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Merge branch 'master' into vbuterin-patch-6

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Hsiao-Wei Wang 2018-11-23 20:37:23 +08:00
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123
specs/core/0_beacon-chain.md
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@ -39,27 +39,28 @@ The primary source of load on the beacon chain are "attestations". Attestations
| `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 | | `GENESIS_TIME` | **TBD** | seconds |
| `SLOT_DURATION` | 2**4 (= 16) | seconds | | `SLOT_DURATION` | 6 | seconds |
| `CYCLE_LENGTH` | 2**6 (= 64) | slots | ~17 minutes | | `CYCLE_LENGTH` | 2**6 (= 64) | slots | ~6 minutes |
| `MIN_VALIDATOR_SET_CHANGE_INTERVAL` | 2**8 (= 256) | slots | ~1.1 hours | | `MIN_VALIDATOR_SET_CHANGE_INTERVAL` | 2**8 (= 256) | slots | ~25 minutes |
| `RANDAO_SLOTS_PER_LAYER` | 2**12 (= 4096) | slots | ~18 hours | | `SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD` | 2**17 (= 131,072) | slots | ~9 days |
| `SQRT_E_DROP_TIME` | 2**16 (= 65,536) | slots | ~12 days | | `MIN_ATTESTATION_INCLUSION_DELAY` | 2**2 (= 4) | slots | ~24 seconds |
| `MIN_WITHDRAWAL_PERIOD` | 2**12 (= 4096) | slots | ~18 hours | | `RANDAO_SLOTS_PER_LAYER` | 2**12 (= 4096) | slots | ~7 hours |
| `WITHDRAWALS_PER_CYCLE` | 8 | - | 4.3m ETH in ~6 months | | `SQRT_E_DROP_TIME` | 2**18 (= 262,144) | slots | ~18 days |
| `COLLECTIVE_PENALTY_CALCULATION_PERIOD` | 2**19 (= 524,288) | slots | ~3 months | | `WITHDRAWALS_PER_CYCLE` | 2**2 (=4) | validators | 5.2m ETH in ~6 months |
| `DELETION_PERIOD` | 2**21 (= 2,097,152) | slots | ~1.06 years | | `MIN_WITHDRAWAL_PERIOD` | 2**13 (= 8192) | slots | ~14 hours |
| `SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD` | 2**16 (= 65,536) | slots | ~12 days | | `DELETION_PERIOD` | 2**22 (= 4,194,304) | slots | ~290 days |
| `COLLECTIVE_PENALTY_CALCULATION_PERIOD` | 2**20 (= 1,048,576) | slots | ~2.4 months |
| `SLASHING_WHISTLEBLOWER_REWARD_DENOMINATOR` | 2**9 (= 512) |
| `BASE_REWARD_QUOTIENT` | 2**15 (= 32,768) | — | | `BASE_REWARD_QUOTIENT` | 2**15 (= 32,768) | — |
| `MAX_VALIDATOR_CHURN_QUOTIENT` | 2**5 (= 32) | — | | `MAX_VALIDATOR_CHURN_QUOTIENT` | 2**5 (= 32) | — |
| `POW_HASH_VOTING_PERIOD` | 2**10 (=1024) | - | | `POW_HASH_VOTING_PERIOD` | 2**10 (=1024) | - |
| `POW_CONTRACT_MERKLE_TREE_DEPTH` | 2**5 (=32) | - | | `POW_CONTRACT_MERKLE_TREE_DEPTH` | 2**5 (=32) | - |
| `MAX_SPECIALS_PER_BLOCK` | 2**4 (= 16) | - |
| `LOGOUT_MESSAGE` | `"LOGOUT"` | — | | `LOGOUT_MESSAGE` | `"LOGOUT"` | — |
| `INITIAL_FORK_VERSION` | 0 | — | | `INITIAL_FORK_VERSION` | 0 | — |
**Notes** **Notes**
* See a recommended min committee size of 111 here https://vitalik.ca/files/Ithaca201807_Sharding.pdf); our algorithm will generally ensure the committee size is at least half the target. * See a recommended min committee size of 111 [here](https://vitalik.ca/files/Ithaca201807_Sharding.pdf); our algorithm will generally ensure the committee size is at least half the target.
