on such matrices. Certain properties of this operation are proven.


Access Structure Secret Share Scheme Illegal Behavior Regular Operation Cryptology ePrint Archive 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Blundo, C., De Bonis, A., Masucci, B.: Metering Schemes with Pricing. In: Herlihy, M.P. (ed.) DISC 2000. LNCS, vol. 1914, pp. 194–208. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  2. 2.
    Blundo, C., De Bonis, A., Masucci, B., Stinson, D.: Dynamic Multi-Threshold Metering Schemes. In: Stinson, D.R., Tavares, S. (eds.) SAC 2000. LNCS, vol. 2012, pp. 130–144. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Blundo, C., Martin, S., Masucci, B., Padro, C.: A Linear Algebraic Approach to Metering Schemes, Cryptology ePrint Archive: Report 2001/087Google Scholar
  4. 4.
    Cramer, R., Damgard, I., Maurer, U.: General Secure Multi-Party Computation from any Linear Secret Sharing Scheme. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 316–334. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Cramer, R., Fehr, S., Ishai, Y., Kushilevitz, E.: Efficient Multi-Party Computation over Rings. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 596–613. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Franklin, M.K., Malkhi, D.: Auditable Metering with Lightweight Security. In: Luby, M., Rolim, J.D.P., Serna, M. (eds.) FC 1997. LNCS, vol. 1318, pp. 151–160. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  7. 7.
    Masucci, B., Stinson, D.: Metering Schemes for General Access Structures. In: Cuppens, F., Deswarte, Y., Gollmann, D., Waidner, M. (eds.) ESORICS 2000. LNCS, vol. 1895, pp. 72–87. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  8. 8.
    Masucci, B., Stinson, D.: Efficient Metering Schemes with Pricing. IEEE Transactions on Information Theory 47(7), 2835–2844 (2001)zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Nikov, V., Nikova, S., Preneel, B., Vandewalle, J.: Applying General Access Structure to Metering Schemes. In: WCC 2003, Cryptology ePrint Archive: Report 2002/102 (2003)Google Scholar
  10. 10.
    Nikov, V., Nikova, S., Preneel, B.: Multi-Party Computation from any Linear Secret Sharing Scheme Secure against Adaptive Adversary: The Zero-Error Case, Cryptology ePrint Archive: Report 2003/006Google Scholar
  11. 11.
    Nikov, V., Nikova, S.: On a relation between Verifiable Secret Sharing Schemes and a class of Error-Correcting Codes, Cryptology ePrint Archive: Report 2003/210Google Scholar
  12. 12.
    Naor, M., Pinkas, B.: Secure and Efficient Metering. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 576–590. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. 13.
    Ogata, W., Kurosawa, K.: Provably Secure Metering Scheme. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 388–398. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  14. 14.
    Pudlak, P., Sgall, J.: Algebraic models of computation and interpolation for algebraic proof systems. In: Proc. Feasible Arithmetic and Proof Complexity. LNCS, pp. 279–295 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ventzislav Nikov
    • 1
  • Svetla Nikova
    • 2
  • Bart Preneel
    • 2
  1. 1.Department of Mathematics and Computing ScienceEindhoven University of TechnologyEindhoventhe Netherlands
  2. 2.Department Electrical EngineeringESAT/COSIC, Katholieke Universiteit LeuvenHeverlee-LeuvenBelgium

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