# Some Observations on Eth2.0 Validators and Super-Full Node

Definitions:

• Eth2.0 Validators: The block producers (BPs) in Eth2.0 are validators that are randomly selected from a validator pool, and each validator is assigned to one shard. Given the initial number of shards M = 1024, we may require V > 100 validators in the network to achieve the desired security level (Security Level of Random Sampling With Sharding).
• Super-Full Node: A super-full node processes the ledgers of all shards, and may be able to produce a block in any shard (as long as the block satisfies the consensus of the shard such as PoW, PoS)

According to the definitions, my first observation is that
Observation 1: The network cost of Eth2.0 (in terms of BP nodes) is O(MV).

Meanwhile, for a super-full node, we have
Proposition 1: A super-full node is equivalent to a cluster of sub-nodes, with

• One-to-one correspondent: Each sub-node processes one shard data and each shard has one sub-node. Therefore, we could safely assume that the cost of a sub-node has the same order as a validator in Eth2.0.
• Trust Within the Cluster: Each sub-node trusts other nodes in the same cluster, and communicate the verified cross-shard messages within the cluster.
• Untrust Between the Clusters: Each sub-node does trust any sub-nodes in other clusters, i.e., other super-full nodes.
• Cost: The cost of a super-full node is O(M).

As a result, I have
Corollary 1: Assuming a sub-node in a super-full node cluster has the same order of the cost of an Eth2.0 validator, the network cost of Eth2.0 has the same order of V super-full nodes, i.e., O(MV).

In fact, from Corollary 1 and Proposition 1, I have
Observation 2: Eth2.0 with MV validators equals to V super-full nodes with all sub-nodes in an untrusted mode.

Now, I give my another observation.
Observation 3: Eth2.0 validator model respects equality, which means

• Each validator is expected to have the same order of cost as other validators (cost of the node and maybe others)
• All validators have the same right to produce a block in a shard (although when and which shard should be unpredictable)

Observation 4: While in reality, the node operator would be diversified in terms that

• Different node operators could have different levels of power to run nodes such as a super-full node, a partial-full node (a cluster with sub-nodes covering a subset of all shards), or a single shard node. E.g., pools, banks, large organzations, or a group of trusted blockchain fans may run a super-full node, while a student working on a blockchain class may run a single shard node for experiment.
• Different node operators may have different interest on different shards. E.g., a bank may manage the assets in some specific shards.
• Different node operators may require different security levels. A BP may just mine a specific shard by running a shard node, while a pool may run a full-node to provide pool service to all shards and make sure every block produced is correct.

In all, my major question is that could we optimize the following parameters for a blockchain network

• Trusted or Untrusted: It is possible to find a middle ground between the trust model of super-full nodes and untrust model of validators in Eth2.0?
• Equality and/or Diversity: Everybody could free to join the network and produce a block. However, depending on their power, interest, and security levels, different node operator could participate in the network in either super-full node, or partial full-node or a single shard node.

Taking M = 1024, and V = 100 as an example, a network offering the middle ground may like

• ~30 super-full node clusters are run by pools, banks, large organizations, groups of trusted blockchain fans, etc, and maintain the full ledgers of all shards.
• ~500 partial-full node clusters are run by smaller pools, organizations. A partial-full node cluster will process the ledgers of several shards of interest, and run as light clients of other shards (using SPV and/or data fraud and availability detection to process cross-shard message and increase security)
• ~10000 single-shard node in the network for solo miners or a developer that is interested in dapp in a shard). The cost of such node is expected to be 1.2x-1.5x cost as current Ethereum (with 0.2x~0.5x for processing cross-shard messages)

Note that the network is completely permissionless, and a node operator is free to run in any type of nodes/clusters.

1 Like

The current sharding system will probably naturally fall into this kind of pattern. The reason is that if you have 32k ETH, ie. 1024 validator slots, then you will have to process 1-\frac{1}{e} \approx 0.6322 of the entire network, at which point it soon makes sense to just run a super-full-node for convenience. So ultra-wealthy stakeholders will be running super-full nodes, and less wealthy stakeholders will be running individual nodes.

Thanks for the information. I think the calculation assumes all validators in the pool are assigned to one of the shard, but if some validators in the pool are not assigned, the result may be different.

So in the case that wealthy stakers is essentially a super-full node, what is the benefit of randomization of all validators rather than running a network with a mix of super-full nodes, partial-full nodes, and single-shard nodes, especially super-full nodes could provide high guarantee of the correctness of ledgers of all shards (and possible other attacks) rather than probability guarantee (and good random source).

I guess first of all we don’t want to assume a particular wealth distribution; we want a protocol that’s robust to different distributions of money and hardware. But also, what do we lose from super-full nodes being a layer-2 concept rather than being explicitly supported by the protocol? The super-full nodes would still be checking correctness of the entire ledger and refusing to build on top of blocks where it is not correct.

Note that the cost of a network can be even lower with the following assumptions:

• The number of shards can grow dynamically (e.g., starting from 10 and then grows to 100 or 1000 as more transactions are added)
• 10-20 super-full nodes (as DNS only has up to 13 root servers) together with other partial-full nodes and single-shard nodes are sufficient to provide data availability of the network.

In addition, compared to EOS (a big supporter of super-full node), which only allows 21 BPs, any node in the network is able to produce a block of a shard of interest.

I believe we already have some hints from Ethereum 1.0 mining statistics (or BTC). Current Ethereum 1.0 has 176.06Th/s, and consider just 1/1000 hashpower as a threshold to join a pool or mine solely by running a full node, the corresponding cost of mining will be (using 1070Ti with 30.5 Mh/s with about 500$in Amazon) • Equipment: 176.06 Th / 1000 / 30.5 Mh/s \approx 5772 graphics cards, which is about$2.8M (using other devices may be lower, so let us use $1M as a conservative number) • Electricity: Suppose the miners get 50% profit from Ethereum mining, then the electric cost of the 1/1000 miner will be 365 * 24 * 3600 / 1.35 (block time) * 2 (Eth per block) * 180 (Eth price) / 1000 =$0.84M

While running a super-full node in a cloud for 1024 shards should be on the order of \$0.1M per year.