Byzantine Agreement Protocol Research Articles

Sublinear message bounds of authenticated implicit Byzantine agreement

This paper studies the message complexity of authenticated Byzantine agreement (BA) in synchronous, fully-connected distributed networks under an honest majority. We focus on the so-called implicit Byzantine agreement problem where each node starts with an input value and at the end a non-empty subset of the honest nodes should agree on a common input value by satisfying the BA properties (i.e., there can be undecided nodes)3. We show that a sublinear (in n, number of nodes) message complexity BA protocol under honest majority is possible in the standard PKI model when the nodes have access to an unbiased global coin and hash function. In particular, we present a randomized Byzantine agreement algorithm which, with high probability achieves implicit agreement, uses O˜(n) messages, and runs in O˜(1) rounds while tolerating (1/2−ϵ)n Byzantine nodes for any fixed ϵ>0, the notation O˜ hides a O(polylogn) factor4. The algorithm requires standard cryptographic setup PKI and hash function with a static Byzantine adversary. The algorithm works in the CONGEST model and each node does not need to know the identity of its neighbors, i.e., works in the KT0 model. The message complexity (and also the time complexity) of our algorithm is optimal up to a polylog n factor, as we show a Ω(n) lower bound on the message complexity. We further extend the result to Byzantine subset agreement, where a non-empty subset of nodes should agree on a common value. Lastly, we analyze several relevant results that follow from the construction of the main result.To the best of our knowledge, this is the first sublinear message complexity result of Byzantine agreement. A quadratic message lower bound is known for any deterministic BA protocol (due to Dolev-Reischuk [JACM 1985]). The existing randomized BA protocols have at least quadratic message complexity in the honest majority setting. Our result shows the power of a global coin in achieving significant improvement over the existing results. It can be viewed as a step towards understanding the message complexity of randomized Byzantine agreement in distributed networks with PKI.

Synchronous Distributed Key Generation without Broadcasts

Distributed key generation (DKG) is a key building block in developing many efficient threshold cryptosystems. This work initiates the study of communication complexity and round complexity of DKG protocols over a point-to-point (bounded) synchronous network. Our key result is the first synchronous DKG protocol for discrete log-based cryptosystems with O ( κ n 3 ) communication complexity ( κ denotes a security parameter) that tolerates any t < n / 2 Byzantine faults among n parties. We present two variants of the protocol: (i) a protocol with worst-case O ( κ n 3 ) communication and O ( t ) rounds, and (ii) a protocol with expected O ( κ n 3 ) communication and expected constant rounds. In the process of achieving our results, we design (1) a novel weak gradecast protocol with a communication complexity of O ( κ n 2 ) for linear-sized inputs and constant rounds, (2) a protocol called “recoverable-set-of-shares” for ensuring recovery of shared secrets, (3) an oblivious leader election protocol with O ( κ n 3 ) communication and constant rounds, and (4) a multi-valued validated Byzantine agreement (MVBA) protocol with O ( κ n 3 ) communication complexity for linear-sized inputs and expected constant rounds. Each of these primitives is of independent interest.

The Bitcoin Backbone Protocol: Analysis and Applications

Bitcoin is the first and most popular decentralized cryptocurrency to date. In this work, we extract and analyze the core of the Bitcoin protocol, which we term the Bitcoin backbone , and prove three of its fundamental properties which we call Common Prefix , Chain Quality and Chain Growth in the static setting where the number of players remains fixed. Our proofs hinge on appropriate and novel assumptions on the “hashing power” of the protocol participants and their interplay with the protocol parameters and the time needed for reliable message passing between honest parties in terms of computational steps. A takeaway from our analysis is that, all else being equal, the protocol’s provable tolerance in terms of the number of adversarial parties (or, equivalently, their “hashing power” in our model) decreases as the duration of a message passing round increases. Next, we propose and analyze applications that can be built “on top” of the backbone protocol, specifically focusing on Byzantine agreement (BA) and on the notion of a public transaction ledger. Regarding BA, we observe that a proposal due to Nakamoto falls short of solving it, and present a simple alternative which works assuming that the adversary’s hashing power is bounded by 1/3. The public transaction ledger captures the essence of Bitcoin’s operation as a cryptocurrency, in the sense that it guarantees the liveness and persistence of committed transactions. Based on this notion we describe and analyze the Bitcoin system as well as a more elaborate BA protocol and we prove them secure assuming the adversary’s hashing power is strictly less than 1/2. Instrumental to this latter result is a technique we call 2-for-1 proof-of-work (PoW) that has proven to be useful in the design of other PoW-based protocols.

