Turn/Token Witness Scheduling Algorithm¶
The algorithm which determines the order of witnesses is referred to as the witness scheduling algorithm.
This was designed by a community bounty in thread https://bitsharestalk.org/index.php/topic,15547.0 however, Graphene has an additional requirement which is not taken into account by the solutions in the thread:
The membership and length of the list of witnesses may change over time.
So in this article I’ll describe my solution.
Turns and tokens¶
The solution is based on terms of turns and tokens.
Newly inserted witnesses start out with a turn and a token.
In order for a witness to be scheduled, it must have a turn and a token.
The scheduler maintains a FIFO of witnesses without tokens.
If no witness has a turn, then the scheduler gives a turn to all witnesses. This is called “emitting a turn.”
While less than half of the witnesses have tokens, give a token to the first witness in the FIFO and remove it from the FIFO.
Schedule a witness by picking randomly from all witnesses with both a turn and token.
When a witness is scheduled, it loses its turn and token.
The generic scheduler¶
The generic scheduler implements turns and tokens. It only depends on the C++11 stdlib and boost (not even using fc). Types provided by Graphene are template parameters.
The generic far future scheduler¶
The far future scheduler is implemented with the following rules:
Run until you emit a turn.
Record all witnesses produced.
Run until you emit a second turn.
The witnesses produced between the emission of the first turn (exclusive) and emission of the second turn (inclusive) are called the far future schedule.
Then the schedule for the rest of time is determined by repeating the future schedule indefinitely. The far future scheduler is required to give the scheduling algorithm bounded runtime and memory usage even in chains involving very long gaps.
Due to dynamic block interval, we must carefully keep in mind the difference between schedule slots and timestamps. A schedule slot number is a positive integer. A slot number of n represents the nth next block-interval-aligned timestamp after the head block.
Note that the mapping between slot numbers and timestamps will change if the block interval changes.
When each block is produced, the blockchain must determine whether the scheduler needs to be run. If fewer than num_witnesses are scheduled, the scheduler will run until 2*num_witnesses are scheduled. A block in which the scheduler runs is called a scheduling block.
Changes in the set of active witnesses do not modify the existing schedule. Rather, they will be incorporated into new schedule entries when the scheduler runs in the next scheduling block. Thus, a witness that has lost an election may still produce 1-2 blocks. Such a witness is called a lame duck.
Near vs. Far Schedule¶
From a particular chain state, it must be possible to specify a mapping from slots to witnesses, called the total witness schedule. The total witness schedule is partitioned into a prefix, called the near schedule; the remainder is the far schedule.
When a block occurs, n entries are drained (removed) from the head of the total schedule, where n is the slot number of the new block according to its parent block.
If the block is a scheduling block, the total schedule is further transformed. The new near schedule contains 2*num_witnesses entries, with the previous near schedule as a prefix. The rest of the near schedule is determined by the current blockchain RNG.
The new far schedule is determined by running the far future scheduler, as described above. The far future scheduler also obtains entropy from the current blockchain RNG.
As an optimization, the implementation does not run the far future scheduler until a far-future slot is actually queried. With this optimization, the only circumstance under which validating nodes must run the far future scheduler is when a block gap longer than num_witnesses occurs (an extremely rare condition).
Minimizing Impact of Selective Dropout¶
The ability of any single malicious witness to affect the results of the shuffle algorithm is limited because the RNG is based on bit commitment of the witnesses. However, a malicious witness is able to refuse to produce a block. A run of m consecutively scheduled malicious witnesses can independently make m independent choices of whether to refuse to produce a block. Basically they are able to control m bits of entropy in the shuffle algorithm’s output.
It is difficult-to-impossible to entirely eliminate “the last person being evil” problem in trustless distributed RNG’s. But we can at least mitigate this vector by rate-limiting changes to the total witness schedule to a very slow rate.
If every block schedules a witness, our adversary with m malicious witnesses gets m chances per round to selectively drop out in order to manipulate the shuffle order, allowing m attacks per round. If witnesses are only scheduled once per round, a selective dropout requires the malicious witness to produce the scheduling block, limiting the probability to m/n attacks per round.
(Vikram Rajkumar edited this page on Jun 10, 2015 · 1 revision )