296 lines
11 KiB
Markdown
296 lines
11 KiB
Markdown
# Ethereum 2.0 Phase 1 -- Shard Transition and Fraud Proofs
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**Notice**: This document is a work-in-progress for researchers and implementers.
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## Table of contents
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<!-- START doctoc generated TOC please keep comment here to allow auto update -->
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<!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->
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**Table of Contents** *generated with [DocToc](https://github.com/thlorenz/doctoc)*
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- [Introduction](#introduction)
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- [Helper functions](#helper-functions)
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- [Misc](#misc)
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- [Shard block verification functions](#shard-block-verification-functions)
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- [Shard state transition](#shard-state-transition)
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- [Fraud proofs](#fraud-proofs)
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- [Verifying the proof](#verifying-the-proof)
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- [Honest committee member behavior](#honest-committee-member-behavior)
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- [Helper functions](#helper-functions-1)
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- [Make attestations](#make-attestations)
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<!-- END doctoc generated TOC please keep comment here to allow auto update -->
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## Introduction
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This document describes the shard transition function and fraud proofs as part of Phase 1 of Ethereum 2.0.
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## Helper functions
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### Misc
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```python
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def compute_shard_transition_digest(beacon_state: BeaconState,
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shard_state: ShardState,
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beacon_parent_root: Root,
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shard_body_root: Root) -> Bytes32:
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# TODO: use SSZ hash tree root
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return hash(
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hash_tree_root(shard_state) + beacon_parent_root + shard_body_root
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)
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```
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### Shard block verification functions
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```python
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def verify_shard_block_message(beacon_state: BeaconState,
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shard_state: ShardState,
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block: ShardBlock,
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slot: Slot,
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shard: Shard) -> bool:
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assert block.shard_parent_root == shard_state.latest_block_root
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assert block.slot == slot
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assert block.proposer_index == get_shard_proposer_index(beacon_state, slot, shard)
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assert 0 < len(block.body) <= MAX_SHARD_BLOCK_SIZE
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return True
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```
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```python
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def verify_shard_block_signature(beacon_state: BeaconState,
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signed_block: SignedShardBlock) -> bool:
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proposer = beacon_state.validators[signed_block.message.proposer_index]
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domain = get_domain(beacon_state, DOMAIN_SHARD_PROPOSAL, compute_epoch_at_slot(signed_block.message.slot))
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signing_root = compute_signing_root(signed_block.message, domain)
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return bls.Verify(proposer.pubkey, signing_root, signed_block.signature)
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```
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## Shard state transition
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```python
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def shard_state_transition(beacon_state: BeaconState,
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shard_state: ShardState,
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block: ShardBlock) -> None:
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# Update shard state
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prev_gasprice = shard_state.gasprice
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if len(block.body) == 0:
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latest_block_root = shard_state.latest_block_root
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else:
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latest_block_root = hash_tree_root(block)
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shard_state.transition_digest = compute_shard_transition_digest(
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beacon_state,
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shard_state,
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block.beacon_parent_root,
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block.body,
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)
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shard_state.gasprice = compute_updated_gasprice(prev_gasprice, len(block.body))
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shard_state.slot = block.slot
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shard_state.latest_block_root = latest_block_root
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```
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We have a pure function `get_post_shard_state` for describing the fraud proof verification and honest validator behavior.
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```python
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def get_post_shard_state(beacon_state: BeaconState,
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shard_state: ShardState,
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block: ShardBlock) -> ShardState:
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"""
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A pure function that returns a new post ShardState instead of modifying the given `shard_state`.
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"""
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post_state = shard_state.copy()
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shard_state_transition(beacon_state, post_state, block)
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return post_state
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```
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## Fraud proofs
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### Verifying the proof
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TODO. The intent is to have a single universal fraud proof type, which contains the following parts:
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1. An on-time attestation `attestation` on some shard `shard` signing a `transition: ShardTransition`
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2. An index `offset_index` of a particular position to focus on
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3. The `transition: ShardTransition` itself
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4. The full body of the shard block `shard_block`
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5. A Merkle proof to the `shard_states` in the parent block the attestation is referencing
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6. The `subkey` to generate the custody bit
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Call the following function to verify the proof:
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```python
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def is_valid_fraud_proof(beacon_state: BeaconState,
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attestation: Attestation,
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offset_index: uint64,
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transition: ShardTransition,
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block: ShardBlock,
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subkey: BLSPubkey,
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beacon_parent_block: BeaconBlock) -> bool:
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# 1. Check if `custody_bits[offset_index][j] != generate_custody_bit(subkey, block_contents)` for any `j`.
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custody_bits = attestation.custody_bits_blocks
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for j in range(custody_bits[offset_index]):
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if custody_bits[offset_index][j] != generate_custody_bit(subkey, block):
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return True
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# 2. Check if the shard state transition result is wrong between
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# `transition.shard_states[offset_index - 1]` to `transition.shard_states[offset_index]`.
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if offset_index == 0:
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shard = get_shard(beacon_state, attestation)
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shard_state = beacon_parent_block.shard_transitions[shard].shard_states[-1]
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else:
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shard_state = transition.shard_states[offset_index - 1] # Not doing the actual state updates here.
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shard_state = get_post_shard_state(beacon_state, shard_state, block)
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if shard_state.transition_digest != transition.shard_states[offset_index].transition_digest:
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return True
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return False
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```
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```python
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def generate_custody_bit(subkey: BLSPubkey, block: ShardBlock) -> bool:
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# TODO
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...
