Abstract
In the consensus problem, n parties want to agree on a common value, even if some of them are corrupt and arbitrarily misbehave. If the parties have a common input m, then they must agree on m.
Protocols solving consensus assume either a synchronous communication network, where messages are delivered within a known time, or an asynchronous network with arbitrary delays. Asynchronous protocols only tolerate \(t_a < n/3\) corrupt parties. Synchronous ones can tolerate \(t_s < n/2\) corruptions with setup, but their security completely breaks down if the synchrony assumptions are violated.
Network-agnostic consensus protocols, as introduced by Blum, Katz, and Loss [TCC’19], are secure regardless of network conditions, tolerating up to \(t_s\) corruptions with synchrony and \(t_a\) without, under provably optimal assumptions \(t_a \le t_s\) and \(2t_s + t_a < n\). Despite efforts to improve their efficiency, all known network-agnostic protocols fall short of the asymptotic complexity of state-of-the-art purely synchronous protocols.
In this work, we introduce a novel technique to compile any synchronous and any asynchronous consensus protocols into a network-agnostic one. This process only incurs a small constant number of overhead rounds, so that the compiled protocol matches the optimal round complexity for synchronous protocols. Our compiler also preserves under a variety of assumptions the asymptotic communication complexity of state-of-the-art synchronous and asynchronous protocols. Hence, it closes the current efficiency gap between synchronous and network-agnostic consensus.
As a plus, our protocols support \(\ell \)-bit inputs, and can be extended to achieve communication complexity \(\mathcal {O}(n^2\kappa + \ell n)\) under the assumptions for which this is known to be possible for purely synchronous protocols.
A full version of this paper is available at https://eprint.iacr.org/2024/317.
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Notes
- 1.
The protocol \(\textsf{ABA}^*\) should also have certain termination properties if the network is synchronous, but such details are not needed to appreciate this technical overview.
- 2.
Grades 0 and 1 suffice for \(\textsf{SBA}^*\) with binary inputs. Expanding the grade range is only necessary for multi-valued inputs, but incurs no asymptotic round or communication complexity overhead, which is why we do not consider the cases separately.
- 3.
The \(\textsf {ABA}\) in [18] is secure statically, or adaptively with a one-time CRS.
- 4.
This coin protocol is secure in the random oracle model.
- 5.
An \(\textsf{SBA}\) protocol concurrent with our work uses threshold signatures to achieve \(\mathcal {O}(nf\kappa )\) complexity, where \(f \le t_s \le \frac{(1 - \varepsilon )n}{2}\) is the actual number of malicious parties [13]. Our work only considers the worst case \(f = t_s\).
- 6.
Since \(2t_s + t_a < n\) is required, this assumption is without loss of generality. One can simply consider \(\delta = (n - 2t_s - t_a)/n\).
- 7.
Actually, \(t_a\)-validity from \(\textsf {ABA}^*\) suffices for \(\textsf {HBA}\).
- 8.
Adaptively secure sub-quadratic extension is possible in the atomic-send model [4].
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Deligios, G., Mizrahi Erbes, M. (2024). Closing the Efficiency Gap Between Synchronous and Network-Agnostic Consensus. In: Joye, M., Leander, G. (eds) Advances in Cryptology – EUROCRYPT 2024. EUROCRYPT 2024. Lecture Notes in Computer Science, vol 14655. Springer, Cham. https://doi.org/10.1007/978-3-031-58740-5_15
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