IC consensus layer

The job consensus layer of the IC is to order transaction requests so that all replicas in a subnet will process transaction requests in the same order. There are many protocols in the literature for this problem. The IC uses a new consensus protocol, which is described here at a high level. For more details, see the paper https://eprint.iacr.org/2021/1330 (in particular, Protocol ICC1 in that paper).

Any secure consensus protocol should guarantee two properties, which (roughly stated) are:

safety: all replicas in fact agree on the same ordering of transaction requests, and
liveness: all replicas should make steady progress,

The paper https://eprint.iacr.org/2021/1330 proves that the IC consensus protocol satisfies both of these properties

The IC consensus protocol is design to be

extremely simple, and
robust (performance degrades gracefully when some replicas are malicious).

As discussed in the introduction, we assume

a subnet of $n$ replicas, and
at most $f < n / 3$ of the replicas are faulty.

Faulty replicas may exhibit arbitrary, malicious (i.e., Byzantine) behavior. To simplify the presentation, we assume here that $n = 3 f + 1$ .

We assume that communication is asynchronous, with no a priori bound on the delay of messages sent between replicas. In fact, the scheduling of message delivery may be completely under adversarial control. The IC consensus protocol guarantees safety under this very weak communication assumption. However, to guarantee liveness, we need to assume a form of partial synchrony, which (roughly stated) says that the network will be timely periodically. Somewhat more precisely, there exists a bound $Δ$ such that periodically all undelivered messages will be delivered within time $Δ$ . The bound $Δ$ does not have to be known in advance (the protocol can adapt itself to an unknown $Δ$ value). Regardless of whether we are assuming an asynchronous or partially synchronous network, we assume that every message sent from one honest party to another will eventually be delivered.

Like a number of consensus protocols, the IC consensus protocol is based in a blockchain. As the protocol progresses, a tree of blocks is grown, starting from a special genesis block that is the root of the tree. Each non-genesis block in the tree contains (among other things) a payload, consisting of a sequence of transaction requests, and a hash of the block's parent in the tree. The honest replicas have a consistent view of this tree: while each replica may have a different, partial view of this tree, all the replicas have a view of the same tree. In addition, as the protocol progresses, there is always a path of finalized blocks in this tree. Again, the honest replicas have a consistent view of this path: while each replica may have a different, partial view of this path, all the parties have a view of the same path. The transaction requests in the payloads of the blocks along this path are the ordered transaction requests will be processed by the execution layer of the Internet Computer.

The protocol proceeds in rounds. In round $h$ of the protocol, one or more blocks of height $h$ are added to the tree. That is, the blocks added in round $h$ are always at a distance of exactly $h$ from the root. In each round, a pseudo-random process is used to assign each replica a unique rank, which is an integer in the range $0, \dots,$ . This is pseudo-random process is implemented using a random beacon (see below). The party of lowest rank is the leader of that round. When the leader is honest and the network is timely, the leader will propose a block, which will be added to the tree; moreover, this will be the only block added to the tree and it will extend the finalized path. If the leader is not honest or the network is not timely, some other parties of higher rank may also propose blocks, and also have their blocks added to the tree. In any case, the logic of the protocol gives highest priority to the leader's proposed block.

The message complexity per round of the IC consensus protocol is typically $O (n^{2})$ . The protocol also enjoys the property known as optimistic responsiveness, which means that so long as the leader is honest, the protocol will proceed at the pace of the actual network delay, rather than some upper bound on the network delay.

To implement the protocol, each replica is associated with a public key for the BLS signature scheme, and each replica also holds the corresponding secret signing key. The association of replicas to public keys is maintained by the network nervous system (NNS) of the Internet Computer. These BLS signatures will be used to authenticate messages, also called artifacts, sent by replicas. The protocol also uses the signature aggregation feature of BLS signatures, which allows many signatures on the same message to be aggregated into a compact multi-signature. FIXME: citation, discussion of rogue key attack mitigation.

Random beacon. In addition to BLS signatures and multi-signatures as discussed above, the protocol makes use of a BLS threshold signature scheme to implement the above-mentioned random beacon. The random beacon for height $h$ is a $(f + 1)$ -threshold signature on a message unique to height $h$ . In each round of the protocol, each replica broadcasts its share of the beacon for the next round, so that when the next round begins, all replicas should have enough shares to reconstruct the beacon for that round. As discussed above, the random beacon at height $h$ is used to assign a pseudo-random rank to each replica that will be used in round $h$ of the protocol. Because of the security properties of the threshold signature, an adversary will not be able to predict the ranking of the replicas more than one round in advance, and these rankings will effectively be as good as random. To set up such a threshold signature scheme, the Internet Computer runs a distributed key generation (DKG) protocol. There are many DKG protocols in the literature. The Internet Computer implements a new non-interactive DKG (NiDKG) protocol.

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