On the Optimality of Keyless Authentication in a Noisy Model

TL;DR

This paper investigates keyless authentication over noisy channels, proposing a protocol with minimal message length dependence on source size, establishing lower bounds on round complexity, and determining the capacity for non-interactive authentication.

Contribution

It introduces a new authentication protocol with optimized round complexity and message length, and derives fundamental bounds and capacities in noisy channel models.

Findings

Protocol message length independent of source size.

Lower bound on round complexity based on source and channel parameters.

Capacity characterization for non-interactive authentication over general DMCs.

Abstract

We further study the keyless authentication problem in a noisy model in our previous work, where no secret setup is available for sender Alice and receiver Bob while there is DMC $W_1$ from Alice to Bob and a two-way noiseless but insecure channel between them. We propose a construction such that the message length over DMC $W_1$ does not depend on the size of the source space. If the source space is ${\cal S}$ and the number of channel $W_1$ uses is $n$, then our protocol only has a round complexity of $\log^*|{\cal S}|-\log^*n+4.$ In addition, we show that the round complexity of any secure protocol in our model is lower bounded by $\log^*|{\cal S}|-\log^* n-5$. We also obtain a lower bound on the success probability when the message size on DMC $W_1$ is given. Finally, we derive the capacity for a non-interactive authentication protocol under general DMCs, which extends the result under BSCs in our previous work.