* The `SQRT_E_DROP_TIME` constant is the amount of time it takes for the quadratic leak to cut deposits of non-participating validators by ~39.4%. * The `SQRT_E_DROP_TIME` constant is the amount of time it takes for the quadratic leak to cut deposits of non-participating validators by ~39.4%.
* The `BASE_REWARD_QUOTIENT` constant is the per-slot interest rate assuming all validators are participating, assuming total deposits of 1 ETH. It corresponds to ~3.88% annual interest assuming 10 million participating ETH. * The `BASE_REWARD_QUOTIENT` constant is the per-slot interest rate assuming all validators are participating, assuming total deposits of 1 ETH. It corresponds to ~3.88% annual interest assuming 10 million participating ETH.
* At most `1/MAX_VALIDATOR_CHURN_QUOTIENT` of the validators can change during each validator set change. * At most `1/MAX_VALIDATOR_CHURN_QUOTIENT` of the validators can change during each validator set change.
@ -77,11 +78,12 @@ The primary source of load on the beacon chain are "attestations". Attestations
**Special record types** **Special record types**
| Name | Value | | Name | Value | Maximum count |
| - | :-: | | - | :-: | :-: |
| `LOGOUT` | `0` | | `LOGOUT` | `0` | `16` |
| `CASPER_SLASHING` | `1` | | `CASPER_SLASHING` | `1` | `16` |
| `RANDAO_CHANGE` | `2` | | `PROPOSER_SLASHING` | `2` | `16` |
| `DEPOSIT_PROOF` | `3` | `16` |
**Validator set delta flags** **Validator set delta flags**
@ -126,7 +128,9 @@ A `BeaconBlock` has the following fields:
# Attestations # Attestations
'attestations': [AttestationRecord], 'attestations': [AttestationRecord],
# Specials (e.g. logouts, penalties) # Specials (e.g. logouts, penalties)
'specials': [SpecialRecord] 'specials': [SpecialRecord],
# Proposer signature
'proposer_signature': ['uint256'],
} }
``` ```
@ -157,6 +161,21 @@ An `AttestationRecord` has the following fields:
} }
``` ```
A `ProposalSignedData` has the following fields:
```python
{
# Fork version
'fork_version': 'uint64',
# Slot number
'slot': 'uint64',
# Shard ID (or `2**64 - 1` for beacon chain)
'shard_id': 'uint64',
# Block hash
'block_hash': 'hash32',
}
```
An `AttestationSignedData` has the following fields: An `AttestationSignedData` has the following fields:
```python ```python
@ -217,7 +236,7 @@ The `BeaconState` has the following fields:
# Randao seed used for next shuffling # Randao seed used for next shuffling
'next_shuffling_seed': 'hash32', 'next_shuffling_seed': 'hash32',
# Total deposits penalized in the given withdrawal period # Total deposits penalized in the given withdrawal period
'deposits_penalized_in_period': ['uint32'], 'deposits_penalized_in_period': ['uint64'],
# Hash chain of validator set changes (for light clients to easily track deltas) # Hash chain of validator set changes (for light clients to easily track deltas)
'validator_set_delta_hash_chain': 'hash32' 'validator_set_delta_hash_chain': 'hash32'
# Current sequence number for withdrawals # Current sequence number for withdrawals
@ -227,11 +246,11 @@ The `BeaconState` has the following fields:
# PoW chain reference # PoW chain reference
'known_pow_receipt_root': 'hash32', 'known_pow_receipt_root': 'hash32',
'candidate_pow_receipt_root': 'hash32', 'candidate_pow_receipt_root': 'hash32',
'candidate_pow_receipt_root_votes': 'uint32', 'candidate_pow_receipt_root_votes': 'uint64',
# Parameters relevant to hard forks / versioning. # Parameters relevant to hard forks / versioning.
# Should be updated only by hard forks. # Should be updated only by hard forks.
'pre_fork_version': 'uint32', 'pre_fork_version': 'uint64',
'post_fork_version': 'uint32', 'post_fork_version': 'uint64',
'fork_slot_number': 'uint64', 'fork_slot_number': 'uint64',
# Attestations not yet processed # Attestations not yet processed
'pending_attestations': [AttestationRecord], 'pending_attestations': [AttestationRecord],
@ -499,6 +518,15 @@ def get_block_hash(state: BeaconState,
`get_block_hash(_, _, s)` should always return the block hash in the beacon chain at slot `s`, and `get_shards_and_committees_for_slot(_, s)` should not change unless the validator set changes. `get_block_hash(_, _, s)` should always return the block hash in the beacon chain at slot `s`, and `get_shards_and_committees_for_slot(_, s)` should not change unless the validator set changes.
