Multi-Dimensional Hash Chains and Application to Micropayment Schemes

  • Quan Son Nguyen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3969)


One-way hash chains have been used in many micropayment schemes due to their simplicity and efficiency. In this paper we introduce the notion of multi-dimensional hash chains, which is a new generalization of traditional one-way hash chains. We show that this construction has storage-computational complexity of O(log2 N) per chain element, which is comparable with the best result reported in recent literature. Based on multi-dimensional hash chains, we then propose two cash-like micropayment schemes, which have a number of advantages in terms of efficiency and security. We also point out some possible improvements to PayWord and similar schemes by using multi-dimensional hash chains.


Hash Function Public Parameter Modular Exponentiation Hash Chain Multiple Vendor 
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  1. 1.
    Anderson, R., Manifavas, H., Sutherland, C.: NetCard - a practical electronic cash system. In: Lomas, M. (ed.) Security Protocols 1996. LNCS, vol. 1189, pp. 49–57. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  2. 2.
    Benaloh, J.C., de Mare, M.: One-Way Accumulators: A Decentralized Alternative to Digital Signatures. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 274–285. Springer, Heidelberg (1994)CrossRefGoogle Scholar
  3. 3.
    Coppersmith, D., Jakobsson, M.: Almost optimal hash sequence traversal. In: Blaze, M. (ed.) FC 2002. LNCS, vol. 2357. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  4. 4.
    Hu, Y., Jakobsson, M., Perrig, A.: Efficient Constructions for One-way Hash Chains. SCS Technical Report Collection (2003),
  5. 5.
    Hauser, R., Steiner, M., Waidner, M.: Micro-payments based on iKP. In: Proceedings of the 14th Worldwide Congress on Computer and Communications Security Protection, Paris, pp. 67–82 (1996)Google Scholar
  6. 6.
    Jakobsson, M.: Fractal hash sequence representation and traversal. In: Proceedings of the 2002 IEEE International Symposium on Information Theory (ISIT 2002), pp. 437–444 (2002)Google Scholar
  7. 7.
    Jutla, C., Yung, M.: PayTree: amortized-signature for flexible micropayments. In: Adam, N.R., Yesha, Y. (eds.) Electronic Commerce 1994. LNCS, vol. 1028, Springer, Heidelberg (1996)Google Scholar
  8. 8.
    Rivest, R., Shamir, A.: PayWord and MicroMint: two simple micropayment schemes. In: Lomas, M. (ed.) Security Protocols 1996. LNCS, vol. 1189, pp. 69–87. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  9. 9.
    Rivest, R., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM 21(2), 120–126 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Schoenmakers, B.: Security Aspects of the EcashTM Payment System. In: Preneel, B., Rijmen, V. (eds.) State of the Art in Applied Cryptography. LNCS, vol. 1528, pp. 338–352. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    Sella, Y.: On the computation-storage trade-offs of hash chain traversal. In: Wright, R.N. (ed.) FC 2003. LNCS, vol. 2742, pp. 270–285. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  12. 12.
    Shamir, A.: On the Generation of Cryptographically Strong Pseudorandom Sequences. ACM Transactions on Computer Systems (TOCS) 1(1), 38–44 (1983)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Quan Son Nguyen
    • 1
  1. 1.Hanoi University of TechnologyHanoiVietnam

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