LWSBFT: Leaderless weakly synchronous BFT protocol

Asynchronous or partially synchronous Byzantine fault-tolerant (BFT) protocols can tolerate up to one-third Byzantine faults, while synchronous Byzantine fault-tolerant protocols can tolerate up to one-half Byzantine faults. The existing synchronous Byzantine fault-tolerant protocols are leader-based protocols, which may lead to unbalanced load between nodes, and constitute a bottleneck that influences the performance of the whole system. In addition, the synchronous BFT protocols rely on a strong assumption: every message sent by an honest node will arrive at its destination within a known bounded time. In this work, in order to obtain better fairness and allow some degree of asynchrony while tolerating one-half faults, we designed LWSBFT, a leaderless BFT protocol in a weakly synchronous model where the synchronous assumption does not have to hold for all nodes all the time. The leaderless BFT protocol is comprised of the weakly synchronous Byzantine reliable broadcast (RBC) protocol and the weakly synchronous binary Byzantine agreement (BA) protocol, both of which can tolerate one-half faults. The weakly synchronous RBC protocol is used by each node to propose its input, and the weakly synchronous binary BA protocol is used to make a decision for each proposed value. The proposed leaderless BFT protocol can ensure both safety and liveness in a weakly synchronous model. We implement our consensus mechanism in Go, and evaluate the proposed consensus mechanism’s performance in terms of throughput and latency.

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.

Efficient deterministic preparation of quantum states using decision diagrams

Loading classical data into quantum registers is one of the most important primitives of quantum computing. While the complexity of preparing a generic quantum state is exponential in the number of qubits, in many practical tasks the state to prepare has a certain structure that allows for faster preparation. In this paper, we consider quantum states that can be efficiently represented by (reduced) decision diagrams, a versatile data structure for the representation and analysis of Boolean functions. We design an algorithm that utilizes the structure of decision diagrams to prepare their associated quantum states. Our algorithm has a circuit complexity that is linear in the number of paths in the decision diagram. Numerical experiments show that our algorithm reduces the circuit complexity by up to 31.85% compared to the state-of-the-art algorithm, when preparing generic $n$-qubit states with ${n}^{3}$ nonzero amplitudes. Additionally, for states with sparse decision diagrams, including the initial state of the quantum Byzantine agreement protocol, our algorithm reduces the number of controlled-nots by 86.61--99.9%.

Communication complexity of byzantine agreement, revisited

As Byzantine Agreement (BA) protocols find application in large-scale decentralized cryptocurrencies, an increasingly important problem is to design BA protocols with improved communication complexity. A few existing works have shown how to achieve subquadratic BA under an adaptive adversary. Intriguingly, they all make a common relaxation about the adaptivity of the attacker, that is, if an honest node sends a message and then gets corrupted in some round, the adversary cannot erase the message that was already sent—henceforth we say that such an adversary cannot perform “after-the-fact removal”. By contrast, many (super-)quadratic BA protocols in the literature can tolerate after-the-fact removal. In this paper, we first prove that disallowing after-the-fact removal is necessary for achieving subquadratic-communication BA. Next, we show new subquadratic binary BA constructions (of course, assuming no after-the-fact removal) that achieve near-optimal resilience and expected constant rounds under standard cryptographic assumptions and a public-key infrastructure (PKI) in both synchronous and partially synchronous settings. In comparison, all known subquadratic protocols make additional strong assumptions such as random oracles or the ability of honest nodes to erase secrets from memory, and even with these strong assumptions, no prior work can achieve the above properties. Lastly, we show that some setup assumption is necessary for achieving subquadratic multicast-based BA.

