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90
specs/core/0_beacon-chain.md
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@ -38,7 +38,6 @@ The primary source of load on the beacon chain are "attestations". Attestations
| `GWEI_PER_ETH` | 10**9 | Gwei/ETH | | `GWEI_PER_ETH` | 10**9 | Gwei/ETH |
| `DEPOSIT_CONTRACT_ADDRESS` | **TBD** | - | | `DEPOSIT_CONTRACT_ADDRESS` | **TBD** | - |
| `TARGET_COMMITTEE_SIZE` | 2**8 (= 256) | validators | | `TARGET_COMMITTEE_SIZE` | 2**8 (= 256) | validators |
| `GENESIS_TIME` | **TBD** | seconds |
| `SLOT_DURATION` | 6 | seconds | | `SLOT_DURATION` | 6 | seconds |
| `CYCLE_LENGTH` | 2**6 (= 64) | slots | ~6 minutes | | `CYCLE_LENGTH` | 2**6 (= 64) | slots | ~6 minutes |
| `MIN_VALIDATOR_SET_CHANGE_INTERVAL` | 2**8 (= 256) | slots | ~25 minutes | | `MIN_VALIDATOR_SET_CHANGE_INTERVAL` | 2**8 (= 256) | slots | ~25 minutes |
@ -92,6 +91,15 @@ The primary source of load on the beacon chain are "attestations". Attestations
| `ENTRY` | `0` | | `ENTRY` | `0` |
| `EXIT` | `1` | | `EXIT` | `1` |
**Domains for BLS signatures**
| Name | Value |
| - | :-: |
| `DOMAIN_DEPOSIT` | `0` |
| `DOMAIN_ATTESTATION` | `1` |
| `DOMAIN_PROPOSAL` | `2` |
| `DOMAIN_LOGOUT` | `3` |
### PoW chain registration contract ### PoW chain registration contract
The initial deployment phases of Ethereum 2.0 are implemented without consensus changes to the PoW chain. A registration contract is added to the PoW chain to deposit ETH. This contract has a `registration` function which takes as arguments `pubkey`, `withdrawal_credentials`, `randao_commitment` as defined in a `ValidatorRecord` below. A BLS `proof_of_possession` of types `bytes` is given as a final argument. The initial deployment phases of Ethereum 2.0 are implemented without consensus changes to the PoW chain. A registration contract is added to the PoW chain to deposit ETH. This contract has a `registration` function which takes as arguments `pubkey`, `withdrawal_credentials`, `randao_commitment` as defined in a `ValidatorRecord` below. A BLS `proof_of_possession` of types `bytes` is given as a final argument.
@ -121,7 +129,7 @@ A `BeaconBlock` has the following fields:
# Specials (e.g. logouts, penalties) # Specials (e.g. logouts, penalties)
'specials': [SpecialRecord], 'specials': [SpecialRecord],
# Proposer signature # Proposer signature
'proposer_signature': ['uint256'], 'proposer_signature': ['uint384'],
} }
``` ```
@ -148,7 +156,7 @@ An `AttestationRecord` has the following fields:
# Hash of last justified beacon block # Hash of last justified beacon block
'justified_block_hash': 'hash32', 'justified_block_hash': 'hash32',
# BLS aggregate signature # BLS aggregate signature
'aggregate_sig': ['uint256'] 'aggregate_sig': ['uint384']
} }
``` ```
@ -156,8 +164,6 @@ A `ProposalSignedData` has the following fields:
```python ```python
{ {
# Fork version
'fork_version': 'uint64',
# Slot number # Slot number
'slot': 'uint64', 'slot': 'uint64',
# Shard number (or `2**64 - 1` for beacon chain) # Shard number (or `2**64 - 1` for beacon chain)
@ -171,8 +177,6 @@ An `AttestationSignedData` has the following fields:
```python ```python
{ {
# Fork version
'fork_version': 'uint64',
# Slot number # Slot number
'slot': 'uint64', 'slot': 'uint64',
# Shard number # Shard number
@ -195,7 +199,7 @@ A `SpecialRecord` has the following fields:
```python ```python
{ {
# Kind # Kind
'kind': 'uint8', 'kind': 'uint64',
# Data # Data
'data': 'bytes' 'data': 'bytes'
} }
@ -258,7 +262,7 @@ A `ValidatorRecord` has the following fields:
```python ```python
{ {
# BLS public key # BLS public key
'pubkey': 'uint256', 'pubkey': 'uint384',
