Cryptology ePrint Archive: Report 2002/124

On Optimal Hash Tree Traversal for Interval Time-Stamping

Helger Lipmaa

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.

Category / Keywords: cryptographic protocols / analysis of algorithms, implementation complexity, interval time-stamping, Laplace's method for integrals, tree traversal

Publication Info: Accepted to ISC 2002.

Date: received 21 Aug 2002

Contact author: helger at tcs hut fi

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Version: 20020822:135530 (All versions of this report)

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