## CryptoDB

### Erica Blum

#### Publications

Year
Venue
Title
2020
CRYPTO
Protocols for secure Multi-Party Computation (MPC) can be classified according to the underlying communication model. Two prominent communication models considered in the literature are the synchronous and asynchronous models, which considerably differ in terms of the achievable security guarantees. Synchronous MPC protocols can achieve the optimal corruption threshold $n/2$ and allow every party to give input, but become completely insecure when synchrony assumptions are violated. On the other hand, asynchronous MPC protocols remain secure under arbitrary network conditions, but can tolerate only $n/3$ corruptions and parties with slow connections unavoidably cannot give input. A natural question is whether there exists a protocol for MPC that can tolerate up to $t_s < n/2$ corruptions under a synchronous network and $t_a < n/3$ corruptions even when the network is asynchronous. We answer this question by showing tight feasibility and impossibility results. More specifically, we show that such a protocol exists if and only if $t_a + 2t_s < n$ and the number of inputs taken into account under an asynchronous network is at most $n-t_s$.
2020
TCC
Understanding the communication complexity of Byzantine agreement (BA) is a fundamental problem in distributed computing. In particular, as protocols are run with a large number of parties (as, e.g., in the context of blockchain protocols), it is important to understand the dependence of the communication on the number of parties~$n$. Although adaptively secure BA protocols with $o(n^2)$ communication are known in the synchronous and partially synchronous settings, no such protocols are known in the fully asynchronous case. We show here an asynchronous BA protocol with subquadratic communication tolerating an adaptive adversary who can corrupt $f<(1-\epsilon)n/3$ of the parties (for any $\epsilon>0$). One variant of our protocol assumes initial setup done by a trusted dealer, after which an unbounded number of BA executions can be run; alternately, we can achieve subquadratic \emph{amortized} communication with no prior setup. We also show that some form of setup is needed for (non-amortized) subquadratic BA tolerating $\Theta(n)$ corrupted parties. As a contribution of independent interest, we show a secure-computation protocol in the same threat model that has $o(n^2)$ communication when computing no-input functionalities with short output (e.g., coin tossing).
2019
TCC
Typically, protocols for Byzantine agreement (BA) are designed to run in either a synchronous network (where all messages are guaranteed to be delivered within some known time $\varDelta$ from when they are sent) or an asynchronous network (where messages may be arbitrarily delayed). Protocols designed for synchronous networks are generally insecure if the network in which they run does not ensure synchrony; protocols designed for asynchronous networks are (of course) secure in a synchronous setting as well, but in that case tolerate a lower fraction of faults than would have been possible if synchrony had been assumed from the start.Fix some number of parties n, and $0< t_a< n/3 \le t_s < n/2$. We ask whether it is possible (given a public-key infrastructure) to design a BA protocol that is resilient to (1) $t_s$ corruptions when run in a synchronous network and (2) $t_a$ faults even if the network happens to be asynchronous. We show matching feasibility and infeasibility results demonstrating that this is possible if and only if $t_a + 2\cdot t_s < n$.

#### Coauthors

Jonathan Katz (2)
Chen-Da Liu-Zhang (2)
Julian Loss (3)