International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: On Optimal Hash Tree Traversal for Interval Time-Stamping

Helger Lipmaa
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Abstract: Skewed trees constitute a two-parameter family of recursively constructed trees. Recently, Willemson proved that suitably picked skewed trees are space-optimal for interval time-stamping. At the same time, Willemson proposed a practical but suboptimal algorithm for nonrecursive traversal of skewed trees. We describe an alternative, extremely efficient traversal algorithm for skewed trees. The new algorithm is surprisingly simple and arguably close to optimal in every imaginable sense. We provide a detailed analysis of the average-case storage (and communication) complexity of our algorithm, by using the Laplace's method for estimating the asymptotic behavior of integrals. Since the skewed trees can be seen as a natural generalization of Fibonacci trees, our results might also be interesting in other fields of computer science.
  title={On Optimal Hash Tree Traversal for Interval Time-Stamping},
  booktitle={IACR Eprint archive},
  keywords={cryptographic protocols / analysis of algorithms, implementation complexity, interval time-stamping, Laplace's method for integrals, tree traversal},
  note={Accepted to ISC 2002. 11920 received 21 Aug 2002},
  author={Helger Lipmaa},