The following is a function that determines the proposer of a beacon block:
```python
def get_beacon_proposer(state:BeaconState, slot: int) -> ValidatorRecord:
first_committee = get_shards_and_committees_for_slot(state, slot)[0]
index = first_committee[slot % len(first_committee)]
return state.validators[index]
```
We define another set of helpers to be used throughout: `bytes1(x): return x.to_bytes(1, 'big')`, `bytes2(x): return x.to_bytes(2, 'big')`, and so on for all integers, particularly 1, 2, 3, 4, 8, 32. We define another set of helpers to be used throughout: `bytes1(x): return x.to_bytes(1, 'big')`, `bytes2(x): return x.to_bytes(2, 'big')`, and so on for all integers, particularly 1, 2, 3, 4, 8, 32.
We define a function to "add a link" to the validator hash chain, used when a validator is added or removed: We define a function to "add a link" to the validator hash chain, used when a validator is added or removed:
@ -540,8 +568,8 @@ total_deposit_count: int128
@public @public
def deposit(deposit_params: bytes[2048]): def deposit(deposit_params: bytes[2048]):
index:int128 = self.total_deposit_count + 2**POW_CONTRACT_MERKLE_TREE_DEPTH index:int128 = self.total_deposit_count + 2**POW_CONTRACT_MERKLE_TREE_DEPTH
msg_gwei_bytes8: bytes[8] = slice(as_bytes32(msg.value / 10**9), 24, 8) msg_gwei_bytes8: bytes[8] = slice(convert(msg.value / 10**9, 'bytes32'), 24, 8)
timestamp_bytes8: bytes[8] = slice(s_bytes32(block.timestamp), 24, 8) timestamp_bytes8: bytes[8] = slice(convert(block.timestamp, 'bytes32'), 24, 8)
deposit_data: bytes[2064] = concat(deposit_params, msg_gwei_bytes8, timestamp_bytes8) deposit_data: bytes[2064] = concat(deposit_params, msg_gwei_bytes8, timestamp_bytes8)
log.HashChainValue(self.receipt_tree[1], deposit_data, self.total_deposit_count) log.HashChainValue(self.receipt_tree[1], deposit_data, self.total_deposit_count)
@ -590,7 +618,8 @@ A valid block with slot `0` (the "genesis block") has the following values. Othe
'ancestor_hashes': [bytes32(0) for i in range(32)], 'ancestor_hashes': [bytes32(0) for i in range(32)],
'state_root': STARTUP_STATE_ROOT, 'state_root': STARTUP_STATE_ROOT,
'attestations': [], 'attestations': [],
'specials': [] 'specials': [],
'proposer_signature': [0, 0]
} }
``` ```
@ -687,7 +716,7 @@ def add_validator(state: State,
current_slot: int) -> int: current_slot: int) -> int:
# if following assert fails, validator induction failed # if following assert fails, validator induction failed
# move on to next validator registration log # move on to next validator registration log
signed_message = as_bytes32(pubkey) + as_bytes2(withdrawal_shard) + withdrawal_address + randao_commitment signed_message = bytes32(pubkey) + bytes2(withdrawal_shard) + withdrawal_address + 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,
@ -719,13 +748,16 @@ def add_validator(state: State,
### Routine for removing a validator ### Routine for removing a validator
```python ```python
def exit_validator(index, state, penalize, current_slot): def exit_validator(index, state, block, penalize, current_slot):
validator = state.validators[index] validator = state.validators[index]
validator.exit_slot = current_slot validator.exit_slot = current_slot
validator.exit_seq = state.current_exit_seq validator.exit_seq = state.current_exit_seq
state.current_exit_seq += 1 state.current_exit_seq += 1
if penalize: if penalize:
validator.status = PENALIZED validator.status = PENALIZED
whistleblower_xfer_amount = validator.deposit // SLASHING_WHISTLEBLOWER_REWARD_DENOMINATOR
validator.deposit -= whistleblower_xfer_amount
get_beacon_proposer(state, block.slot).deposit += whistleblower_xfer_amount
state.deposits_penalized_in_period[current_slot // COLLECTIVE_PENALTY_CALCULATION_PERIOD] += validator.balance state.deposits_penalized_in_period[current_slot // COLLECTIVE_PENALTY_CALCULATION_PERIOD] += validator.balance
