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

Example

• 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.