The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Time-Stamping with Binary Linking Schemes
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Efficient Algorithms for Computing Differential Properties of Addition
FSE '01 Revised Papers from the 8th International Workshop on Fast Software Encryption
Optimally Efficient Accountable Time-Stamping
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Collision free hash functions and public key signature schemes
EUROCRYPT'87 Proceedings of the 6th annual international conference on Theory and application of cryptographic techniques
Optimal trade-off for Merkle tree traversal
Theoretical Computer Science
CT-RSA'03 Proceedings of the 2003 RSA conference on The cryptographers' track
Efficient data structures for tamper-evident logging
SSYM'09 Proceedings of the 18th conference on USENIX security symposium
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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.