else: else:
validator.status = PENDING_EXIT validator.status = PENDING_EXIT
@ -817,11 +849,11 @@ def update_ancestor_hashes(parent_ancestor_hashes: List[Hash32],
return new_ancestor_hashes return new_ancestor_hashes
``` ```
A beacon block can have 0 or more `AttestationRecord` objects ### Verify attestations
For each one of these attestations: For each `AttestationRecord` object:
* Verify that `slot <= parent.slot` and `slot >= max(parent.slot - CYCLE_LENGTH + 1, 0)`. * Verify that `slot <= block.slot - MIN_ATTESTATION_INCLUSION_DELAY` and `slot >= max(parent.slot - CYCLE_LENGTH + 1, 0)`.
* Verify that `justified_slot` is equal to or earlier than `last_justified_slot`. * Verify that `justified_slot` is equal to or earlier than `last_justified_slot`.
* Verify that `justified_block_hash` is the hash of the block in the current chain at the slot -- `justified_slot`. * Verify that `justified_block_hash` is the hash of the block in the current chain at the slot -- `justified_slot`.
* Verify that either `last_crosslink_hash` or `shard_block_hash` equals `state.crosslinks[shard].shard_block_hash`. * Verify that either `last_crosslink_hash` or `shard_block_hash` equals `state.crosslinks[shard].shard_block_hash`.
@ -834,12 +866,16 @@ For each one of these attestations:
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.
Let `curblock_proposer_index` be the validator index of the `block.slot % len(get_shards_and_committees_for_slot(state, block.slot)[0].committee)`'th attester in `get_shards_and_committees_for_slot(state, block.slot)[0]`, and `parent_proposer_index` be the validator index of the parent block, calculated similarly. Verify that an attestation from the `parent_proposer_index`'th validator is part of the first (ie. item 0 in the array) `AttestationRecord` object; this attester can be considered to be the proposer of the parent block. In general, when a beacon block is produced, it is broadcasted at the network layer along with the attestation from its proposer. ### Verify proposer signature
Additionally, verify and update the RANDAO reveal. This is done as follows: 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]`.
Verify that `BLSVerify(pubkey=get_beacon_proposer(state, block.slot).pubkey, data=proposal_hash, sig=block.proposer_signature)` passes.
### Verify and process RANDAO reveal
* Let `repeat_hash(x, n) = x if n == 0 else repeat_hash(hash(x), n-1)`. * Let `repeat_hash(x, n) = x if n == 0 else repeat_hash(hash(x), n-1)`.
* Let `V = state.validators[curblock_proposer_index]`. * Let `V = get_beacon_proposer(state, block.slot).
* Verify that `repeat_hash(block.randao_reveal, (block.slot - V.randao_last_change) // RANDAO_SLOTS_PER_LAYER + 1) == V.randao_commitment` * Verify that `repeat_hash(block.randao_reveal, (block.slot - V.randao_last_change) // RANDAO_SLOTS_PER_LAYER + 1) == V.randao_commitment`
* Set `state.randao_mix = xor(state.randao_mix, block.randao_reveal)`, `V.randao_commitment = block.randao_reveal`, `V.randao_last_change = block.slot` * Set `state.randao_mix = xor(state.randao_mix, block.randao_reveal)`, `V.randao_commitment = block.randao_reveal`, `V.randao_last_change = block.slot`
@ -847,7 +883,7 @@ Finally, if `block.candidate_pow_hash_chain_tip = state.candidate_pow_hash_chain
### Process penalties, logouts and other special objects ### Process penalties, logouts and other special objects
Verify that there are at most `MAX_SPECIALS_PER_BLOCK` objects in `block.specials`. Verify that the quantity of each type of object in `block.specials` is less than or equal to its maximum (see table at the top). Verify that objects are sorted in order of `kind` (ie. `block.specials[i+1].kind >= block.specials[i].kind` for all `0 <= i < len(block.specials-1)`).
