## Cryptology ePrint Archive: Report 2017/710

Distributed Computing with Channel Noise

Abhinav Aggarwal and Varsha Dani and Thomas P. Hayes and Jared Saia

Abstract: A group of $n$ users want to run a distributed protocol $\pi$ over a network where communication occurs via private point-to-point channels. Unfortunately, an adversary, who knows $\pi$, is able to maliciously flip bits on the channels. Can we efficiently simulate $\pi$ in the presence of such an adversary?

We show that this is possible, even when $L$, the number of bits sent in $\pi$, and $T$, the number of bits flipped by the adversary are not known in advance. In particular, we show how to create a robust version of $\pi$ that 1) fails with probability at most $\delta$, for any $\delta > 0$; and 2) sends $\tilde{O}(L+T)$ bits, where the $\tilde{O}$ notation hides a $\log(nL/\delta)$ term multiplying $L$.

Additionally, we show how to improve this result when the average message size $\alpha$ is not constant. In particular, we give an algorithm that sends $O(L(1 + (1/\alpha) \log(nL/\delta) + T )$ bits. This algorithm is adaptive in that it does not require a priori knowledge of $\alpha$. We note that if $\alpha$ is $\Omega (log(nL/\delta))$, then this improved algorithm sends only $O(L + T)$ bits, and is therefore within a constant factor of optimal.

Category / Keywords: foundations / interactive communication, information theoretic security