Perfectly Secure Message Transmission in Two Rounds

TL;DR

This paper presents a simpler, more efficient two-round protocol for perfectly secure message transmission over multiple channels, reducing communication complexity and extending secure message size thresholds.

Contribution

It introduces a conceptually simpler protocol that reduces communication complexity from O(n^3 log n) to O(n^2 log n) and improves secure message size thresholds.

Findings

Reduced communication complexity significantly.

Extended secure message size threshold to O(n log n) bits.

Adapted protocol for network coding contexts.

Abstract

In the model that has become known as "Perfectly Secure Message Transmission"(PSMT), a sender Alice is connected to a receiver Bob through n parallel two-way channels. A computationally unbounded adversary Eve controls t of these channels, meaning she can acquire and alter any data that is transmitted over these channels. The sender Alice wishes to communicate a secret message to Bob privately and reliably, i.e. in such a way that Eve will not get any information about the message while Bob will be able to recover it completely. In this paper, we focus on protocols that work in two transmission rounds for n= 2t+1. We break from previous work by following a conceptually simpler blueprint for achieving a PSMT protocol. We reduce the previously best-known communication complexity, i.e. the number of transmitted bits necessary to communicate a 1-bit secret, from O(n^3 log n) to O(n^2 log n). Our protocol also answers a question raised by Kurosawa and Suzuki and hitherto left open: their protocol reaches optimal transmission rate for a secret of size O(n^2 log n) bits, and the authors raised the problem of lowering this threshold. The present solution does this for a secret of O(n log n) bits. Additionally, we show how our protocol can be adapted to a Network Coding context.