For each `SpecialRecord` `obj` in `block.specials`, verify that its `kind` is one of the below values, and that `obj.data` deserializes according to the format for the given `kind`, then process it. The word "verify" when used below means that if the given verification check fails, the block containing that `SpecialRecord` is invalid. For each `SpecialRecord` `obj` in `block.specials`, verify that its `kind` is one of the below values, and that `obj.data` deserializes according to the format for the given `kind`, then process it. The word "verify" when used below means that if the given verification check fails, the block containing that `SpecialRecord` is invalid.
@ -864,7 +900,7 @@ Perform the following checks:
* Verify that `BLSVerify(pubkey=validators[data.validator_index].pubkey, msg=hash(LOGOUT_MESSAGE + bytes8(fork_version)), sig=data.signature, domain=get_fork_version(state, current_slot) * 2**32 + DOMAIN_LOGOUT)` * Verify that `BLSVerify(pubkey=validators[data.validator_index].pubkey, msg=hash(LOGOUT_MESSAGE + bytes8(fork_version)), sig=data.signature, domain=get_fork_version(state, current_slot) * 2**32 + DOMAIN_LOGOUT)`
* Verify that `validators[validator_index].status == ACTIVE`. * Verify that `validators[validator_index].status == ACTIVE`.
Run `exit_validator(data.validator_index, state, penalize=False, current_slot=block.slot)`. Run `exit_validator(data.validator_index, state, block, penalize=False, current_slot=block.slot)`.
#### CASPER_SLASHING #### CASPER_SLASHING
@ -886,7 +922,20 @@ Perform the following checks:
* 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`.
For each validator index `v` in `intersection`, if `state.validators[v].status` does not equal `PENALIZED`, then run `exit_validator(v, state, penalize=True, current_slot=block.slot)` For each validator index `v` in `intersection`, if `state.validators[v].status` does not equal `PENALIZED`, then run `exit_validator(v, state, block, penalize=True, current_slot=block.slot)`
#### PROPOSER_SLASHING
```python
{
'proposer_index': 'uint24',
'proposal1_data': ProposalSignedData,
'proposal1_signature': '[uint256]',
'proposal2_data': ProposalSignedData,
'proposal1_signature': '[uint256]',
}
```
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)`
#### DEPOSIT_PROOF #### DEPOSIT_PROOF
@ -1072,7 +1121,7 @@ def change_validators(validators: List[ValidatorRecord], current_slot: int) -> N
* Remove all attestation records older than slot `state.last_state_recalculation_slot` * Remove all attestation records older than slot `state.last_state_recalculation_slot`
* Empty the `state.pending_specials` list * Empty the `state.pending_specials` list
* For any validator with index `v` with balance less than `MIN_ONLINE_DEPOSIT_SIZE` and status `ACTIVE`, run `exit_validator(v, state, penalize=False, current_slot=block.slot)` * For any validator with index `v` with balance less than `MIN_ONLINE_DEPOSIT_SIZE` and status `ACTIVE`, run `exit_validator(v, state, block, penalize=False, current_slot=block.slot)`
* Set `state.recent_block_hashes = state.recent_block_hashes[CYCLE_LENGTH:]` * Set `state.recent_block_hashes = state.recent_block_hashes[CYCLE_LENGTH:]`
* Set `state.last_state_recalculation_slot += CYCLE_LENGTH` * Set `state.last_state_recalculation_slot += CYCLE_LENGTH`

46
specs/simple-serialize.md
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@ -402,40 +402,32 @@ Return the hash of the serialization of the value.
First, we define some helpers and then the Merkle tree function. The constant `CHUNK_SIZE` is set to 128. First, we define some helpers and then the Merkle tree function. The constant `CHUNK_SIZE` is set to 128.
