Paper 2023/449

Multidimensional Approximate Agreement with Asynchronous Fallback

Diana Ghinea, ETH Zurich
Chen-Da Liu-Zhang, NTT Research
Roger Wattenhofer, ETH Zurich

Multidimensional Approximate Agreement considers a setting of $n$ parties, where each party holds a vector in $\mathbb{R}^D$ as input. The honest parties are required to obtain very close outputs in $\mathbb{R}^D$ that lie inside the convex hull of their inputs. Existing Multidimensional Approximate Agreement protocols achieve resilience against $t_s < n / (D + 1)$ corruptions under a synchronous network where messages are delivered within some time $\Delta$, but become completely insecure as soon as a single message is further delayed. On the other hand, asynchronous solutions do not rely on any delay upper bound, but only achieve resilience up to $t_a < n / (D + 2)$ corruptions. We investigate the feasibility of achieving Multidimensional Approximate Agreement protocols that achieve simultaneously guarantees in both network settings: We want to tolerate $t_s$ corruptions when the network is synchronous, and also tolerate $t_a \leq t_s$ corruptions when the network is asynchronous. We provide a protocol that works as long as $(D + 1) \cdot t_s + t_a < n$, and matches several existing lower bounds.

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. 35th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA ’23)
Approximate AgreementMultidimensional Approximate Agreementhybrid protocols
Contact author(s)
ghinead @ ethz ch
chendaliu @ gmail com
wattenhofer @ ethz ch
2023-03-29: approved
2023-03-27: received
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      author = {Diana Ghinea and Chen-Da Liu-Zhang and Roger Wattenhofer},
      title = {Multidimensional Approximate Agreement with Asynchronous Fallback},
      howpublished = {Cryptology ePrint Archive, Paper 2023/449},
      year = {2023},
      note = {\url{}},
      url = {}
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