# Withdrawal credentials # Withdrawal credentials
'withdrawal_credentials': 'hash32', 'withdrawal_credentials': 'hash32',
# RANDAO commitment # RANDAO commitment
@ -268,7 +272,7 @@ A `ValidatorRecord` has the following fields:
# Balance in Gwei # Balance in Gwei
'balance': 'uint64', 'balance': 'uint64',
# Status code # Status code
'status': 'uint8', 'status': 'uint64',
# Slot when validator last changed status (or 0) # Slot when validator last changed status (or 0)
'last_status_change_slot': 'uint64' 'last_status_change_slot': 'uint64'
# Sequence number when validator exited (or 0) # Sequence number when validator exited (or 0)
@ -337,7 +341,7 @@ For a block on the beacon chain to be processed by a node, four conditions have
* The parent pointed to by the `ancestor_hashes[0]` has already been processed and accepted * The parent pointed to by the `ancestor_hashes[0]` has already been processed and accepted
* An attestation from the _proposer_ of the block (see later for definition) is included along with the block in the network message object * An attestation from the _proposer_ of the block (see later for definition) is included along with the block in the network message object
* The PoW chain block pointed to by the `processed_pow_receipt_root` has already been processed and accepted * The PoW chain block pointed to by the `processed_pow_receipt_root` has already been processed and accepted
* The node's local clock time is greater than or equal to the minimum timestamp as computed by `GENESIS_TIME + block.slot * SLOT_DURATION` * The node's local clock time is greater than or equal to the minimum timestamp as computed by `state.genesis_time + block.slot * SLOT_DURATION`
If these conditions are not met, the client should delay processing the beacon block until the conditions are all satisfied. If these conditions are not met, the client should delay processing the beacon block until the conditions are all satisfied.
@ -358,10 +362,13 @@ The beacon chain fork choice rule is a hybrid that combines justification and fi
```python ```python
def lmd_ghost(store, start): def lmd_ghost(store, start):
validators = start.state.validators validators = start.state.validators
active_validators = [validators[i] for i in get_active_validator_indices(validators, start.slot)] active_validators = [validators[i] for i in
attestation_targets = [get_latest_attestation_target(store, validator) for validator in active_validators] get_active_validator_indices(validators, start.slot)]
attestation_targets = [get_latest_attestation_target(store, validator)
for validator in active_validators]
def get_vote_count(block): def get_vote_count(block):
return len([target for target in attestation_targets if get_ancestor(store, target, block.slot) == block]) return len([target for target in attestation_targets if
get_ancestor(store, target, block.slot) == block])
head = start head = start
while 1: while 1:
@ -706,7 +713,7 @@ The `add_validator` routine is defined below.
This routine should be run for every validator that is inducted as part of a log created on the PoW chain [TODO: explain where to check for these logs]. The status of the validators added after genesis is `PENDING_ACTIVATION`. These logs should be processed in the order in which they are emitted by the PoW chain. This routine should be run for every validator that is inducted as part of a log created on the PoW chain [TODO: explain where to check for these logs]. The status of the validators added after genesis is `PENDING_ACTIVATION`. These logs should be processed in the order in which they are emitted by the PoW chain.