Cob: a leaderless protocol for parallel Byzantine agreement in incomplete networks

In this paper we extend the Multidimensional Byzantine Agreement (MBA) Protocol, a leaderless Byzantine agreement for lists of arbitrary values, into a protocol suitable for wide gossiping networks: Cob. This generalization allows the consensus process to be run by an incomplete network of nodes provided with (non-synchronized) same-speed clocks. Not all nodes are active in every step, so the network size does not hamper the efficiency, as long as the gossiping broadcast delivers the messages to every node in reasonable time. These network assumptions model more closely real-life communication channels, so Cob may be applicable to a variety of practical problems, such as blockchain platforms implementing sharding. Cob has the same Bernoulli-like distribution that upper-bounds the number of steps as the MBA protocol. We prove its correctness and security assuming a supermajority of honest nodes in the network, and compare its performance with Algorand.

Multidimensional Byzantine agreement in a synchronous setting

AbstractIn this paper we present the Multidimensional Byzantine Agreement (MBA) Protocol, a leaderless Byzantine agreement protocol defined for complete and synchronous networks that allows a network of nodes to reach consensus on a vector of relevant information regarding a set of observed events. The consensus process is carried out in parallel on each component, and the output is a vector whose components are either values with wide agreement in the network (even if no individual node agrees on every value) or a special value $$\bot $$ ⊥ that signals irreconcilable disagreement. The MBA Protocol is probabilistic and its execution halts with probability 1, and the number of steps necessary to halt follows a Bernoulli-like distribution. The design combines a Multidimensional Graded Consensus and a Multidimensional Binary Byzantine Agreement, the generalization to the multidimensional case of two protocols presented by Micali et al. (SIAM J Comput 26(4):873–933, 1997; Byzantine agreement, made trivial, 2016). We prove the correctness and security of the protocol assuming a synchronous network where less than a third of the nodes are malicious.

On the Round Complexity of Randomized Byzantine Agreement

We prove lower bounds on the round complexity of randomized Byzantine agreement (BA) protocols, bounding the halting probability of such protocols after one and two rounds. In particular, we prove that: 1. BA protocols resilient against n/3 [resp., n/4] corruptions terminate (under attack) at the end of the first round with probability at most o(1) [resp., $$1/2+ o(1)$$ ]. 2. BA protocols resilient against a fraction of corruptions greater than 1/4 terminate at the end of the second round with probability at most $$1-\Theta (1)$$ . 3. For a large class of protocols (including all BA protocols used in practice) and under a plausible combinatorial conjecture, BA protocols resilient against a fraction of corruptions greater than 1/3 [resp., 1/4] terminate at the end of the second round with probability at most o(1) [resp., $$1/2 + o(1)$$ ]. The above bounds hold even when the parties use a trusted setup phase, e.g., a public-key infrastructure (PKI). The third bound essentially matches the recent protocol of Micali (ITCS’17) that tolerates up to n/3 corruptions and terminates at the end of the third round with constant probability.

REDUCING OVERHEAD OF SELF-STABILIZING BYZANTINE AGREEMENT PROTOCOLS FOR BLOCKCHAIN USING HTTP/3 PROTOCOL: A PERSPECTIVE VIEW

