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  • only a small fraction of nodes are Byzantine
  • Use votes to form quorums of supermajority to defend against Byzantine failures.

Basic Idea

  • Node Identity: Each node has private/public keys to sign messages
  • Everyone knows others' public key and can verify
  • Primary: the leader node that drives the consensus
  • Normal Case: Primary forwards requests to all nodes. Each node collecte 2f+1 votes from others and process requests.
  • Why 2f+1 quorum
    • 2f+1 quorums must have f+1 overlapping nodes
  • If only wait for majority >50%?

View Change

  • View change commit point: when 2f+1 replicas initiate view change
  • Handle malicious primary case
  • O(N2)O(N^2) messages in a view change.
  • Each view change message collects up to O(N)O(N) certificates
  • O(N3)O(N^3) data to transmit in total.

Normal Case

  • All to all messages in each round, O(N2)O(N^2) messages.

Comparison Between Consensus

Nakamoto Consensus

  • Tolerate up to 50% malicious
  • Permission-less
  • Strong against DDoS
  • Not partition tolerant
  • Slow ~10tx/s
  • Scale 10-100k full nodes


  • Tolerate 1/3 malicious nodes
  • Permissioned (not open for everyone to join network)
  • Partition tolerant
  • Weak against DDoS
  • Fast, thousands of tx/s
  • Not Scalable, dozens of nodes