RLMD-GHOST

RLMD-GHOST is a synchronous consensus protocol designed to support dynamic participation while allowing for bounded tolerance of temporary asynchrony. It builds upon the techniques of the Goldfish protocol, while modifying the strict 1-slot vote expiry to provide greater safety and flexibility in asynchronous environments.

RLMD-GHOST operates in slots of length 3Δ, where Δ is an upper bound on network delay. This ensures synchronous operation during periods of synchrony. The protocol involves n validators, with no use of committees. The absence of committees is necessary to prevent ex-ante reorgs that could occur if votes were allowed to accumulate from multiple committees over time.

Vote Expiry Parameter η

The key innovation of RLMD-GHOST is the introduction of a vote expiry period parameter η. Only the votes from the most recent η slots are considered valid and utilized by the fork choice function. In contrast, Goldfish employs a strict 1-slot vote expiry window. Similarly, when $\eta$ = $\infty$, the protocol is similar to the traditional implementation of LMD-GHOST, which is subject to long-range attacks.

Setting η > 1 provides tolerance for temporary asynchrony. Votes remain valid for multiple slots, so if a period of asynchrony disrupts the network for up to η-1 slots, the protocol can recover using the votes cast before the asynchrony began. This comes at the cost of weakening dynamic participation assumptions, as stale votes from offline validators could potentially sway the fork choice.

Generalized Sleepy Model

The generalized sleepy model expands the formalization of the standard sleepy model that RLMD-GHOST operates under. It introduces a parameter τ that acts as a "sleepiness" coefficient.

A consensus protocol is said to be τ-dynamically available if it satisfies safety and liveness under the τ-sleepy model. This is a model where the set of honest validators active in slots t-τ to t-1 need to exceed adversarial validators in slot t.

As τ grows larger, it becomes harder to satisfy τ-dynamic availability. The standard sleepy model is equivalent to 1-dynamic availability.

RLMD-GHOST is η-dynamically available under the generalized sleepy model, for any η ≤ τ. This model is important because of the η-slot vote expiry.

Valid votes can remain valid for validators that are now offline. So to preserve safety, we need sufficient honest validators from η slots ago to overpower any current adversaries combined with validators that became inactive since their votes were cast.

The generalized sleepy model captures this notion, which expands the standard model to account for vote expiry over multiple slots.

Phases

Similar to Goldfish, RLMD-GHOST operates in cycles of Propose, Vote, and Merge phases. RLMD-GHOST's authors calls the family of protocols with these phases propose-vote-merge protocols.

Propose Phase:

• At the beginning of each slot, the proposer selected by the verifiable random function (VRF) merges its view with its buffer and empties the buffer.
• The proposer runs the fork choice function, utilizing only the latest η slots' votes, to determine the head of its local canonical chain.
• The proposer extends the chain with a new block and updates its chain.
• Finally, the proposer broadcasts its entire view along with the newly proposed block.