Interactive Non-Malleable Codes Against Desynchronizing Attacks in the Multi-Party Setting

Interactive Non-Malleable Codes were introduced by Fleischhacker et al. (TCC 2019) in the two party setting with synchronous tampering. The idea of this type of non-malleable code is that it "encodes" an interactive protocol in such a way that, even if the messages are tampered with according to some class F of tampering functions, the result of the execution will either be correct, or completely unrelated to the inputs of the participating parties. In the synchronous setting the adversary is able to modify the messages being exchanged but cannot drop messages nor desynchronize the two parties by first running the protocol with the first party and then with the second party. In this work, we define interactive non-malleable codes in the non-synchronous multi-party setting and construct such interactive non-malleable codes for the class F^s_bounded of bounded-state tampering functions

Noisy Beeping Networks

We introduce noisy beeping networks, where nodes have limited communication capabilities, namely, they can only emit energy or sense the channel for energy. Furthermore, imperfections may cause devices to malfunction with some fixed probability when sensing the channel, which amounts to deducing a noisy received transmission. Such noisy networks have implications for ultra-lightweight sensor networks and biological systems. We show how to compute tasks in a noise-resilient manner over noisy beeping networks of arbitrary structure. In particular, we transform any algorithm that assumes a noiseless beeping network (of size $n$) into a noise-resilient version while incurring a multiplicative overhead of only $O(\log n)$ in its round complexity, with high probability. We show that our coding is optimal for some tasks, such as node-coloring of a clique. We further show how to simulate a large family of algorithms designed for distributed networks in the CONGEST($B$) model over a noisy beeping network. The simulation succeeds with high probability and incurs an asymptotic multiplicative overhead of $O(B\cdot \Delta \cdot \min(n,\Delta^2))$ in the round complexity, where $\Delta$ is the maximal degree of the network. The overhead is tight for certain graphs, e.g., a clique. Further, this simulation implies a constant overhead coding for constant-degree networks

Optimal Short-Circuit Resilient Formulas

We consider fault-tolerant boolean formulas in which the output of a faulty gate is short-circuited to one of the gate\u27s inputs. A recent result by Kalai et al. [FOCS 2012] converts any boolean formula into a resilient formula of polynomial size that works correctly if less than a fraction 1/6 of the gates (on every input-to-output path) are faulty. We improve the result of Kalai et al., and show how to efficiently fortify any boolean formula against a fraction 1/5 of short-circuit gates per path, with only a polynomial blowup in size. We additionally show that it is impossible to obtain formulas with higher resilience and sub-exponential growth in size. Towards our results, we consider interactive coding schemes when noiseless feedback is present; these produce resilient boolean formulas via a Karchmer-Wigderson relation. We develop a coding scheme that resists up to a fraction 1/5 of corrupted transmissions in each direction of the interactive channel. We further show that such a level of noise is maximal for coding schemes with sub-exponential blowup in communication. Our coding scheme takes a surprising inspiration from Blockchain technology