Distributed Merkle’s Puzzles

Itai Dinur, Ben Hasson

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations


Merkle’s puzzles were proposed in 1974 by Ralph Merkle as a key agreement protocol between two players based on symmetric-key primitives. In order to agree on a secret key, each player makes T queries to a random function (oracle), while any eavesdropping adversary has to make Ω(T2) queries to the random oracle in order to recover the key with high probability. The quadratic gap between the query complexity of the honest players and the eavesdropper was shown to be optimal by Barak and Mahmoody [CRYPTO’09]. We consider Merkle’s puzzles in a distributed setting, where the goal is to allow all pairs among M honest players with access to a random oracle to agree on secret keys. We devise a protocol in this setting, where each player makes T queries to the random oracle and communicates at most T bits, while any adversary has to make Ω(M· T2) queries to the random oracle (up to logarithmic factors) in order to recover any one of the keys with high probability. Therefore, the amortized (per-player) complexity of achieving secure communication (for a fixed security level) decreases with the size of the network. Finally, we prove that the gap of T· M between the query complexity of each honest player and the eavesdropper is optimal.

Original languageEnglish
Title of host publicationTheory of Cryptography - 19th International Conference, TCC 2021, Proceedings
EditorsKobbi Nissim, Brent Waters, Brent Waters
PublisherSpringer Science and Business Media Deutschland GmbH
Number of pages23
ISBN (Print)9783030904524
StatePublished - 1 Jan 2021
Event19th International Conference on Theory of Cryptography, TCC 2021 - Raleigh, United States
Duration: 8 Nov 202111 Nov 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13043 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference19th International Conference on Theory of Cryptography, TCC 2021
Country/TerritoryUnited States

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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