Asynchronous Byzantine Agreement Research Articles

Almost-surely terminating asynchronous Byzantine agreement against general adversaries with optimal resilience

In this work, we study almost-surely terminating asynchronous Byzantine agreement (ABA) for n parties tolerating a computationally-unbounded adversary. While the existing works in this domain have primarily considered a threshold adversarial model where the adversary can corrupt any subset of up to t parties, very little attention has been paid to the non-threshold adversarial model. In the latter model, the corruption capacity of the adversary is characterized by an adversary structure Z, which enumerates all possible subsets of potentially corrupt parties and where the adversary can select any one subset from Z for corruption. While the optimal resilience for ABA against threshold adversaries is t<n/3, against non-threshold adversaries one can design an ABA protocol, provided Z satisfies the Q(3) condition; i.e. if the union of no three subsets from Z covers all the n parties. We present the first almost-surely terminating ABA protocol against Q(3) adversary structures. Previously, almost-surely terminating ABA protocol is known with non-optimal resilience where Z satisfies the Q(4) condition; i.e. if the union of no four subsets from Z covers all the n parties. To design our protocol, we present a shunning asynchronous verifiable secret-sharing (SAVSS) scheme for Q(3) adversary structures, which is of independent interest.

Reaching consensus for asynchronous distributed key generation

We give a protocol for Asynchronous Distributed Key Generation (A-DKG) that is optimally resilient (can withstand \({{\varvec{f}}}<\frac{{{\varvec{n}}}}{{{\varvec{3}}}}\) faulty parties), has a constant expected number of rounds, has \({{\varvec{O}}}({\varvec{\lambda }} {{\varvec{n}}}^{{\varvec{3}}})\) expected communication complexity, and assumes only the existence of a PKI. Prior to our work, the best A-DKG protocols required \({\varvec{\Omega }}({{\varvec{n}}})\) expected number of rounds, and \({\varvec{\Omega }}({{\varvec{n}}}^4)\) expected communication. Our A-DKG protocol relies on several building blocks that are of independent interest. We define and design a Proposal Election (PE) protocol that allows parties to retrospectively agree on a valid proposal after enough proposals have been sent from different parties. With constant probability the elected proposal was proposed by a nonfaulty party. In building our PE protocol, we design a Verifiable Gather protocol which allows parties to communicate which proposals they have and have not seen in a verifiable manner. The final building block to our A-DKG is a Validated Asynchronous Byzantine Agreement (VABA) protocol. We use our PE protocol to construct a VABA protocol that does not require leaders or an asynchronous DKG setup. Our VABA protocol can be used more generally when it is not possible to use threshold signatures.

Revisiting asynchronous fault tolerant computation with optimal resilience

The celebrated result of Fischer, Lynch and Paterson is the fundamental lower bound for asynchronous fault tolerant computation: any 1-crash resilient asynchronous agreement protocol must have some (possibly measure zero) probability of not terminating. In 1994, Ben-Or, Kelmer and Rabin published a proof-sketch of a lesser known lower bound for asynchronous fault tolerant computation with optimal resilience in face of a Byzantine adversary: if $$n\le 4t$$ then any t-resilient asynchronous verifiable secret sharing protocol must have some non-zero probability of not terminating. Our main contribution is to revisit this lower bound and provide a rigorous and more general proof. Our second contribution is to show how to avoid this lower bound. We provide a protocol with optimal resilience that is almost surely terminating for a strong common coin functionality. Using this new primitive we provide an almost surely terminating protocol with optimal resilience for asynchronous Byzantine agreement that has a new fair validity property. To the best of our knowledge this is the first asynchronous Byzantine agreement with fair validity in the information theoretic setting.

Asynchronous Byzantine Agreement with optimal resilience

We present an efficient, optimally-resilient Asynchronous Byzantine Agreement (ABA) protocol involving \(n = 3t+1\) parties over a completely asynchronous network, tolerating a computationally unbounded Byzantine adversary, capable of corrupting at most \(t\) out of the \(n\) parties. In comparison with the best known optimally-resilient ABA protocols of Canetti and Rabin (STOC 1993) and Abraham et al. (PODC 2008), our protocol is significantly more efficient in terms of the communication complexity. Our ABA protocol is built on a new statistical asynchronous verifiable secret sharing (AVSS) protocol with optimal resilience. Our AVSS protocol significantly improves the communication complexity of the only known statistical and optimally-resilient AVSS protocol of Canetti et al. Our AVSS protocol is further built on an asynchronous primitive called asynchronous weak commitment (AWC), while the AVSS of Canetti et al. is built on the primitive called asynchronous weak secret sharing (AWSS). We observe that AWC has weaker requirements than AWSS and hence it can be designed more efficiently than AWSS. The common coin primitive is one of the most important building blocks for the construction of an ABA protocol. In this paper, we extend the existing common coin protocol to make it compatible with our new AVSS protocol that shares multiple secrets simultaneously. As a byproduct, our new common coin protocol is more communication efficient than all the existing common coin protocols.

