Secure Cascade Channel Synthesis

TL;DR

This paper characterizes the optimal tradeoff between communication rates and common randomness in secure cascade channel synthesis, ensuring correlated sequences appear iid to eavesdroppers, and extends results to longer cascades.

Contribution

It provides a complete characterization of the rate tradeoffs for secure cascade channel synthesis, including for arbitrarily long cascades, with new bounds and solutions.

Findings

Optimal rate tradeoff characterized for secure cascade synthesis.

Inner bounds provided for cascade synthesis without eavesdropper.

Extension of results to arbitrarily long cascades.

Abstract

We investigate channel synthesis in a cascade setting where nature provides an iid sequence $X^n$ at node 1. Node 1 can send a message at rate $R_1$ to node 2 and node 2 can send a message at rate $R_2$ to node 3. Additionally, all 3 nodes share bits of common randomness at rate $R_0$. We want to generate sequences $Y^n$ and $Z^n$ along nodes in the cascade such that $(X^n,Y^n,Z^n)$ appears to be appropriately correlated and iid even to an eavesdropper who is cognizant of the messages being sent. We characterize the optimal tradeoff between the amount of common randomness used and the required rates of communication. We also solve the problem for arbitrarily long cascades and provide an inner bound for cascade channel synthesis without an eavesdropper.