Today, there is a tendency to reduce the dependence on local computation in favor of cloud computing. However, this inadvertently increases the reliance upon distributed fault-tolerant systems. In a condition that forced to work together, these systems often need to reach an agreement on some state or task, and possibly even in the presence of some misbehaving Byzantine nodes. Although non-trivial, Byzantine Agreement (BA) protocols now exist that are resilient to these types of faults. However, there is still a risk for inconsistencies in the application state in practice, even if a BA protocol is used. A single transient fault may put a node into an illegal state, creating a need for new self-stabilizing BA protocols to recover from illegal states. As self-stabilization often comes with a cost, primarily in the form of communication overhead, a potential lowering of latency - the cost of each message - could significantly impact how fast the protocol behaves overall. Thereby, there is a need for new network protocols such as QUIC, which, among other things, aims to reduce latency. In this paper, we survey current state-of-the-art agreement protocols. Based on previous work, some researchers try to implement pseudocode like QUIC protocol for Ethereum blockchain to have a secure network, resulting in slightly slower performance than the IP-based blockchain. We focus on consensus in the context of blockchain as it has prompted the development and usage of new open-source BA solutions that are related to proof of stake. We also discuss extensions to some of these protocols, specifically the possibility of achieving self-stabilization and the potential integration of the QUIC protocol, such as PoS and PBFT. Finally, further challenges faced in the field and how they might be overcome are discussed.

Optimal extension protocols for byzantine broadcast and agreement

The problems of Byzantine Broadcast (BB) and Byzantine Agreement (BA) are of interest to both the distributed computing and cryptography communities. Extension protocols for these primitives have been introduced to handle long messages efficiently at the cost of small number of single-bit broadcasts, referred to as seed broadcasts. While the communication optimality has remained the most sought-after property of an extension protocol in the literature, we prioritize both communication and round optimality in this work. In a setting with n parties and a static adversary controlling at most t parties in Byzantine fashion, we present BB and BA extension protocols with $$t<n$$ , $$t < n/2$$ and $$t<n/3$$ that are simultaneously optimal in terms of communication and round complexity. The best communication that an extension protocol can achieve in any setting is $$\mathcal {O}(\ell n)$$ bits for a message of length $$\ell $$ bits. The best achievable round complexity is $$\mathcal {O}(n)$$ for the setting $$t< n$$ and $$\mathcal {O}(1)$$ in the other two settings $$t < n/2$$ and $$t<n/3$$ . The existing constructions are either optimal only in terms of communication complexity, or require more rounds than our protocols, or achieve optimal round complexity at the cost of sub-optimal communication. Specifically, we construct communication-optimal protocols in the three corruption scenarios with the following round complexities: A concrete protocol from an extension protocol is obtained by replacing the seed broadcasts with a BB protocol for a single bit. Our extension protocols minimize the seed-round complexity and seed-communication complexity. The former refers to the number of rounds in an extension protocol in which seed broadcasts are invoked and impacts the round complexity of a concrete protocol due to a number of sequential calls to bit broadcast. The latter refers to the number of bits communicated through the seed broadcasts and impacts the round and communication complexity due to parallel instances of single-bit broadcast. In the settings of $$t<n/3$$ , $$t<n/2$$ and $$t<n$$ , our protocols improve the seed-round complexity from $$\mathcal {O}(\sqrt{\ell } + n^2)$$ to 1, from 3 to 2 and from $$\mathcal {O}(n^2)$$ to $$\mathcal {O}(n)$$ respectively. Our protocols keep the seed-communication complexity independent of the message length $$\ell $$ and, either improve or keep the complexity almost in the same order compared to the existing protocols.

The Design of Hierarchical Consensus Mechanism Based on Service-Zone Sharding

The byzantine agreement protocol has a disadvantage that there are many limitations on node scalability, because the performance degradation may occur due to a large amount of traffic. Hence, this classical byzantine agreement algorithm seems to be infeasible to achieve scale-out performance with the same level of security as a Bitcoin. In order to improve the performance degradation due to a large amount of traffic, we propose the hierarchical consensus mechanism based on service-zone sharding rather than how all nodes participate in the consensus process. In the proposed consensus mechanism (SZHBFT), a disjoint set of transactions is locally processed by a secure consensus subgroup or globally processed between consensus subgroups. Thus, the transactions that occur related to multiple Service-Zone Consensus Groups are updated and maintained in the Inter-Service Zone Public Ledger, whereas service transactions occurring locally are processed in parallel by each Service-Zone Consensus Group and then distributed into a local Service-Zone Private Ledger. The scheme of the proposed SZHBFT mechanism provides the hierarchical agreement solution along with distributed multiledger structure for the scalable byzantine resilient agreement by forming secure consensus subgroups in order to minimize the overhead of overall communication messages.

