# Minimal Light Client Design

**Notice**: This document is a work-in-progress for researchers and implementers.

## Table of contents

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- [Introduction](#introduction)
- [Custom types](#custom-types)
- [Constants](#constants)
- [Containers](#containers)
  - [`LightClientUpdate`](#lightclientupdate)
- [Helpers](#helpers)
  - [`LightClientMemory`](#lightclientmemory)
  - [`get_persistent_committee_pubkeys_and_balances`](#get_persistent_committee_pubkeys_and_balances)
- [Light client state updates](#light-client-state-updates)
- [Data overhead](#data-overhead)

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## Introduction

Ethereum 2.0 is designed to be light client friendly. This allows low-resource clients such as mobile phones to access Ethereum 2.0 with reasonable safety and liveness. It also facilitates the development of "bridges" to external blockchains. This document suggests a minimal light client design for the beacon chain.

## Custom types

We define the following Python custom types for type hinting and readability:

| Name | SSZ equivalent | Description |
| - | - | - |
| `CompactValidator` | `uint64` | compact representation of a validator for light clients |

## Constants

| Name | Value |
| - | - |
| `BEACON_CHAIN_ROOT_IN_SHARD_BLOCK_HEADER_DEPTH` | `4` |
| `BEACON_CHAIN_ROOT_IN_SHARD_BLOCK_HEADER_INDEX` | **TBD** |
| `PERIOD_COMMITTEE_ROOT_IN_BEACON_STATE_DEPTH` | `5` |
| `PERIOD_COMMITTEE_ROOT_IN_BEACON_STATE_INDEX` | **TBD** |

## Containers

### `LightClientUpdate`

```python
class LightClientUpdate(container):
    # Shard block root (and authenticating signature data)
    shard_block_root: Root
    fork_version: Version
    aggregation_bits: Bitlist[MAX_VALIDATORS_PER_COMMITTEE]
    signature: BLSSignature
    # Updated beacon header (and authenticating branch)
    header: BeaconBlockHeader
    header_branch: Vector[Bytes32, BEACON_CHAIN_ROOT_IN_SHARD_BLOCK_HEADER_DEPTH]
    # Updated period committee (and authenticating branch)
    committee: CompactCommittee
    committee_branch: Vector[Bytes32, PERIOD_COMMITTEE_ROOT_IN_BEACON_STATE_DEPTH + log_2(SHARD_COUNT)]
```

## Helpers

### `LightClientMemory`

```python
@dataclass
class LightClientMemory(object):
    shard: Shard  # Randomly initialized and retained forever
    header: BeaconBlockHeader  # Beacon header which is not expected to revert
    # period committees corresponding to the beacon header
    previous_committee: CompactCommittee
    current_committee: CompactCommittee
    next_committee: CompactCommittee
```

### `get_persistent_committee_pubkeys_and_balances`

```python
def get_persistent_committee_pubkeys_and_balances(memory: LightClientMemory,
                                                  epoch: Epoch) -> Tuple[Sequence[BLSPubkey], Sequence[uint64]]:
    """
    Return pubkeys and balances for the persistent committee at ``epoch``.
    """
    current_period = compute_epoch_at_slot(memory.header.slot) // EPOCHS_PER_SHARD_PERIOD
    next_period = epoch // EPOCHS_PER_SHARD_PERIOD
    assert next_period in (current_period, current_period + 1)
    if next_period == current_period:
        earlier_committee, later_committee = memory.previous_committee, memory.current_committee
    else:
        earlier_committee, later_committee = memory.current_committee, memory.next_committee

    pubkeys = []
    balances = []
    for pubkey, compact_validator in zip(earlier_committee.pubkeys, earlier_committee.compact_validators):
        index, slashed, balance = unpack_compact_validator(compact_validator)
        if epoch % EPOCHS_PER_SHARD_PERIOD < index % EPOCHS_PER_SHARD_PERIOD:
            pubkeys.append(pubkey)
            balances.append(balance)
    for pubkey, compact_validator in zip(later_committee.pubkeys, later_committee.compact_validators):
        index, slashed, balance = unpack_compact_validator(compact_validator)
        if epoch % EPOCHS_PER_SHARD_PERIOD >= index % EPOCHS_PER_SHARD_PERIOD:
            pubkeys.append(pubkey)
            balances.append(balance)
    return pubkeys, balances
```

