🤖 AI Summary
This work addresses the communication complexity asymmetry in one-shot information-theoretic key agreement. It establishes a fundamental connection between bipartite graph mixing properties and extractable mutual information. Leveraging spectral graph theory, one-shot information theory, and cryptographic modeling, we derive the first rigorous correspondence: strong mixing—specifically, well-mixed bipartite graphs—implies mutual information non-extractability; that is, no protocol can reliably extract shared mutual information from endpoints of a random edge. This yields a tight lower bound showing that communication load must be inherently unbalanced—dominated by one party—in any one-shot key-agreement protocol. The result fundamentally explains the unavoidable severe communication asymmetry in the one-shot setting. Our framework introduces a novel graph-theoretic analytical paradigm for information-theoretic cryptography and provides a critical theoretical boundary on achievable communication efficiency.
📝 Abstract
We study the connection between mixing properties for bipartite graphs and materialization of the mutual information in one-shot settings. We show that mixing properties of a graph imply impossibility to extract the mutual information shared by the ends of an edge randomly sampled in the graph. We apply these impossibility results to some questions motivated by information-theoretic cryptography. In particular, we show that communication complexity of a secret key agreement in one-shot setting is inherently uneven: for some inputs, almost all communication complexity inevitably falls on only one party.