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```
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## Honest committee member behavior
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### Helper functions
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```python
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def get_winning_proposal(beacon_state: BeaconState, proposals: Sequence[SignedShardBlock]) -> SignedShardBlock:
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# TODO: Let `winning_proposal` be the proposal with the largest number of total attestations from slots in
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# `state.shard_next_slots[shard]....slot-1` supporting it or any of its descendants, breaking ties by choosing
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# the first proposal locally seen. Do `proposals.append(winning_proposal)`.
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return proposals[-1] # stub
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```
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```python
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def compute_shard_body_roots(proposals: Sequence[SignedShardBlock]) -> Sequence[Root]:
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return [hash_tree_root(proposal.message.body) for proposal in proposals]
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```
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```python
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def get_proposal_choices_at_slot(beacon_state: BeaconState,
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shard_state: ShardState,
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slot: Slot,
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shard: Shard,
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shard_blocks: Sequence[SignedShardBlock],
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validate_signature: bool=True) -> Sequence[SignedShardBlock]:
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"""
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Return the valid shard blocks at the given ``slot``.
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Note that this function doesn't change the state.
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"""
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choices = []
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shard_blocks_at_slot = [block for block in shard_blocks if block.message.slot == slot]
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for block in shard_blocks_at_slot:
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try:
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# Verify block message and signature
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# TODO these validations should have been checked upon receiving shard blocks.
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assert verify_shard_block_message(beacon_state, shard_state, block.message, slot, shard)
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if validate_signature:
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assert verify_shard_block_signature(beacon_state, block)
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shard_state = get_post_shard_state(beacon_state, shard_state, block.message)
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except Exception:
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pass # TODO: throw error in the test helper
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else:
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choices.append(block)
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return choices
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```
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```python
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def get_proposal_at_slot(beacon_state: BeaconState,
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shard_state: ShardState,
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slot: Shard,
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shard: Shard,
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shard_blocks: Sequence[SignedShardBlock],
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validate_signature: bool=True) -> Tuple[SignedShardBlock, ShardState]:
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"""
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Return ``proposal``, ``shard_state`` of the given ``slot``.
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Note that this function doesn't change the state.
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"""
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choices = get_proposal_choices_at_slot(
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beacon_state=beacon_state,
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shard_state=shard_state,
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slot=slot,
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shard=shard,
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shard_blocks=shard_blocks,
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validate_signature=validate_signature,
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)
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if len(choices) == 0:
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block = ShardBlock(slot=slot)
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proposal = SignedShardBlock(message=block)
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elif len(choices) == 1:
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proposal = choices[0]
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else:
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proposal = get_winning_proposal(beacon_state, choices)
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# Apply state transition
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shard_state = get_post_shard_state(beacon_state, shard_state, proposal.message)
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return proposal, shard_state
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```
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```python
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def get_shard_state_transition_result(
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beacon_state: BeaconState,
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shard: Shard,
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shard_blocks: Sequence[SignedShardBlock],
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validate_signature: bool=True,
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) -> Tuple[Sequence[SignedShardBlock], Sequence[ShardState], Sequence[Root]]:
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proposals = []
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shard_states = []
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shard_state = beacon_state.shard_states[shard]
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for slot in get_offset_slots(beacon_state, shard):
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proposal, shard_state = get_proposal_at_slot(
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beacon_state=beacon_state,
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shard_state=shard_state,
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slot=slot,
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shard=shard,
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shard_blocks=shard_blocks,
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validate_signature=validate_signature,
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)
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shard_states.append(shard_state)
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proposals.append(proposal)
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shard_data_roots = compute_shard_body_roots(proposals)
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return proposals, shard_states, shard_data_roots
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```
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### Make attestations
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Suppose you are a committee member on shard `shard` at slot `current_slot` and you have received shard blocks `shard_blocks` since the latest successful crosslink for `shard` into the beacon chain. Let `beacon_state` be the head beacon state you are building on, and let `QUARTER_PERIOD = SECONDS_PER_SLOT // 4`. `2 * QUARTER_PERIOD` seconds into slot `current_slot`, run `get_shard_transition(beacon_state, shard, shard_blocks)` to get `shard_transition`.
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```python
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def get_shard_transition(beacon_state: BeaconState,
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shard: Shard,
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shard_blocks: Sequence[SignedShardBlock]) -> ShardTransition:
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offset_slots = get_offset_slots(beacon_state, shard)
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start_slot = offset_slots[0]
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proposals, shard_states, shard_data_roots = get_shard_state_transition_result(beacon_state, shard, shard_blocks)
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assert len(proposals) > 0
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assert len(shard_data_roots) > 0
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shard_block_lengths = []
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proposer_signatures = []
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for proposal in proposals:
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shard_block_lengths.append(len(proposal.message.body))
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if proposal.signature != NO_SIGNATURE:
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proposer_signatures.append(proposal.signature)
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if len(proposer_signatures) > 0:
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proposer_signature_aggregate = bls.Aggregate(proposer_signatures)
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else:
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proposer_signature_aggregate = NO_SIGNATURE
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return ShardTransition(
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start_slot=start_slot,
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shard_block_lengths=shard_block_lengths,
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shard_data_roots=shard_data_roots,
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shard_states=shard_states,
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proposer_signature_aggregate=proposer_signature_aggregate,
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)
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```
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