First, a helper function: First, some helper functions:
```python ```python
def min_empty_validator(validators: List[ValidatorRecord], current_slot: int): def min_empty_validator(validators: List[ValidatorRecord], current_slot: int):
@ -716,10 +723,18 @@ def min_empty_validator(validators: List[ValidatorRecord], current_slot: int):
return None return None
``` ```
```python
def get_fork_version(state: State, slot: int) -> int:
return state.pre_fork_version if slot < state.fork_slot_number else state.post_fork_version
def get_domain(state: State, slot: int, base_domain: int) -> int:
return get_fork_version(state, slot) * 2**32 + base_domain
```
Now, to add a validator: Now, to add a validator:
```python ```python
def add_validator(validators: List[ValidatorRecord], def add_validator(state: State,
pubkey: int, pubkey: int,
proof_of_possession: bytes, proof_of_possession: bytes,
withdrawal_credentials: Hash32, withdrawal_credentials: Hash32,
@ -731,9 +746,10 @@ def add_validator(validators: List[ValidatorRecord],
signed_message = bytes32(pubkey) + bytes2(withdrawal_shard) + withdrawal_credentials + randao_commitment signed_message = bytes32(pubkey) + bytes2(withdrawal_shard) + withdrawal_credentials + randao_commitment
assert BLSVerify(pub=pubkey, assert BLSVerify(pub=pubkey,
msg=hash(signed_message), msg=hash(signed_message),
sig=proof_of_possession) sig=proof_of_possession,
domain=get_domain(state, current_slot, DOMAIN_DEPOSIT))
# Pubkey uniqueness # Pubkey uniqueness
assert pubkey not in [v.pubkey for v in validators] assert pubkey not in [v.pubkey for v in state.validators]
rec = ValidatorRecord( rec = ValidatorRecord(
pubkey=pubkey, pubkey=pubkey,
withdrawal_credentials=withdrawal_credentials, withdrawal_credentials=withdrawal_credentials,
@ -744,15 +760,17 @@ def add_validator(validators: List[ValidatorRecord],
last_status_change_slot=current_slot, last_status_change_slot=current_slot,
exit_seq=0 exit_seq=0
) )
index = min_empty_validator(validators) index = min_empty_validator(state.validators)
if index is None: if index is None:
validators.append(rec) state.validators.append(rec)
return len(validators) - 1 return len(state.validators) - 1
else: else:
validators[index] = rec state.validators[index] = rec
return index return index
``` ```
`BLSVerify` is a function for verifying a BLS12-381 signature, defined in the BLS12-381 spec.
### Routine for removing a validator ### Routine for removing a validator
```python ```python
@ -814,18 +832,18 @@ Verify that there are at most `MAX_ATTESTATION_COUNT` `AttestationRecord` object
* Compute `parent_hashes` = `[get_block_hash(state, block, slot - CYCLE_LENGTH + i) for i in range(1, CYCLE_LENGTH - len(oblique_parent_hashes) + 1)] + oblique_parent_hashes` (eg, if `CYCLE_LENGTH = 4`, `slot = 5`, the actual block hashes starting from slot 0 are `Z A B C D E F G H I J`, and `oblique_parent_hashes = [D', E']` then `parent_hashes = [B, C, D' E']`). Note that when *creating* an attestation for a block, the hash of that block itself won't yet be in the `state`, so you would need to add it explicitly. * Compute `parent_hashes` = `[get_block_hash(state, block, slot - CYCLE_LENGTH + i) for i in range(1, CYCLE_LENGTH - len(oblique_parent_hashes) + 1)] + oblique_parent_hashes` (eg, if `CYCLE_LENGTH = 4`, `slot = 5`, the actual block hashes starting from slot 0 are `Z A B C D E F G H I J`, and `oblique_parent_hashes = [D', E']` then `parent_hashes = [B, C, D' E']`). Note that when *creating* an attestation for a block, the hash of that block itself won't yet be in the `state`, so you would need to add it explicitly.
* Let `attestation_indices` be `get_shards_and_committees_for_slot(state, slot)[x]`, choosing `x` so that `attestation_indices.shard` equals the `shard` value provided to find the set of validators that is creating this attestation record. * Let `attestation_indices` be `get_shards_and_committees_for_slot(state, slot)[x]`, choosing `x` so that `attestation_indices.shard` equals the `shard` value provided to find the set of validators that is creating this attestation record.
* Verify that `len(attester_bitfield) == ceil_div8(len(attestation_indices))`, where `ceil_div8 = (x + 7) // 8`. Verify that bits `len(attestation_indices)....` and higher, if present (i.e. `len(attestation_indices)` is not a multiple of 8), are all zero. * Verify that `len(attester_bitfield) == ceil_div8(len(attestation_indices))`, where `ceil_div8 = (x + 7) // 8`. Verify that bits `len(attestation_indices)....` and higher, if present (i.e. `len(attestation_indices)` is not a multiple of 8), are all zero.