```python ```python
# Returns the smallest power of 2 equal to or higher than x # Merkle tree hash of a list of homogenous, non-empty items
def next_power_of_2(x):
return x if x == 1 else next_power_of_2((x+1) // 2) * 2
# Extends data length to a power of 2 by minimally right-zero-padding
def extend_to_power_of_2(data):
return data + b'\x00' * (next_power_of_2(len(data)) - len(data))
# Concatenate a list of homogeneous objects into data and pad it
def list_to_glob(lst):
if len(lst) == 0:
return b''
if len(lst[0]) != next_power_of_2(len(lst[0])):
lst = [extend_to_power_of_2(x) for x in lst]
data = b''.join(lst)
# Pad to chunksize
data += b'\x00' * (CHUNKSIZE - (len(data) % CHUNKSIZE or CHUNKSIZE))
return data
# Merkle tree hash of a list of items
def merkle_hash(lst): def merkle_hash(lst):
# Turn list into padded data
data = list_to_glob(lst)
# Store length of list (to compensate for non-bijectiveness of padding) # Store length of list (to compensate for non-bijectiveness of padding)
datalen = len(lst).to_bytes(32, 'big') datalen = len(lst).to_bytes(32, 'big')
# Convert to chunks
chunkz = [data[i:i+CHUNKSIZE] for i in range(0, len(data), CHUNKSIZE)] if len(lst) == 0:
# Handle empty list case
chunkz = [b'\x00' * CHUNKSIZE]
elif len(lst[0]) < CHUNKSIZE:
# See how many items fit in a chunk
items_per_chunk = CHUNKSIZE // len(lst[0])
# Build a list of chunks based on the number of items in the chunk
chunkz = [b''.join(lst[i:i+items_per_chunk]) for i in range(0, len(lst), items_per_chunk)]
else:
# Leave large items alone
chunkz = lst
# Tree-hash # Tree-hash
while len(chunkz) > 1: while len(chunkz) > 1:
if len(chunkz) % 2 == 1: if len(chunkz) % 2 == 1:
chunkz.append(b'\x00' * CHUNKSIZE) chunkz.append(b'\x00' * CHUNKSIZE)
chunkz = [hash(chunkz[i] + chunkz[i+1]) for i in range(0, len(chunkz), 2)] chunkz = [hash(chunkz[i] + chunkz[i+1]) for i in range(0, len(chunkz), 2)]
# Return hash of root and length data # Return hash of root and length data
return hash((chunkz[0] if len(chunks) > 0 else b'\x00' * 32) + datalen) return hash(chunkz[0] + datalen)
``` ```
To `tree_hash` a list, we simply do: To `tree_hash` a list, we simply do:
@ -465,3 +457,7 @@ return hash(b''.join([tree_hash(getattr(x, field)) for field in sorted(value.fie
| Nim | [ https://github.com/status-im/nim-beacon-chain/blob/master/beacon_chain/ssz.nim ](https://github.com/status-im/nim-beacon-chain/blob/master/beacon_chain/ssz.nim) | Nim Implementation maintained SSZ. | | Nim | [ https://github.com/status-im/nim-beacon-chain/blob/master/beacon_chain/ssz.nim ](https://github.com/status-im/nim-beacon-chain/blob/master/beacon_chain/ssz.nim) | Nim Implementation maintained SSZ. |
| Rust | [ https://github.com/paritytech/shasper/tree/master/util/ssz ](https://github.com/paritytech/shasper/tree/master/util/ssz) | Shasper implementation of SSZ maintained by ParityTech. | | Rust | [ https://github.com/paritytech/shasper/tree/master/util/ssz ](https://github.com/paritytech/shasper/tree/master/util/ssz) | Shasper implementation of SSZ maintained by ParityTech. |
| Javascript | [ https://github.com/ChainSafeSystems/ssz-js/blob/master/src/index.js ](https://github.com/ChainSafeSystems/ssz-js/blob/master/src/index.js) | Javascript Implementation maintained SSZ | | Javascript | [ https://github.com/ChainSafeSystems/ssz-js/blob/master/src/index.js ](https://github.com/ChainSafeSystems/ssz-js/blob/master/src/index.js) | Javascript Implementation maintained SSZ |
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