Key-agreement exists if and only if the"interactive vs non interactive Kolmogorov problem"is not in ioBPP: a short proof

2025-04-22

AI Summary

This paper addresses the fundamental existence conditions for key agreement protocols. Method: The authors establish an exact equivalence between the existence of such protocols and the average-case incomputability—specifically, the problem’s hardness against infinitely-often probabilistic polynomial-time (ioBPP) algorithms—of distinguishing interactive from non-interactive Kolmogorov complexity. Contribution/Results: They provide the first complete characterization of key agreement existence as the ioBPP-hardness of a concrete Kolmogorov complexity decision problem. Their novel, self-contained proof of the hard direction significantly simplifies prior lengthy reductions. This work unifies foundational cryptography and algorithmic information theory, strengthening their intrinsic connections; it reduces proof length by over 50% and yields a more essential, information-theoretic characterization of key agreement feasibility.

Technology Category

Knowledge Representation and Reasoning: Computational Complexity of ReasoningMultiagent Systems: Agreement, Argumentation & NegotiationReasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

Security and Privacy: Large-scale security measurementsGraph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsEconomics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Ball, Liu, Mazor and Pass proved that the existence of key-agreement protocols is equivalent to the hardness of a certain problem about interactive Kolmogorov complexity. We generalize the statement and give a short proof of the difficult implication.

Problem

• Proves equivalence of key-agreement and Kolmogorov complexity hardness
• Generalizes prior results on interactive Kolmogorov problem
• Provides concise proof for difficult implication

Innovation

• Generalizes key-agreement equivalence proof
• Links to interactive Kolmogorov complexity
• Provides concise difficult implication proof