The Power of Shunning

The problem of Byzantine Agreement (BA) is of interest to both the distributed computing and cryptography communities. Following well-known results from distributed computing literature, the BA problem in the asynchronous network setting encounters inevitable non-termination issues. The impasse is overcome via randomization that allows construction of BA protocols in two flavors of termination guarantee—with overwhelming probability and with probability one. The latter type, termed as almost-surely terminating BA, is the main focus of this article. An eluding problem in the domain of almost-surely terminating BA is achieving a constant expected running time. Our primary contribution in this work makes significant progress in this direction. In a setting with n parties and an adversary with unbounded computing power controlling at most t parties in a Byzantine fashion, we present two almost-surely terminating BA protocols in the asynchronous setting: ○ With the optimal resilience of t &lt; n /3, our first protocol runs for an expected O ( n ) time. The existing protocols in the same setting either run for an expected O ( n 2 ) time (Abraham et al., PODC 2008) or require exponential computing power from the honest parties (Wang, CoRR 2015). In terms of communication complexity, our construction outperforms all the known constructions with t &lt; n /3 that offer almost-surely terminating feature. ○ With the resilience of t &lt; n /3 + ϵ for any ϵ &gt; 0, our second protocol runs for an expected O (1/ϵ) time. The expected running time of our protocol turns constant when ϵ is a constant fraction. The known constructions with a constant expected running time either require ϵ to be at least 1 (Feldman-Micali, STOC 1988 and Patra-Pandu Rangan, PODC 2010), implying t &lt; n /4, or call for exponential computing power from the parties (Wang, CoRR 2015). We follow the traditional route of building BA via common coin protocol that in turn reduces to Asynchronous Verifiable Secret-Sharing (AVSS). Our constructions are built on a variant of AVSS that is termed as shunning . A shunning AVSS fails to offer the properties of AVSS when the corrupt parties strike, but allows the honest parties to locally detect and shun a set of corrupt parties for any future communication. Our shunning AVSS with t &lt; n /3 and t &lt; n /3 + ϵ guarantee Ω( n ) and, respectively, Ω(ϵ t 2 ) conflicts to be revealed when failure occurs. Turning this shunning AVSS to a common coin protocol efficiently constitutes yet another contribution of this work. As a secondary contribution, we show the power of the shunning technique and present a highly efficient cryptographically secure shunning AVSS, which is used further to design an asynchronous BA protocol with the optimal resilience of t &lt; n /3 in the cryptographic setting. Our construct achieves an amortized expected communication complexity of O ( n 2 ) bits for reaching agreement on a single bit while consuming a constant expected running time. This property has been achieved for the first time in the cryptographic setting and that, too, with standard cryptographic assumptions. The best-known existing construction (Cachin et al., CCS 2002), while still needing more communication complexity than ours, is proven secure only in the Random-Oracle Model (ROM).

Fair Byzantine Agreements for Blockchains

Byzantine general problem is the core problem of the consensus algorithm, and many protocols are proposed recently to improve the decentralization level, the performance and the security of the blockchain. There are two challenging issues when the blockchain is operating in practice. First, the outcomes of the consensus algorithm are usually related to the incentive model, so whether each participant's value has an equal probability of being chosen becomes essential. However, the issues of fairness are not captured in the traditional security definition of Byzantine agreement. Second, the blockchain should be resistant to network failures, such as cloud services shut down or malicious attack, while remains the high performance most of the time. This paper has two main contributions. First, we propose a novel notion called fair validity for Byzantine agreement. Intuitively, fair validity lower-bounds the expected numbers that honest nodes' values being decided if the protocol is executed many times. However, we also show that any Byzantine agreement could not achieve fair validity in an asynchronous network, so we focus on synchronous protocols. This leads to our second contribution: we propose a fair, responsive and partition-resilient Byzantine agreement protocol tolerating up to 1/3 corruptions. Fairness means that our protocol achieves fair validity. Responsiveness means that the termination time only depends on the actual network delay instead of depending on any pre-determined time bound. Partition-resilience means that the safety still holds even if the network is partitioned, and the termination will hold if the partition is resolved.

