Brief Announcement: Optimal Adaptive Multi-Valued Byzantine Agreement

Abstract

In Byzantine Agreement (BA), n parties, out of which t can be Byzantine, run a distributed protocol to agree on a common valid input. Traditionally, these protocols have a linear latency and quadratic communication complexity, making them impractical at a large scale. In their recent work, Constantinescu, Dufay, Paramonov, and Wattenhofer [PODC'26] consider the actual number of byzantine parties f ≤ t and work toward decoupling the dependency on n and t in the complexity. They obtain a BA protocol with 𝒪̃(n + t⋅f) communication complexity and 𝒪̃(f) round complexity.
However, their results are strictly limited to agreement on a binary value. Using the framework given by their work along with novel techniques, we extend these results for BA on an L-bit value. With κ being a security parameter, and with optimal resiliency (t < n/2 in the synchronous setting or t < n/3 otherwise), we obtain:  
- In synchrony, a deterministic protocol with 𝒪(n⋅ (L + f⋅κ)) bit complexity and 𝒪(f + log n) round complexity. 
- In synchrony and partial synchrony, deterministic protocols with 𝒪̃(n⋅κ + t⋅ (L + f⋅κ)) bit complexity and 𝒪(f) round complexity. 
- In asynchrony, a protocol with 𝒪̃(n ⋅ κ + t⋅(L + t⋅κ)) expected bit complexity and expected 𝒪(1) latency.