* Derive a group public key by adding the public keys of all of the attesters in `attestation_indices` for whom the corresponding bit in `attester_bitfield` (the ith bit is `(attester_bitfield[i // 8] >> (7 - (i %8))) % 2`) equals 1. * Derive a `group_public_key` by adding the public keys of all of the attesters in `attestation_indices` for whom the corresponding bit in `attester_bitfield` (the ith bit is `(attester_bitfield[i // 8] >> (7 - (i % 8))) % 2`) equals 1.
* Let `fork_version = pre_fork_version if slot < fork_slot_number else post_fork_version`. * Let `data = AttestationSignedData(slot, shard, parent_hashes, shard_block_hash, last_crosslinked_hash, shard_block_combined_data_root, justified_slot)`.
* Verify that `aggregate_sig` verifies using the group pubkey generated and the serialized form of `AttestationSignedData(fork_version, slot, shard, parent_hashes, shard_block_hash, last_crosslinked_hash, shard_block_combined_data_root, justified_slot)` as the message. * Check `BLSVerify(pubkey=group_public_key, msg=data, sig=aggregate_sig, domain=get_domain(state, slot, DOMAIN_ATTESTATION))`.
* [TO BE REMOVED IN PHASE 1] Verify that `shard_block_hash == bytes([0] * 32)` * [TO BE REMOVED IN PHASE 1] Verify that `shard_block_hash == bytes([0] * 32)`.
Extend the list of `AttestationRecord` objects in the `state` with those included in the block, ordering the new additions in the same order as they came in the block. Extend the list of `AttestationRecord` objects in the `state` with those included in the block, ordering the new additions in the same order as they came in the block.
### Verify proposer signature ### Verify proposer signature
Let `proposal_hash = hash(ProposalSignedData(fork_version, block.slot, 2**64 - 1, block_hash_without_sig))` where `block_hash_without_sig` is the hash of the block except setting `proposer_signature` to `[0, 0]`. Let `proposal_hash = hash(ProposalSignedData(block.slot, 2**64 - 1, block_hash_without_sig))` where `block_hash_without_sig` is the hash of the block except setting `proposer_signature` to `[0, 0]`.
Verify that `BLSVerify(pubkey=get_beacon_proposer(state, block.slot).pubkey, data=proposal_hash, sig=block.proposer_signature)` passes. Verify that `BLSVerify(pubkey=get_beacon_proposer(state, block.slot).pubkey, data=proposal_hash, sig=block.proposer_signature, domain=get_domain(state, block.slot, DOMAIN_PROPOSAL))` passes.
### Verify and process RANDAO reveal ### Verify and process RANDAO reveal
@ -859,12 +877,12 @@ For each `SpecialRecord` `obj` in `block.specials`, verify that its `kind` is on
```python ```python
{ {
'validator_index': 'uint64', 'validator_index': 'uint64',
'signature': '[uint256]' 'signature': '[uint384]'
} }
``` ```
Perform the following checks: Perform the following checks:
* Let `fork_version = pre_fork_version if block.slot < fork_slot_number else post_fork_version`. Verify that `BLSVerify(pubkey=validators[data.validator_index].pubkey, msg=hash(LOGOUT_MESSAGE + bytes8(fork_version)), sig=data.signature)` * Verify that `BLSVerify(pubkey=validators[data.validator_index].pubkey, msg=bytes([0] * 32), sig=data.signature, domain=get_domain(state, current_slot, DOMAIN_LOGOUT))`
* Verify that `validators[validator_index].status == ACTIVE`. * Verify that `validators[validator_index].status == ACTIVE`.
