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Ethereum 2.0 Phase 1 -- Shard Transition and Fraud Proofs

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

TODO

Introduction

This document describes the shard transition function and fraud proofs as part of Phase 1 of Ethereum 2.0.

Fraud proofs

TODO. The intent is to have a single universal fraud proof type, which contains the following parts:

An on-time attestation on some shard signing a ShardTransition
An index i of a particular position to focus on
The ShardTransition itself
The full body of the block
A Merkle proof to the shard_states in the parent block the attestation is referencing

The proof verifies that one of the two conditions is false:

custody_bits[i][j] != generate_custody_bit(subkey, block_contents) for any j
execute_state_transition(shard, slot, transition.shard_states[i-1].data, hash_tree_root(parent), get_shard_proposer_index(state, shard, slot), block_contents) != transition.shard_states[i].data (if i=0 then instead use parent.shard_states[shard][-1].data)

Shard state transition function

def shard_state_transition(shard: Shard,
                           slot: Slot,
                           pre_state: Hash,
                           previous_beacon_root: Hash,
                           proposer_pubkey: BLSPubkey,
                           block_data: BytesN[MAX_SHARD_BLOCK_CHUNKS * SHARD_BLOCK_CHUNK_SIZE]) -> Hash:
    # We will add something more substantive in phase 2
    return hash(pre_state + hash_tree_root(previous_beacon_root) + hash_tree_root(block_data))

Honest committee member behavior

Suppose you are a committee member on shard shard at slot current_slot. Let state be the head beacon state you are building on, and let QUARTER_PERIOD = SECONDS_PER_SLOT // 4. 2 * QUARTER_PERIOD seconds into slot slot, run the following procedure:

Initialize proposals = [], shard_states = [], shard_state = state.shard_states[shard][-1], start_slot = shard_state.slot.
For slot in get_offset_slots(state, start_slot), do the following:
- Look for all valid proposals for slot; that is, a Bytes proposal where shard_state_transition(shard, slot, shard_state, get_block_root_at_slot(state, state.slot - 1), get_shard_proposer_index(state, shard, slot), proposal) returns a result and does not throw an exception. Let choices be the set of non-empty valid proposals you discover.
- If len(choices) == 0, do proposals.append(make_empty_proposal(shard_state, slot))
- If len(choices) == 1, do proposals.append(choices[0])
- If len(choices) > 1, let winning_proposal be the proposal with the largest number of total attestations from slots in state.shard_next_slots[shard]....slot-1 supporting it or any of its descendants, breaking ties by choosing the first proposal locally seen. Do proposals.append(winning_proposal).
- If proposals[-1] is NOT an empty proposal, set shard_state = shard_state_transition(shard, slot, shard_state, get_block_root_at_slot(state, state.slot - 1), get_shard_proposer_index(state, shard, slot), proposals[-1]) and do shard_states.append(shard_state). If it is an empty proposal, leave shard_state unchanged.

Make an attestation using shard_data_roots = [hash_tree_root(proposal) for proposal in proposals] and shard_state_roots = shard_states.

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