Validator rotation in CBC Casper

How to realize validator rotation in CBC Casper is an open question.
In this post, I present a modification of CBC Casper for validator rotation.
The more formal version of this proposal is here.

Prerequisite

The latest CBC Casper paper with the draft of Section7 by Nate Rush (The compiled version is here.)
I reuse definitions and lemmas in the original paper.

Overview

• Replace weight in CBC parameters with weights \mathcal{W}, which is a set of all possible weight.
• Define a function to calculate a weight from a consensus value (block)
• E.g. Calculate a weight from the information (e.g. entry/exit transactions, slashing transactions, etc.) included in the chain until its parent block
\mathrm{Weight}: \mathcal{C} \rightarrow \mathcal{W}
• Modify the fork choice rule (estimator) to use \mathrm{Weight} so that the result is deterministic regardless of validator rotation.
• E.g. Modify LMD GHOST to score a block b by \mathrm{Weight}(b) in the â€śbest children selectionâ€ť.
• This is originally proposed in the previous draft of Casper TFG paper.
• Validators make a decision on a chain if all blocks in the chain are decided to win best children selection in GHOST at its height for any future states where there are t equivocations or less by \mathrm{Weight}(b).
• To detect this finality, we use clique oracle for the best children properties.
• Validators decide on a chain if there are cliques for any blocks in the chain.
• We weight a clique agreeing on a block b by \mathrm{Weight}(b).
• From these, the protocol has safety i.e. validators do not decide on conflicting blocks if there are t equivocations or less by \mathrm{Weight}(b) for any b they decided on.
• For liveness, we allow validators to exit by a bounded ratio every time a block is supported by a certain size of a clique (on-chain finalized).
• Any exited validatorâ€™s weight is set to 0. They can not create a valid message by his public key.
• For any block b, validators who have a non-zero weight in \mathrm{Weight}(b) can exit up to \alpha by weight.
• Hence the 1 - \alpha weight (by ratio) can contribute to the clique agreeing on the block
• For plausible liveness, fault tolerance is < (1 - 2\alpha)/3 (by ratio)
• An on-chain finalized block is defined as a block which is supported by a clique larger than or equal to (2 - \alpha)/3 (by ratio).
• This is the maximal threshold which does not break plausible liveness.
• Strictly speaking, we need to subtract 1 unit from this threshold.
• The blockchain can include an exit transaction if and only if it does not make the exiting weight exceed \alpha for the oldest non-on-chain-finalized block.
• Any validator can go offline when her exit transaction is included in a block and the block gets finalized subjectively by t such that t < (1 - 2\alpha)/3.

N.B. Proofs of these claims are WIP.

8 Likes

E.g. Modify LMD GHOST to score a block b by Weight(b) in the â€śbest children selectionâ€ť.

To be clear, this means that if a block b has children c_1 ... c_n, we use the weights in b to choose between c_1 ... c_n, and then if we choose c_i with children d_1 .... d_n we use the weights in c_i to choose one of them, and so on and so forth, correct?

For liveness, we allow validators to exit by a bounded ratio every time a block is supported by a certain size of a clique ( on-chain finalized ).

So this basically means â€śenshrine a specific finality oracle in-protocol and allow some bounded quantity of exits every time a finality event happensâ€ť, correct?

If we donâ€™t want to enshrine a specific finality oracle, what do you think of our current proposed approach of simply having a bounded exit rate of N per period, so the weak subjectivity bound (which is already a synchrony assumption) becomes a more explicit synchrony assumption?

To be clear, this means thatâ€¦

Yes!

So this basically means â€śenshrine a specific finality oracle in-protocol and allow some bounded quantity of exits every time a finality event happensâ€ť, correct?

Yes!

If we donâ€™t want to enshrine a specific finality oracle, what do you think of our current proposed approach of simply having a bounded exit rate of N per period, so the weak subjectivity bound (which is already a synchrony assumption) becomes a more explicit synchrony assumption?

I guess you mean the one in the proposal of CBCification of beacon chain?
Then, how are weights used in GHOST decided there?

The on-chain finalization in my proposal might incentivize forming a cartel of 1/3 weight by ratio to stop validator rotation, although the finality of a block is still subjective.

Then, how are weights used in GHOST decided there?

Exactly the way that you suggest: you choose between children of a block B by using the weights in the state of the block B.

The on-chain finalization in my proposal might incentivize forming a cartel of 1/3 weight by ratio to stop validator rotation, although the finality of a block is still subjective.

Right, this is what we are trying to prevent by making validator rotation be time-based only.

Exactly the way that you suggest: you choose between children of a block B by using the weights in the state of the block B.

Then, I think itâ€™s OK
Do you have any idea to recover if the protocol gets stuck? (inactivity leak?)

What I wanted to do here is to keep the fault tolerance as much as possible after some temporal liveness failure i.e. a situation in which small messages are generated to contribute to clique for blocks over a few epochs but a large number of validators (e.g. maximum allowed) exited. Adding in-protocol finality threshold (only for entry & exit) is a simple but dirty way for this.

Instead, I think we can have such an advantage by making the exit rate dynamic using some formula which depends on the progress of consensus.
How do you think?

It becomes very costly to execute this in each step of the fork choice. Some clever tricks mentioned here (â€śDynamic validator setsâ€ť, https://github.com/ethereum/eth2.0-specs/issues/433) can be used to increase fork choice efficiency!