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IEEE INFOCOM 2015 Workshop on Inter-Dependent Networks (WIDN) A New Direction for Solving the Consensus Problem in Networked Systems 1 Chien-Fu Cheng Department of Computer Science and Information Engineering, Tamkang University New Taipei City, Taiwan 2015/04/27 OUTLINE Introduction Agreement Problems Byzantine Agreement (BA) Problem Interactive Consistency (IC) Problem Consensus Problem Motivation Immediacy Harmonized Consensus Protocol (IHCP) Conclusion 2 OUTLINE Introduction Agreement Problems Byzantine Agreement (BA) Problem Interactive Consistency (IC) Problem Consensus Problem Motivation Immediacy Harmonized Consensus Protocol (IHCP) Conclusion 3 INTRODUCTION Distributed It is a collection of loosely coupled interconnected by a communication network. Reliable machines System In a cooperative network, we need a mechanism that allows all non-faulty processors to reach a common agreement. A common agreement should be reached among all nonfaulty processors before executing certain special missions. System Synchronization, resource allocation, replicated file system That is, we can provide fault tolerance by solving the agreement problems 4 OUTLINE Introduction Agreement Problems Byzantine Agreement (BA) Problem Interactive Consistency (IC) Problem Consensus Problem Motivation Immediacy Harmonized Consensus Protocol (IHCP) Conclusion 5 BYZANTINE AGREEMENT PROBLEM 1453 AD A city is surrounded by the Byzantine Generals, and their troops. The Generals must come to an agreement about whether to attack or retreat. An attack/retreat by only some of the divisions were result in defeat. Generals may be traitors, trying to prevent the loyal generals from reaching an agreement. 6 attack or retreat ?? traitors ?? attack / retreat 7 BYZANTINE AGREEMENT PROBLEM (CONT.) 1982 AD BA_Agreement: The situation above describes a classical coordination problem in distributed computing known as Byzantine agreement which was introduced by Lamport, Pease and Shostak. All non-faulty processors agree on a common value; BA_Validity: If the source (commander) processor is fault-free, then all non-faulty processors agree on the initial value that the source processor sends. link: Impossibility Results-1 link: Impossibility Results-2 link: Impossibility Results-3 8 BYZANTINE AGREEMENT PROBLEM (CONT.) Such an agreement may not take place for several reasons. The communication medium may be faulty Resulting in lost or garbled messages The processors themselves may be faulty Resulting in unpredictable processors behavior 9 IMPOSSIBILITY RESULTS Constraints: n≥4 n > 3pm , ( pm < n/3 ) attack or retreat ?? attack If n < 4 ? No solution exists for three generals that works in the presence of a single traitor attack he said retreat For BA_Validity to be satisfied, General 1 must obey the order to attack 10 IMPOSSIBILITY RESULTS (CONT.) If n ≤ 3pm ? Ex: n = 4, pm = 2 Constraints: n≥4 n > 3pm , ( pm < n/3 ) 0 1 1 011 100 0 1 0 1 0 1 1 101 0 For BA_Agreement to be satisfied, General 1 and General 2 should have the same decision. Worst case 11 IMPOSSIBILITY RESULTS (CONT.) Constraints: n≥4 n > 3pm , ( pm < n/3 ) 1 011 Ex: n = 4, pm = 1 0 1 110 1 1 0 1 0 1 1 101 1 Worst case 12 OUTLINE Introduction Agreement Problems Byzantine Agreement (BA) Problem Interactive Consistency (IC) Problem Consensus Problem Motivation Immediacy Harmonized Consensus Protocol (IHCP) Conclusion 13 INTERACTIVE CONSISTENCY PROBLEM The Interactive Consistency (IC) problem is another agreement-related problem. All the processors in the IC problem have an initialvalue. Through message exchange, they obtain a common vector (i.e. a set of common values) to ensure consistency. IC_Agreement: Each non-faulty processors agrees on a common vector Vec=[v1,v2,…,vn]; IC_Validity: If the i-th processor is non-faulty and its initial-value is vi, then the i-th value in the common vector Vec should be vi. 14 CONSENSUS PROBLEM Like the IC problem, the Consensus problem is characterized by all processors having an initialvalue. Consensus_Agreement: While the goal of the IC problem is to obtain a common vector, the goal of the consensus problem is to obtain a common value (i.e. consensus value). All non-faulty processors agree on a common value; Consensus_Validity: If the initial-value of each non-faulty processor is vi , then the common value v should be equal to vi. 15 THE RELATION AMONG BA, IC AND CONSENSUS PROBLEMS 16 OUTLINE Introduction Agreement Problems Byzantine Agreement (BA) Problem Interactive Consistency (IC) Problem Consensus Problem Motivation Immediacy Harmonized Consensus Protocol (IHCP) Conclusion 17 MOTIVATION In the classical BA, IC and Consensus protocols, non-faulty processors are not allowed to change their initial-values during message exchange. This implies if a processor proposes an initialvalue that is a minority value or even an unique value in the system, this value will not become the final consensus value. 