* Verify that `block.slot >= last_status_change_slot + SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD` * Verify that `block.slot >= last_status_change_slot + SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD`
@ -876,16 +894,16 @@ Run `exit_validator(data.validator_index, state, block, penalize=False, current_
{ {
'vote1_aggregate_sig_indices': '[uint24]', 'vote1_aggregate_sig_indices': '[uint24]',
'vote1_data': AttestationSignedData, 'vote1_data': AttestationSignedData,
'vote1_aggregate_sig': '[uint256]', 'vote1_aggregate_sig': '[uint384]',
'vote2_aggregate_sig_indices': '[uint24]', 'vote2_aggregate_sig_indices': '[uint24]',
'vote2_data': AttestationSignedData, 'vote2_data': AttestationSignedData,
'vote2_aggregate_sig': '[uint256]', 'vote2_aggregate_sig': '[uint384]',
} }
``` ```
Perform the following checks: Perform the following checks:
* For each `aggregate_sig`, verify that `BLSVerify(pubkey=aggregate_pubkey([validators[i].pubkey for i in aggregate_sig_indices]), msg=vote_data, sig=aggsig)` passes. * For each `vote`, verify that `BLSVerify(pubkey=aggregate_pubkey([validators[i].pubkey for i in vote_aggregate_sig_indices]), msg=vote_data, sig=vote_aggregate_sig, domain=get_domain(state, vote_data.slot, DOMAIN_ATTESTATION))` passes.
* Verify that `vote1_data != vote2_data`. * Verify that `vote1_data != vote2_data`.
* Let `intersection = [x for x in vote1_aggregate_sig_indices if x in vote2_aggregate_sig_indices]`. Verify that `len(intersection) >= 1`. * Let `intersection = [x for x in vote1_aggregate_sig_indices if x in vote2_aggregate_sig_indices]`. Verify that `len(intersection) >= 1`.
* Verify that `vote1_data.justified_slot < vote2_data.justified_slot < vote2_data.slot <= vote1_data.slot`. * Verify that `vote1_data.justified_slot < vote2_data.justified_slot < vote2_data.slot <= vote1_data.slot`.
@ -898,12 +916,12 @@ For each validator index `v` in `intersection`, if `state.validators[v].status`
{ {
'proposer_index': 'uint24', 'proposer_index': 'uint24',
'proposal1_data': ProposalSignedData, 'proposal1_data': ProposalSignedData,
'proposal1_signature': '[uint256]', 'proposal1_signature': '[uint384]',
'proposal2_data': ProposalSignedData, 'proposal2_data': ProposalSignedData,
'proposal1_signature': '[uint256]', 'proposal1_signature': '[uint384]',
} }
``` ```
For each `proposal_signature`, verify that `BLSVerify(pubkey=validators[proposer_index].pubkey, msg=hash(proposal_data), sig=proposal_signature)` passes. Verify that `proposal1_data.slot == proposal2_data.slot` but `proposal1 != proposal2`. If `state.validators[proposer_index].status` does not equal `PENALIZED`, then run `exit_validator(proposer_index, state, penalize=True, current_slot=block.slot)` For each `proposal_signature`, verify that `BLSVerify(pubkey=validators[proposer_index].pubkey, msg=hash(proposal_data), sig=proposal_signature, domain=get_domain(state, proposal_data.slot, DOMAIN_PROPOSAL))` passes. Verify that `proposal1_data.slot == proposal2_data.slot` but `proposal1 != proposal2`. If `state.validators[proposer_index].status` does not equal `PENALIZED`, then run `exit_validator(proposer_index, state, penalize=True, current_slot=block.slot)`
#### DEPOSIT_PROOF #### DEPOSIT_PROOF

76
specs/core/1_shard-data-chains.md
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@ -19,7 +19,14 @@ Phase 1 depends upon all of the constants defined in [Phase 0](0_beacon-chain.md
| Constant | Value | Unit | Approximation | | Constant | Value | Unit | Approximation |
|------------------------|-----------------|-------|---------------| |------------------------|-----------------|-------|---------------|
| `CHUNK_SIZE` | 2**8 (= 256) | bytes | | | `CHUNK_SIZE` | 2**8 (= 256) | bytes | |
| `MAX_SHARD_BLOCK_SIZE` | 2**15 (= 32768) | bytes | | | `SHARD_BLOCK_SIZE` | 2**14 (= 16384) | bytes | |
