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Errorfree multivalued broadcast and Byzantine agreement with optimal communication complexity
 In Proceedings of the 15th international conference on Principles of Distributed Systems, OPODIS ’11
, 2011
"... In this paper we present first ever errorfree, asynchronous broadcast (called as Acast) and Byzantine Agreement (called as ABA) protocols with optimal communication complexity and fault tolerance. Our protocols are multivalued, meaning that they deal with ℓ bit input and achieve communication com ..."
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In this paper we present first ever errorfree, asynchronous broadcast (called as Acast) and Byzantine Agreement (called as ABA) protocols with optimal communication complexity and fault tolerance. Our protocols are multivalued, meaning that they deal with ℓ bit input and achieve communication complexity of
Broadcast Amplification
"... Abstract. A dbroadcast primitive is a communication primitive that allows a sender to send a value from a domain of size d to a set of parties. A broadcast protocol emulates the dbroadcast primitive using only pointtopoint channels, even if some of the parties cheat, in the sense that all correc ..."
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Abstract. A dbroadcast primitive is a communication primitive that allows a sender to send a value from a domain of size d to a set of parties. A broadcast protocol emulates the dbroadcast primitive using only pointtopoint channels, even if some of the parties cheat, in the sense that all correct recipients agree on the same value v (consistency), and if the sender is correct, then v is the value sent by the sender (validity). A celebrated result by Pease, Shostak and Lamport states that such a broadcast protocol exists if and only if t < n/3, where n denotes the total number of parties and t denotes the upper bound on the number of cheaters. This paper is concerned with broadcast protocols for any number of cheaters (t < n), which can be possible only if, in addition to pointtopoint channels, another primitive is available. Broadcast amplification is the problem of achieving dbroadcast when d ′broadcast can be used once, for d ′ < d. Let φn(d) denote the minimal such d ′ for domain size d. We show that for n = 3 parties, broadcast for any domain size is possible if only a single 3broadcast is available, and broadcast of a single bit (d ′ = 2) is not sufficient, i.e., φ3(d) = 3 for any d ≥ 3. In contrast, for n> 3 no broadcast amplification is possible, i.e., φn(d) = d for any d. However, if other parties than the sender can also broadcast some short messages, then broadcast amplification is possible for any n. Let φ ∗ n(d) denote the minimal d ′ such that dbroadcast can be constructed from primitives d ′ 1broadcast,..., d ′ kbroadcast, where d ′ = ∏ i d ′ i (i.e., log d ′ ∑ i log d ′ i). Note that φ ∗ n(d) ≤ φn(d). We show that broadcasting 8n log n bits in total suffices, independently of d, and that at least n−2 parties, including the sender, must broadcast at least one bit. Hence min(log d, n − 2) ≤ log φ ∗ n(d) ≤ 8n log n.
MultiValued Byzantine Broadcast: the t < n Case
"... All known protocols implementing broadcast from synchronous pointtopoint channels tolerating any t < n Byzantine corruptions have communication complexity at least Ω(ℓn 2). We give cryptographically secure and informationtheoretically secure protocols for t < n that communicate O(ℓn) bits i ..."
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All known protocols implementing broadcast from synchronous pointtopoint channels tolerating any t < n Byzantine corruptions have communication complexity at least Ω(ℓn 2). We give cryptographically secure and informationtheoretically secure protocols for t < n that communicate O(ℓn) bits in order to broadcast sufficiently long ℓ bit messages. This matches the optimal communication complexity bound for any protocol allowing to broadcast ℓ bit messages. While broadcast protocols with the optimal communication complexity exist in cases where t < n/3 (by Liang and Vaidya in PODC ’11) or t < n/2 (by Fitzi and Hirt in PODC ’06), this paper is the first to present such protocols for t < n.
Asynchronous Byzantine Systems: From Multivalued to Binary Consensus with t < n/3, O(n2) Messages, O(1) Time, and no Signature
, 2015
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
AlltoAll Gradecast using Coding with Byzantine Failures
"... Abstract. This paper presents a method that uses forward error correction codes to minimize the message bit complexity when acquiring consistent global information in the presence of faulty processes. We show a modification to the gradecast algorithm that implements our method. Gradecast, first pr ..."
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Abstract. This paper presents a method that uses forward error correction codes to minimize the message bit complexity when acquiring consistent global information in the presence of faulty processes. We show a modification to the gradecast algorithm that implements our method. Gradecast, first proposed by Feldman and Micali, is a broadcast algorithm for distributed systems that can handle Byzantine failures. It can be used as a basic building block to solve many important problems in distributed computing in the presence of Byzantine failures, such as agreement, clock synchronization, and approximate agreement. Many of these problems require a step where all processes need to send information to all other processes. We refer to the version of gradecast where all processes broadcast to all other processes as alltoall gradecast. In a distributed system with n processes, using n instances of the original gradecast algorithm to perform alltoall gradecast has a message bit complexity of O(mn3), where m is the length of the message. In this paper, we present an alltoall gradecast algorithm that takes O(mtn2) message bits, where t is the maximum number of faulty processes. This is a significant reduction in message bit complexity in real systems where t << n. Our alltoall gradecast algorithm uses coding theory to mask Byzantine failures and has wide applicability in distributed systems. For example, by replacing the original gradecast in the byzantine agreement algorithm proposed by BenOr, Dolev and Hoch with O(mtn3) message bit complexity, we get a new byzantine agreement algorithm with O(mt2n2) message bit complexity. Also, this algorithm can be used with their approximate agreement algorithm to get O(kn2t) instead of O(kn3) message bit complexity. 1
MultiValued Byzantine Broadcast: the t < n Case Anonymous submission
"... Abstract. Byzantine broadcast is a distributed primitive that allows a specific party to consistently distribute a message among n parties in the presence of potential misbehavior of up to t of the parties. All known protocols implementing broadcast of an ℓbit message from pointtopoint channels t ..."
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Abstract. Byzantine broadcast is a distributed primitive that allows a specific party to consistently distribute a message among n parties in the presence of potential misbehavior of up to t of the parties. All known protocols implementing broadcast of an ℓbit message from pointtopoint channels tolerating any t < n Byzantine corruptions have communication complexity at least Ω(ℓn 2). In this paper we give cryptographically secure and informationtheoretically secure protocols for t < n that communicate O(ℓn) bits when ℓ is sufficiently large. This matches the optimal communication complexity bound for any protocol allowing to broadcast ℓbit messages. While broadcast protocols with the optimal communication complexity exist for t < n/2, this paper is the first to present such protocols for t < n.