Fast asynchronous Byzantine agreement and leader election with full information

We resolve two long-standing open problems in distributed computation by describing polylogarithmic protocols for Byzantine agreement and leader election in the asynchronous full information model with a nonadaptive malicious adversary. All past protocols for asynchronous Byzantine agreement had been exponential, and no protocol for asynchronous leader election had been known. Our protocols tolerate up to (1/3 − ϵ) ⋅ n faulty processors, for any positive constant ϵ. They are Monte Carlo, succeeding with probability 1 − o (1) for Byzantine agreement, and constant probability for leader election. A key technical contribution of our article is a new approach for emulating Feige's lightest bin protocol, even with adversarial message scheduling.

Asynchronous Byzantine Agreement Protocol based on verifiable signature sharing

An ([n/3] − 1)-resilient Asynchronous Byzantine Agreement Protocol (ABAP) that combines verifiable signature sharing and random secret sharing is proposed. The protocol works in the asynchronous network environment and produces Byzantine agreement within a fixed expected number of computational rounds. The correctness of the protocol is proved in theory.

Random Oracles in Constantinople: Practical Asynchronous Byzantine Agreement Using Cryptography

Byzantine agreement requires a set of parties in a distributed system to agree on a value even if some parties are maliciously misbehaving. A new protocol for Byzantine agreement in a completely asynchronous network is presented that makes use of new cryptographic protocols, specifically protocols for threshold signatures and coin-tossing. These cryptographic protocols have practical and provably secure implementations in the random oracle model. In particular, a coin-tossing protocol based on the Diffie-Hellman problem is presented and analyzed. The resulting asynchronous Byzantine agreement protocol is both practical and theoretically optimal because it tolerates the maximum number of corrupted parties, runs in constant expected rounds, has message and communication complexity close to the optimum, and uses a trusted dealer only once in a setup phase, after which it can process a virtually unlimited number of transactions. The protocol is formulated as a transaction processing service in a cryptographic security model, which differs from the standard information-theoretic formalization and may be of independent interest.

Asynchronous Byzantine agreement protocols

A consensus protocol enables a system of n asynchronous processes, some of them faulty, to reach agreement. Both the processes and the message system are capable of cooperating to prevent the correct processes from reaching decision. A protocol is t -resilient if in the presence of up to t faulty processes it reaches agreement with probability 1. Byzantine processes are faulty processes that can deviate arbitrarily from the protocol; Fail-Stop processes can just stop participating in it. In a recent paper, t -resilient randomized consensus protocols were presented for t< n 5 . We improve this to t < n 3 , thus matching the known lower bound on the number of correct processes necessary for consensus. The protocol uses a general technique in which the behavior of the Byzantine processes is restricted by the use of a broadcast protocol that filters some of the messages. The apparent behavior of the Byzantine processes, filtered by the broadcast protocol, is similar to that of Fail-Stop processes. Plugging the broadcast protocol as a communicating primitive into an agreement protocol for Fail-Stop processes gives the result. This technique, of using broadcast protocols to reduce the power of the faulty processes and then using them as communication primitives in algorithms designed for weaker failure models, was used succesfully in other contexts.

Asynchronous consensus and broadcast protocols

A consensus protocol enables a system of n asynchronous processes, some of which are faulty, to reach agreement. There are two kinds of faulty processes: fail-stop processes that can only die and malicious processes that can also send false messages. The class of asynchronous systems with fair schedulers is defined, and consensus protocols that terminate with probability 1 for these systems are investigated. With fail-stop processes, it is shown that ⌈( n + 1)/2⌉ correct processes are necessary and sufficient to reach agreement. In the malicious case, it is shown that ⌈(2 n + 1)/3⌉ correct processes are necessary and sufficient to reach agreement. This is contrasted with an earlier result, stating that there is no consensus protocol for the fail-stop case that always terminates within a bounded number of steps, even if only one process can fail. The possibility of reliable broadcast (Byzantine Agreement) in asynchronous systems is also investigated. Asynchronous Byzantine Agreement is defined, and it is shown that ⌈(2 n + 1)/3⌉ correct processes are necessary and sufficient to achieve it.