Consensus among n parties tolerating up to t Byzantine faults requires n > 2t in synchronous networks and n > 3t in asynchronous networks. The higher resilience achievable in synchrony relies on a known message delay bound Δ, whereas asynchronous protocols make no timing assumptions but must tolerate fewer faults. Prior work addressed this gap only partially. Some protocols achieve responsiveness under synchrony, meaning that their running time adapts to the actual network delay, but offer no guarantees under asynchrony, while others guarantee correctness under both network conditions but sacrifice responsiveness. Only recently, Elsheimy, Kamp, Loss, and Nielsen (IACR 2026) showed for binary validated Byzantine agreement (VBA) that if ts, ta, and tr denote the synchronous, asynchronous, and responsiveness thresholds, respectively, then the conditions n > 2ts + ta and n > ts + 2tr are necessary and sufficient to simultaneously achieve asynchronous security, synchronous security, and responsiveness. While binary BA (or VBA) can be extended to multi-valued Byzantine agreement (MVBA) via standard reductions, such transformations generally incur blow-up in the communication. Whether these tight resilience conditions can be achieved for MVBA with optimal communication complexity remained open.

In distributed systems with asymmetric trust, each participant is free to make its own trust assumptions about others, captured by an asymmetric quorum system. This contrasts with ordinary, symmetric quorum systems and threshold models, where trust assumptions are uniformly shared among participants. Fundamental problems like reliable broadcast and consensus are unsolvable in the asymmetric model if quorum systems satisfy only the classical properties of consistency and availability. Existing approaches overcome this by introducing stronger assumptions. We show that some of these assumptions are overly restrictive, so much so that they effectively eliminate the benefits of asymmetric trust. To address this, we propose a new approach to characterize asymmetric problems and, building upon it, present algorithms for reliable broadcast and consensus that require weaker assumptions than previous solutions. Our methods are general and can be extended to other core problems in systems with asymmetric trust.

We present simple and practical protocols for generating randomness as used by asynchronous total-order broadcast. The protocols are secure in a proof-of-stake setting with dynamically changing stake. They can be plugged into existing protocols for asynchronous total-order broadcast and will turn these into asynchronous total-order broadcast with dynamic stake. Our contribution relies on two important techniques. The paper "Random Oracles in Constantinople: Practical Asynchronous Byzantine Agreement using Cryptography" [Cachin, Kursawe, and Shoup, PODC 2000] has influenced the design of practical total-order broadcast through its use of threshold cryptography. However, it needs a setup protocol to be efficient. In a proof-of-stake setting with dynamic stake this setup would have to be continually recomputed, making the protocol impractical. The work "Asynchronous Byzantine Agreement with Subquadratic Communication" [Blum, Katz, Liu-Zhang, and Loss, TCC 2020] showed how to use an initial setup for broadcast to asymptotically efficiently generate sub-sequent setups. The protocol, however, resorted to fully homomorphic encryption and was therefore not practically efficient. We adopt their approach to the proof-of-stake setting with dynamic stake, apply it to the Constantinople paper, and remove the need for fully homomorphic encryption. This results in simple and practical proof-of-stake protocols.