### 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 language | English (US) |
---|---|

Pages (from-to) | 26-36 |

Number of pages | 11 |

Journal | Theoretical Computer Science |

Volume | 372 |

Issue number | 1 |

DOIs | |

State | Published - Mar 6 2007 |

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### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Theoretical Computer Science*,

*372*(1), 26-36. https://doi.org/10.1016/j.tcs.2006.11.029

}

*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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Optimal trade-off for Merkle tree traversal

AU - Berman, Piotr

AU - Karpinski, Marek

AU - Nekrich, Yakov

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.

UR - http://www.scopus.com/inward/record.url?scp=33846898460&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846898460&partnerID=8YFLogxK

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 -