Optimal trade-off for Merkle tree traversal

Piotr Berman, Marek Karpinski, Yakov Nekrich

    Research output: Contribution to journalArticle

    10 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish (US)
    Pages (from-to)26-36
    Number of pages11
    JournalTheoretical Computer Science
    Volume372
    Issue number1
    DOIs
    StatePublished - Mar 6 2007

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    Trade-offs
    Hash functions
    Fractals
    Authentication
    Space Complexity
    Hash Function
    Time Complexity
    Fractal
    Leaves
    Path

    All Science Journal Classification (ASJC) codes

    • Theoretical Computer Science
    • Computer Science(all)

    Cite this

    Berman, Piotr ; Karpinski, Marek ; Nekrich, Yakov. / Optimal trade-off for Merkle tree traversal. In: Theoretical Computer Science. 2007 ; Vol. 372, No. 1. pp. 26-36.
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    abstract = "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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    Berman, P, Karpinski, M & Nekrich, Y 2007, 'Optimal trade-off for Merkle tree traversal', Theoretical Computer Science, vol. 372, no. 1, pp. 26-36. https://doi.org/10.1016/j.tcs.2006.11.029

    Optimal trade-off for Merkle tree traversal. / Berman, Piotr; Karpinski, Marek; Nekrich, Yakov.

    In: Theoretical Computer Science, Vol. 372, No. 1, 06.03.2007, p. 26-36.

    Research output: Contribution to journalArticle

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