Tight communication-complexity lower bounds under reorder attacks

Establish tight lower bounds on the communication complexity of Byzantine agreement protocols that remain secure under parallel or concurrent composition against party corruptions and communication-channel reorder attacks.

Background

The paper establishes upper bounds for compositionally secure Byzantine agreement through general and optimized compilers. In particular, the refined reliable message transmission and reliable broadcast constructions reduce message-dependent overhead for long messages, but the paper does not characterize the minimum communication required by any secure protocol in the extended adversary model.

A tight lower-bound theory would clarify the inherent communication cost of protecting Byzantine agreement executions against cross-instance message reordering, and would determine whether the overheads of the proposed compilers are unavoidable.

References

Further improving the complexity of our protocols and proving complexity lower-bounds in our model are interesting open problems.

— Scalable Composition of Byzantine Agreements under Reorder Attacks  (2609.09623 - Chen et al., 9 Sep 2026) in Section 2, 'Related Work' (subsection 'Computation and Communication Complexity')