Quantum Byzantine Agreement with Tripartite Entangled States

We present a quantum protocol for resolving the detectable Byzantine agreement (BA) problem using tripartite Greenberger–Horne–Zeilinger(GHZ)-like states and homodyne measurements in the continuous variable (CV) scenario. The protocol considers the simplest (i.e., three-player) BA problem involving one broadcaster and two receivers who jointly participant in the distribution, test, and agreement phases. The GHZ-like states provide the quantum resources for implementing the primitive of BA and satisfy a priori entanglement bound. Analyses demonstrate that the proposed quantum solution adheres to the agreement, validity, and termination criteria. Conveniently, the beam splitter strategy along with photon detection offers a method for comparing quantum messages. The paper shows that a potential high-efficiency CV-based BA protocol can be achieved using standard off-the-shelf components in quantum optics, maintaining the desirable characteristics of CVs when compared with discrete-variable BA protocol.

Database and distributed computing fundamentals for scalable, fault-tolerant, and consistent maintenance of blockchains

Bitcoin is a successful and interesting example of a global scale peer-to-peer cryptocurrency that integrates many techniques and protocols from cryptography, distributed systems, and databases. The main underlying data structure is blockchain, a scalable fully replicated structure that is shared among all participants and guarantees a consistent view of all user transactions by all participants in the cryptocurrency system. In this tutorial, we discuss the basic protocols used in blockchain, and elaborate on its main advantages and limitations. To overcome these limitations, we provide the necessary distributed systems background in managing large scale fully replicated ledgers, using Byzantine Agreement protocols to solve the consensus problem. Finally, we expound on some of the most recent proposals to design scalable and efficient blockchains. The focus of the tutorial is on the distributed systems and database technical aspects of the recent innovations in blockchains.

Multi-Cloud Data Management using Shamir's Secret Sharing and Quantum Byzantine Agreement Schemes

Cloud computing is a phenomenal distributed computing paradigm that provides flexible, low-cost on-demand data management to businesses. However, this so-called outsourcing of computing resources causes business data security and privacy concerns. Although various methods have been proposed to deal with these concerns, none of these relates to multi-clouds. This paper presents a practical data management model in a public and private multi-cloud environment. The proposed model BFT-MCDB incorporates Shamir's Secret Sharing approach and Quantum Byzantine Agreement protocol to improve trustworthiness and security of business data storage, without compromising performance. The performance evaluation is carried out using a cloud computing simulator called CloudSim. The experimental results show significantly better performance in terms of data storage and data retrieval compared to other common cloud cryptographic based models. The performance evaluation based on CloudSim experiments demonstrates the feasibility of the proposed multi-cloud data management model.

The optimal generalized Byzantine Agreement in Cluster-based Wireless Sensor Networks

A Wireless Sensor Network (WSN) is a wireless network consisting of spatially distributed autonomous devices using sensor nodes in a wide range of applications in various domains. In the future, WSNs are expected to be integrated into the “Internet of Things” (IoT), where sensor nodes join the Internet dynamically, and use them to collaborate and accomplish their tasks. Because of the communications of WSN will produce a broadcast storm, the Cluster-based Wireless Sensor Network (CWSN) was proposed to ameliorate the broadcast storm. However, the capability of the fault-tolerance and reliability of CWSNs must be carefully investigated and analyzed. To cope with the influence of faulty components, reaching a common agreement in the presence of faults before performing certain tasks is essential. Byzantine Agreement (BA) problem is a fundamental problem in fault-tolerant distributed systems. To enhance fault-tolerance and reliability of CWSN, the BA problem in CWSN is revisited in this paper. In this paper, a new BA protocol is proposed that adapts to the CWSN and derives its limit of allowable faulty components, while maintaining the minimum number of message exchanges.

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.