Optimality of the communication and computation complexity of the compiled protocols

Determine whether the Byzantine agreement protocols produced by the proposed parallel and concurrent composition compilers are optimal in communication and computation complexity.

Background

The paper introduces black-box compilers that transform single-instance Byzantine agreement protocols into protocols secure under parallel or concurrent executions in the presence of party corruptions and channel-reorder attacks. These compilers provide polynomial communication and computation complexity, while refined reliable message transmission and reliable broadcast primitives reduce the overhead for long messages.

The authors do not establish that these complexity guarantees are optimal. The unresolved issue concerns whether the communication and computation costs achieved by the compiled protocols can be improved, or whether they are inherent for compositionally secure Byzantine agreement under the proposed adversary model.

References

Although it remains unknown whether our protocols are optimal in terms of their complexity, they do achieve polynomial communication and computation.

— 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')