HotStuff-M Sample Clauses

HotStuff-M. HotStuff with Minority Corruption ≤ − Our first result improves HotStuff to tolerate a t ( 1 s)n corruption while still retaining its linear communication complexity per view. In particular, we show the following result:

HotStuff-M. Towards Minority Corruption The arguments for safety and liveness of HotStuff crucially rely on having fewer than one-third Byzantine faults. Otherwise, Byzantine parties could create multiple σkey, σlock, σcommit by partitioning the honest parties. Similarly, across views, Byzantine parties could send an incorrect (stale) σkey to the leader, as well as vote for a message in the promote phase without respecting the locking condition, leading to both safety and liveness concerns. Our goal is to increase the corruption threshold from one-third to a minority while still retaining the linear communication complexity. The trusted hardware provides a non-equivocation guarantee, i.e., it ensures that once a value v has been appended to a position in a specified log, no other value can be appended at that position in that log. Moreover, the hardware provides an attestation, i.e., verifiable proof of the existence of Phase validate(id, (v, σin)) validateNeighbor(id, (v, σin), (attlogId,j, attheads,j ), σj ) promote cond: ext-valid(v) = true, σin.val = σlock.val or view(σin) > view(σlock ) proof: σi := attlock (σin.val = σlock.val or view(σin) > view(σlock )), and lock log in attheads,j is at view(σlock ), and progress log in attheads,j is at e − 1, and attlogId,j is a valid attestation from HWj for value v in the promote log and sequence number e key cond: view(σin) = e and phase(σin) = promote proof: σi := ⊥ progress log in attheads,j is at e − 1, and key log in attheads,j is at e, and attlogId,j is a valid attestation from HWj for value v in the key log and sequence number e lock cond: view(σin) = e and phase(σin) = key proof: σi := ⊥ progress log in attheads,j is at e − 1, and lock log in attheads,j is at e, and attlogId,j is a valid attestation from HWj for value v in the lock log and sequence number e Table 1. Validation functions passed to provable broadcast in different phases of view e. We assume end attestations attlock (containing σlock) is invoked during validate() call as needed. Also note that (attlogId,i, attheads,i) are sent by every party to their neighbor as a part of provable broadcast and generated in the invocation of createAttestations(id, (v, σin)). Algorithm 4 HotStuff-M: HotStuff with Minority Corruption (for party pi). 1: for e := 1, 2, 3, . . . do 2: as a leader d new-view phase