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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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

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

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