The Forked History: Byzantine Witness and the 3-of-4 Quorum — Tested

Part 19 of the series titled The Forked History: Byzantine Witness and the 3-of-4 Quorum — Tested delves into the limitations of the Byzantine authority and the need for a witness set with specific properties. The main focus is on how a compromised authority can present forked views to different observers, making it impossible to determine the truth when one view is compromised.

The sealed floor introduced in Part 18 is not sufficient to establish a global history. A compromised authority can present different signed checkpoints to different jobs, each with locally valid signatures and inclusion proofs, without a single history existing. This highlights the need for a separate witness set that can detect and prevent such equivocations.

The witness gap is addressed in this part, highlighting the importance of a third property – witness agreement – that makes conflicting views externally detectable. This property, combined with the first two (signature trust and inclusion proofs), ensures that conflicting views are not privately accepted by isolated jobs.

The quorum arithmetic reveals that a 2-of-3 witness threshold is not enough to prevent forking. With up to one Byzantine witness (f=1), any two valid quorums must intersect in more than f members (q ≥ (n+f)/2). This means that a 3-of-4 threshold is required to ensure fork safety. The rule emphasizes that the threshold fraction alone is not enough to guarantee fork safety, and the explicit quorum intersection under the defined f is crucial.