## Light client state updates

The state of a light client is stored in a `memory` object of type `LightClientMemory`. To advance its state a light client requests an `update` object of type `LightClientUpdate` from the network by sending a request containing `(memory.shard, memory.header.slot, slot_range_end)` and calls `update_memory(memory, update)`.

```python
def update_memory(memory: LightClientMemory, update: LightClientUpdate) -> None:
    # Verify the update does not skip a period
    current_period = compute_epoch_at_slot(memory.header.slot) // EPOCHS_PER_SHARD_PERIOD
    next_epoch = compute_epoch_of_shard_slot(update.header.slot)
    next_period = next_epoch // EPOCHS_PER_SHARD_PERIOD
    assert next_period in (current_period, current_period + 1)  

    # Verify update header against shard block root and header branch
    assert is_valid_merkle_branch(
        leaf=hash_tree_root(update.header),
        branch=update.header_branch,
        depth=BEACON_CHAIN_ROOT_IN_SHARD_BLOCK_HEADER_DEPTH,
        index=BEACON_CHAIN_ROOT_IN_SHARD_BLOCK_HEADER_INDEX,
        root=update.shard_block_root,
    )

    # Verify persistent committee votes pass 2/3 threshold
    pubkeys, balances = get_persistent_committee_pubkeys_and_balances(memory, next_epoch)
    assert 3 * sum(filter(lambda i: update.aggregation_bits[i], balances)) > 2 * sum(balances)

    # Verify shard attestations
    pubkeys = filter(lambda i: update.aggregation_bits[i], pubkeys)
    domain = compute_domain(DOMAIN_SHARD_ATTESTER, update.fork_version)
    signing_root = compute_signing_root(update.shard_block_root, domain)
    assert bls.FastAggregateVerify(pubkeys, signing_root, update.signature)

    # Update period committees if entering a new period
    if next_period == current_period + 1:
        assert is_valid_merkle_branch(
            leaf=hash_tree_root(update.committee),
            branch=update.committee_branch,
            depth=PERIOD_COMMITTEE_ROOT_IN_BEACON_STATE_DEPTH + log_2(SHARD_COUNT),
            index=PERIOD_COMMITTEE_ROOT_IN_BEACON_STATE_INDEX << log_2(SHARD_COUNT) + memory.shard,
            root=hash_tree_root(update.header),
        )
        memory.previous_committee = memory.current_committee
        memory.current_committee = memory.next_committee
        memory.next_committee = update.committee

    # Update header
    memory.header = update.header
```

## Data overhead

Once every `EPOCHS_PER_SHARD_PERIOD` epochs (~27 hours) a light client downloads a `LightClientUpdate` object:

* `shard_block_root`: 32 bytes
* `fork_version`: 4 bytes
* `aggregation_bits`: 16 bytes
* `signature`: 96 bytes
* `header`: 8 + 32 + 32 + 32 + 96 = 200 bytes
* `header_branch`: 4 * 32 = 128 bytes
* `committee`: 128 * (48 + 8) = 7,168 bytes
* `committee_branch`: (5 + 10) * 32 = 480 bytes

The total overhead is 8,124 bytes, or ~0.083 bytes per second. The Bitcoin SPV equivalent is 80 bytes per ~560 seconds, or ~0.143 bytes per second. Various compression optimisations (similar to [these](https://github.com/RCasatta/compressedheaders)) are possible.

A light client can choose to update the header (without updating the committee) more frequently than once every `EPOCHS_PER_SHARD_PERIOD` epochs at a cost of 32 + 4 + 16 + 96 + 200 + 128 = 476 bytes per update.