Asymptotically Optimal Two-Round Perfectly Secure Message Transmission

The problem of perfectly secure message transmission concerns two synchronized non-faulty processors sender (

${\mathcal{S}}$

) and receiver (

${\mathcal{R}}$

) that are connected by a synchronous network of

n

≥2

t

+1 noiseless 2-way communication channels. Their goal is to communicate privately and reliably, despite the presence of an adversary that may actively corrupt at most

t

of those channels. These properties should hold information theoretically and without error.

We propose an asymptotically optimal solution for this problem. The proposed protocol consists of two communication rounds, and a total of

O

(ℓ

n

) bits are exchanged in order to transmit a message of ℓ bits. Earlier, at CRYPTO 2004, an equally optimal solution has been claimed. However, we give a counter-example showing that their result is not perfectly reliable. The flaw seems to be fundamental and non-trivial to repair. Our approach is overall entirely different, yet it also makes essential use of their neat communication efficient technique for reliably transmitting conflict graphs.

What distinguishes our approach from previous ones is a technique that allows to identify

all actively corrupted channels

, initially trading it off against privacy. A perfectly secure and reliable secret key is then distilled by privacy amplification.