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Key-Agreement with Perfect Completeness from Random Oracles

Author Noam Mazor

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  • Security and privacy → Information-theoretic techniques
Keywords
  • Key-Agreement
  • Random Oracle
  • Merkle’s Puzzles
  • Perfect Completeness

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Abstract

In the Random Oracle Model (ROM) all parties have oracle access to a common random function, and the parties are limited in the number of queries they can make to the oracle. The Merkle’s Puzzles protocol, introduced by Merkle [CACM '78], is a key-agreement protocol in the ROM with a quadratic gap between the query complexity of the honest parties and the eavesdropper. This quadratic gap is known to be optimal, by the works of Impagliazzo and Rudich [STOC ’89] and Barak and Mahmoody [Crypto ’09].
When the oracle function is injective or a permutation, Merkle’s Puzzles has perfect completeness. That is, it is certain that the protocol results in agreement between the parties. However, without such an assumption on the random function, there is a small error probability, and the parties may end up holding different keys. This fact raises the question: Is there a key-agreement protocol with perfect completeness and super-linear security in the ROM?
In this paper we give a positive answer to the above question, showing that changes to the query distribution of the parties in Merkle’s Puzzles, yield a protocol with perfect completeness and roughly the same security.

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Noam Mazor. Key-Agreement with Perfect Completeness from Random Oracles. In 6th Conference on Information-Theoretic Cryptography (ITC 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 343, pp. 12:1-12:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITC.2025.12

Author Details

Noam Mazor
  • Simons Institute, UC Berkeley, CA, USA

Funding

Supported in part by NSF CNS-2149305 and NSF CNS-2128519. This work was done while being at Cornell Tech.

Acknowledgements

We thank Tal Yankovitz and Jad Silbak for very useful discussions.

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