### Flags, domains, etc.
| Constant | Value |
|------------------------|-----------------|
| `SHARD_PROPOSER_DOMAIN`| 129 |
| `SHARD_ATTESTER_DOMAIN`| 130 |
## Data Structures ## Data Structures
@ -43,7 +50,9 @@ A `ShardBlock` object has the following fields:
'data_root': 'hash32' 'data_root': 'hash32'
# State root (placeholder for now) # State root (placeholder for now)
'state_root': 'hash32', 'state_root': 'hash32',
# Attestation (including block signature) # Block signature
'signature': ['uint256'],
# Attestation
'attester_bitfield': 'bytes', 'attester_bitfield': 'bytes',
'aggregate_sig': ['uint256'], 'aggregate_sig': ['uint256'],
} }
@ -61,31 +70,27 @@ To validate a block header on shard `shard_id`, compute as follows:
* Verify that `beacon_chain_ref` is the hash of a block in the beacon chain with slot less than or equal to `slot`. Verify that `beacon_chain_ref` is equal to or a descendant of the `beacon_chain_ref` specified in the `ShardBlock` pointed to by `parent_hash`. * Verify that `beacon_chain_ref` is the hash of a block in the beacon chain with slot less than or equal to `slot`. Verify that `beacon_chain_ref` is equal to or a descendant of the `beacon_chain_ref` specified in the `ShardBlock` pointed to by `parent_hash`.
* Let `state` be the state of the beacon chain block referred to by `beacon_chain_ref`. Let `validators` be `[validators[i] for i in state.current_persistent_committees[shard_id]]`. * Let `state` be the state of the beacon chain block referred to by `beacon_chain_ref`. Let `validators` be `[validators[i] for i in state.current_persistent_committees[shard_id]]`.
* Assert `len(attester_bitfield) == ceil_div8(len(validators))` * Assert `len(attester_bitfield) == ceil_div8(len(validators))`
* Let `curblock_proposer_index = hash(state.randao_mix + bytes8(shard_id) + bytes8(slot)) % len(validators)`. Let `parent_proposer_index` be the same value calculated for the parent block. * Let `proposer_index = hash(state.randao_mix + bytes8(shard_id) + bytes8(slot)) % len(validators)`. Let `msg` be the block but with the `block.signature` set to `[0, 0]`. Verify that `BLSVerify(pub=validators[proposer_index].pubkey, msg=hash(msg), sig=block.signature, domain=get_domain(state, slot, SHARD_PROPOSER_DOMAIN))` passes.
* Make sure that the `parent_proposer_index`'th bit in the `attester_bitfield` is set to 1. * Generate the `group_public_key` by adding the public keys of all the validators for whom the corresponding position in the bitfield is set to 1. Verify that `BLSVerify(pub=group_public_key, msg=parent_hash, sig=block.aggregate_sig, domain=get_domain(state, slot, SHARD_ATTESTER_DOMAIN))` passes.
* Generate the group public key by adding the public keys of all the validators for whom the corresponding position in the bitfield is set to 1. Verify the `aggregate_sig` using this as the pubkey and the `parent_hash` as the message.
### Block Merklization helper
```python
def merkle_root(block_body):
assert len(block_body) == SHARD_BLOCK_SIZE
chunks = SHARD_BLOCK_SIZE // CHUNK_SIZE
o = [0] * chunks + [block_body[i * CHUNK_SIZE: (i+1) * CHUNK_SIZE] for i in range(chunks)]
for i in range(chunks-1, 0, -1):
o[i] = hash(o[i*2] + o[i*2+1])
return o[1]
```
### Verifying shard block data ### Verifying shard block data
At network layer, we expect a shard block header to be broadcast along with its `block_body`. First, we define a helper function that takes as input beacon chain state and outputs the max block size in bytes: At network layer, we expect a shard block header to be broadcast along with its `block_body`.
```python * Verify that `len(block_body) == SHARD_BLOCK_SIZE`
def shard_block_maxbytes(state): * Verify that `merkle_root(block_body)` equals the `data_root` in the header.
max_grains = MAX_SHARD_BLOCK_SIZE // CHUNK_SIZE
validators_at_target_committee_size = SHARD_COUNT * TARGET_COMMITTEE_SIZE
# number of grains per block is proportional to the number of validators
# up until `validators_at_target_committee_size`
grains = min(
len(get_active_validator_indices(state.validators)) * max_grains // validators_at_target_committee_size,
max_grains
)
return CHUNK_SIZE * grains
```
* Verify that `len(block_body) == shard_block_maxbytes(state)`
* Define `filler_bytes = next_power_of_2(len(block_body)) - len(block_body)`. Compute a simple binary Merkle tree of `block_body + bytes([0] * filler_bytes)` and verify that the root equals the `data_root` in the header.
