Efficient Signature-Free Validated Agreement

TL;DR

The paper tackles the problem of synchronous validated Byzantine agreement with external validity in a signature-free setting, where values are long and must be validated. It introduces HashExt, a hash-based protocol that achieves $O(nL + n^3\kappa)$ bit complexity (optimal for $L \ge n^2\kappa$) and ErrorFreeExt, a cryptography-free protocol achieving $O((nL + n^2) \log n)$ bit complexity, both with optimal resilience ($t < n/3$) and early stopping in $O(f+1)$ rounds. HashExt relies on implicit proofs via digest-based data dissemination built on Reed–Solomon coding and Merkle accumulators to avoid transmitting full $L$-bit values per message, while ErrorFreeExt employs a recursive, two-half design with graded consensus and a finisher to achieve near-optimal performance without cryptography. Together, they close a substantial gap toward the Omega($nL + n^2$) lower bound for signature-free validated agreement and offer practically relevant solutions for state machine replication and blockchain protocols. The results demonstrate that efficient, signature-free validated agreement is achievable and pave the way for robust, scalable consensus in distributed systems without cryptographic trust assumptions.

Abstract

Byzantine agreement enables n processes to agree on a common L-bit value, despite up to t > 0 arbitrary failures. A long line of work has been dedicated to improving the bit complexity of Byzantine agreement in synchrony. This has culminated in COOL, an error-free (deterministically secure against a computationally unbounded adversary) solution that achieves O(nL + n^2 logn) worst-case bit complexity (which is optimal for L >= n logn according to the Dolev-Reischuk lower bound). COOL satisfies strong unanimity: if all correct processes propose the same value, only that value can be decided. Strong unanimity is, however, not sufficient for today's state machine replication (SMR) and blockchain protocols. These systems value progress and require a decided value to always be valid, excluding default decisions (such as EMPTY) even in cases where there is no unanimity a priori. Validated Byzantine agreement satisfies this property (called external validity). Yet, the best error-free (or even signature-free) validated agreement solutions achieve only O(n^2L) bit complexity, a far cry from the Omega(nL + n^2) Dolev-Reishcuk lower bound. In this paper, we present two new synchronous algorithms for validated Byzantine agreement, HashExt and ErrorFreeExt, with different trade-offs. Both algorithms are (1) signature-free, (2) optimally resilient (tolerate up to t < n / 3 failures), and (3) early-stopping (terminate in O(f+1) rounds, where f <= t is the actual number of failures). On the one hand, HashExt uses only hashes and achieves O(nL + n^3 kappa) bit complexity, which is optimal for L >= n^2 kappa (where kappa is the size of a hash). On the other hand, ErrorFreeExt is error-free, using no cryptography whatsoever, and achieves O( (nL + n^2) logn ) bit complexity, which is near-optimal for any L.

Figures (1)

• Figure 1: The recursive structure of ErrorFreeExt (and SlowExt).

Theorems & Definitions (64)

• Theorem 1
• Theorem 2
• Theorem 3: Strong unanimity
• Theorem 4: Justification
• Theorem 5: Integrity
• Theorem 6: Termination
• Lemma 7
• Theorem 8: Consistency
• Theorem 9: Exchanged bits
• Theorem 10: Rounds