TY - JOUR

T1 - Optimal trade-off for Merkle tree traversal

AU - Berman, Piotr

AU - Karpinski, Marek

AU - Nekrich, Yakov

N1 - Funding Information:
∗Corresponding author. Tel.: +49 228 734209. E-mail addresses: berman@cse.psu.edu (P. Berman), marek@cs.uni-bonn.de (M. Karpinski), yasha@cs.uni-bonn.de (Y. Nekrich). 1Research done in part while visiting Department of Computer Science, University of Bonn. Work partially supported by NSF grant CCR-9700053 and NIH grant 9R01HG02238-12. 2Work partially supported by DFG grants, Max-Planck Research Prize, DIMACS, and IST grant 14036 (RAND-APX). 3Work partially supported by IST grant 14036 (RAND-APX).

PY - 2007/3/6

Y1 - 2007/3/6

N2 - In this paper we describe optimal trade-offs between time and space complexity of Merkle tree traversals with their associated authentication paths, improving on the previous results of M. Jakobsson, T. Leighton, S. Micali, and M. Szydlo [Fractal Merkle tree representation and traversal, in: RSA Cryptographers Track, RSA Security Conference, 2003] and M. Szydlo [Merkle tree traversal in log space and time, in: Proc. Eurocrypt, in: LNCS, vol. 3027, 2004, pp. 541-554; Merkle tree traversal in log space and time, Preprint version 2003, available at http://www.szydlo.com]. In particular, we show that our algorithm requires 2 log n / log(3) n hash function computations and storage for less than (log n / log(3) n + 1) log log n + 2 log n hash values, where n is the number of leaves in the Merkle tree. We also prove that these trade-offs are optimal, i.e. there is no algorithm that requires less than O (log n / log t) time and less than O (t log n / log t) space for any choice of parameter t ≥ 2. Our algorithm could be of special interest in the case when both time and space are limited.

AB - In this paper we describe optimal trade-offs between time and space complexity of Merkle tree traversals with their associated authentication paths, improving on the previous results of M. Jakobsson, T. Leighton, S. Micali, and M. Szydlo [Fractal Merkle tree representation and traversal, in: RSA Cryptographers Track, RSA Security Conference, 2003] and M. Szydlo [Merkle tree traversal in log space and time, in: Proc. Eurocrypt, in: LNCS, vol. 3027, 2004, pp. 541-554; Merkle tree traversal in log space and time, Preprint version 2003, available at http://www.szydlo.com]. In particular, we show that our algorithm requires 2 log n / log(3) n hash function computations and storage for less than (log n / log(3) n + 1) log log n + 2 log n hash values, where n is the number of leaves in the Merkle tree. We also prove that these trade-offs are optimal, i.e. there is no algorithm that requires less than O (log n / log t) time and less than O (t log n / log t) space for any choice of parameter t ≥ 2. Our algorithm could be of special interest in the case when both time and space are limited.

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U2 - 10.1016/j.tcs.2006.11.029

DO - 10.1016/j.tcs.2006.11.029

M3 - Article

AN - SCOPUS:33846898460

VL - 372

SP - 26

EP - 36

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

IS - 1

ER -