18 MOTIVATION (CONT.) For example, the consensus protocol is usually used to solve the leader election problem. Protocol design for the leader election problem is used to elect a single processor as the organizer, coordinator, initiator or sequencer of some task distributed among several processors. Processors prefer to elect a closer processor containing computing resources they need to be the leader in mobile ad hoc networks. 19 MOTIVATION (CONT.) In order to increase the chances that all processors agree on a consensus value they prefer and accept, we design a new consensus protocol that allows change of the initial-value within certain limitations during message exchange. Simply put, processors can adjust their initialvalues based on messages they have collected during message exchange. This way, even if the final consensus value is not a value they have originally expected, it is still a value they prefer and accept. 20 OUTLINE Introduction Agreement Problems Byzantine Agreement (BA) Problem Interactive Consistency (IC) Problem Consensus Problem Motivation Immediacy Harmonized Consensus Protocol (IHCP) Conclusion 21 IMMEDIACY HARMONIZED CONSENSUS PROTOCOL (IHCP) The proposed protocol is called Immediacy Harmonized Consensus Protocol (IHCP). Tend_Inquiring Phase Msg_Exchanging Phase Cons_Making Phase 22 IMMEDIACY HARMONIZED CONSENSUS PROTOCOL (IHCP) (CONT.) IHCP Tend_Inquiring Phase (link) The Tend_Inquiring Phase is the phase where processors adjust their initial-values in the hope that the consensus value is a value they prefer and accept. Msg_Collecting Phase (link) The Msg_Exchanging Phase is a phase where processors collect messages from other processors. Cons_Making Phase (link) The Cons_Making Phase is used to compute the consensus value. 23 PROCEDURE OF REMOVING INFLUENCE : The messages under the influence from malicious faulty sender processor and malicious faulty intermediate processors : The messages under the influence from malicious faulty sender processor : The messages without influence from any faulty processors Round (t+1)# Round 1 1 # Round 1 1 * Round 2# 1 Round 2* 1 …… 2 2 Msg_Exchanging Phase Round (t+1)* 1 1 2 2 3 . . . . t+1 3 . . . . t+1 voteHCP function Cons_Making Phase 24 THE TEND_INQUIRING PHASE Each processor Pi will send the 1st priority value to other processors. After receiving the preferred values from other processors, each processor will reselect their initial-values. Through re-selection of initial-value, each processor will become more likely to agree on a consensus value that it prefers and also matches with the values preferred by other processors. 25 link: IHCP protocol THE MSG_EXCHANGING PHASE We use the term “round” to indicate a complete course of message exchange. A round of message exchange comprises three steps as follows: (1) send messages to any set of processors; (2) receive messages from other processors in this round; (3) do local processing. The number of rounds required of our protocol in the Msg_Exchanging Phase is t+1, where t= (n-1)/3. 26 link: IHCP protocol HCP-TREE In the Msg_Exchanging phase, each processor stores the received messages in its HCP-tree. The HCP-tree is a tree structure. The following figure shows a 2-level HCP-tree constructed by P1 with seven processors after two rounds of message exchange. 27 HCP-TREE (CONT.) In this HCP-tree, vertex P3P2 denotes that the message is sent from P3 to P2 and stored in P1’s HCP-tree. Moreover, we keep no vertices with repeated names in order to avoid the repeatedly influenced by the same Byzantine faulty processor. For example, vertex P3P3 is a vertex with repeated name. 28 link: IHCP protocol THE CONS_MAKING PHASE In the Cons_Making Phase, the voteHCP function is used to compute the consensus value at the root of the HCP-tree (from the leaves to the root). After t+1 rounds of message exchange, each nonfaulty processor can receive enough messages to remove the influence from Byzantine faulty processors by using the voteHCP function. 29 VOTEHCP FUNCTION The voteHCP function has three conditions: If the vertex α is a leaf, then there is only one value in the vertex α. So, the majority value is the value of vertex α (condition 1); Condition 2 is used to get the majority value; If the majority value is not existed, then output the default value , where V (condition3). 30 IHCP PROTOCOL 31 OUTLINE Introduction Agreement Problems Byzantine Agreement (BA) Problem Interactive Consistency (IC) Problem Consensus Problem Motivation Immediacy Harmonized Consensus Protocol (IHCP) Conclusion 32 CONCLUSION The classical consensus protocols do not allow non-faulty processors to change their initialvalues during message exchange. Under this limitation, non-faulty processors may agree on a consensus value they do not prefer. In this paper, the IHCP protocol is proposed to deal with this problem. The proposed IHCP protocol allows each nonfaulty processor to change its initial-value during message exchange for the purpose of making the consensus value match the preference of most processors. 33 Thank you for your listening! Email: [email protected] 34
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