### Verifying a crosslink ### Verifying a crosslink
@ -93,23 +98,13 @@ A node should sign a crosslink only if the following conditions hold. **If a nod
First, the conditions must recursively apply to the crosslink referenced in `last_crosslink_hash` for the same shard (unless `last_crosslink_hash` equals zero, in which case we are at the genesis). First, the conditions must recursively apply to the crosslink referenced in `last_crosslink_hash` for the same shard (unless `last_crosslink_hash` equals zero, in which case we are at the genesis).
Second, we verify the `shard_block_combined_data_root`. Let `h` be the slot _immediately after_ the slot of the shard block included by the last crosslink, and `h+n-1` be the slot number of the block directly referenced by the current `shard_block_hash`. Let `B[i]` be the block at slot `h+i` in the shard chain. Let `bodies[0] .... bodies[n-1]` be the bodies of these blocks and `roots[0] ... roots[n-1]` the data roots. If there is a missing slot in the shard chain at position `h+i`, then `bodies[i] == b'\x00' * shard_block_maxbytes(state[i])` and `roots[i]` be the Merkle root of the empty data. Define `compute_merkle_root` be a simple Merkle root calculating function that takes as input a list of objects, where the list's length must be an exact power of two. Let `state[i]` be the beacon chain state at height `h+i` (if the beacon chain is missing a block at some slot, the state is unchanged), and `depths[i]` be equal to `log2(next_power_of_2(shard_block_maxbytes(state[i]) // CHUNK_SIZE))` (ie. the expected depth of the i'th data tree). We define the function for computing the combined data root as follows: Second, we verify the `shard_block_combined_data_root`. Let `h` be the slot _immediately after_ the slot of the shard block included by the last crosslink, and `h+n-1` be the slot number of the block directly referenced by the current `shard_block_hash`. Let `B[i]` be the block at slot `h+i` in the shard chain. Let `bodies[0] .... bodies[n-1]` be the bodies of these blocks and `roots[0] ... roots[n-1]` the data roots. If there is a missing slot in the shard chain at position `h+i`, then `bodies[i] == b'\x00' * shard_block_maxbytes(state[i])` and `roots[i]` be the Merkle root of the empty data. Define `compute_merkle_root` be a simple Merkle root calculating function that takes as input a list of objects, where the list's length must be an exact power of two. We define the function for computing the combined data root as follows:
```python ```python
def get_zeroroot_at_depth(n): ZERO_ROOT = merkle_root(bytes([0] * SHARD_BLOCK_SIZE))
o = b'\x00' * CHUNK_SIZE
for i in range(n):
o = hash(o + o)
return o
def mk_combined_data_root(depths, roots): def mk_combined_data_root(roots):
default_value = get_zeroroot_at_depth(max(depths)) data = roots + [ZERO_ROOT for _ in range(len(roots), next_power_of_2(len(roots)))]
data = [default_value for _ in range(next_power_of_2(len(roots)))]
for i, (depth, root) in enumerate(zip(depths, roots)):
value = root
for j in range(depth, max(depths)):
value = hash(value, get_zeroroot_at_depth(depth + j))
data[i] = value
return compute_merkle_root(data) return compute_merkle_root(data)
``` ```
@ -117,12 +112,7 @@ This outputs the root of a tree of the data roots, with the data roots all adjus
```python ```python
def mk_combined_data_root(depths, bodies): def mk_combined_data_root(depths, bodies):
default_value = get_zeroroot_at_depth(max(depths)) data = b''.join(bodies)
padded_body_length = max([CHUNK_SIZE * 2**d for d in depths])
data = b''
for body in bodies:
padded_body = body + bytes([0] * (padded_body_length - len(body)))
data += padded_body
data += bytes([0] * (next_power_of_2(len(data)) - len(data)) data += bytes([0] * (next_power_of_2(len(data)) - len(data))
return compute_merkle_root([data[pos:pos+CHUNK_SIZE] for pos in range(0, len(data), CHUNK_SIZE)]) return compute_merkle_root([data[pos:pos+CHUNK_SIZE] for pos in range(0, len(data), CHUNK_SIZE)])
``` ```