Byzantine Paxos

Byzantine failures: “malicious” participants

  • including crashes/slowness
  • hacked/compromised servers
  • other rare failures: disk/memory/network corruption

How many good servers needed to tolerate f byz-failures?

  • Apparently greater than f+1, i.e., has to cover normal consensus
  • f+1 is not enough
    • divide the system into 3 groups
      • f byz servers
      • f good servers
      • 1 good server
    • counter-example
      • f good servers offline
      • f byz servers and 1 good server come to a decision v-1
      • 1 good server offline, f good server online.
      • f byz servers act like never deciding anything
      • f good servers and f byz servers will decide a different value v-2
  • f+x is not enough for any x <= f
  • so we at least need 2f+1 good servers to tolerate f byz servers; that is 3f+1 in total

Starting point

  • in Paxos we have our quorum as majority, which is f+1 out of 2f+1 servers.
  • now we have f possible liars in each message round.
  • can we enlarge the quorum size by f to outvote the byz-servers?
    • f+1 -> 2f+1, in prepare and accept


  • good: S1, S2, S3, byz: S4
  • S1 prepares all with ballot 1
  • S1 accepts S1, S3, S4 with (1, v1), considers this value chosen.
  • S1 stands down
  • S2 tries to prepare S2,S3,S4
  • S3 replies (1, v1), S4 replies (1, v2)
  • S2 is stuck!

Prevent lies at non-proposers

  • assume proposers don’t lie for now
  • lies in phase1b (ack to prepare), should->lie
    • type 1: okay -> reject
    • type 2: okay (b1, v1) -> okay (no-value)
    • type 3: okay (b1, v1) -> okay (bx, vx)
      • let the phase1b message include the previous phase2a as proof
    • type 4: reject -> okay (no-value)
    • type 5: reject -> okay (bx, vx)
  • lies in phase 2b, does it hurt?
    • type 1: okay -> reject
    • type 2: reject -> okay

Prevent lies at proposers

  • lies in phase1a, does it hurt?
    • no, only a number.
  • lies in phase2a, a single type: (b1, v1)->(bx, vx)
    • let phase2a include previous phase1b responses as proof.
    • or, add another phase phase1c to send these proof before phase2a
  • what about commit messages?
    • include phase2b?
    • add another phase phase2av to broadcast accepted values.