Merge branch 'master' into hwwhww/patch-1
This commit is contained in:
Hsiao-Wei Wang
commit
829e6d9034
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@ -13,7 +13,7 @@ Core specifications for eth2.0 client validation can be found in [specs/core](sp
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## Design goals
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The following are the broad design goals for Ethereum 2.0:
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* to minimize complexity, even at the cost of some losses in efficiency
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* to remain live through major network partitions and when very large portions of nodes going offline
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* to remain live through major network partitions and when very large portions of nodes go offline
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* to select all components such that they are either quantum secure or can be easily swapped out for quantum secure counterparts when available
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* to utilize crypto and design techniques that allow for a large participation of validators in total and per unit time
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* to allow for a typical consumer laptop with `O(C)` resources to process/validate `O(1)` shards (including any system level validation such as the beacon chain)
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@ -0,0 +1,64 @@
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### BLS Verification
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**Warning: This document is pending academic review and should not yet be considered secure.**
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See https://z.cash/blog/new-snark-curve/ for BLS-12-381 parameters.
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We represent coordinates as defined in https://github.com/zkcrypto/pairing/tree/master/src/bls12_381/.
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Specifically, a point in G1 as a 384-bit integer `z`, which we decompose into:
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* `x = z % 2**381`
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* `highflag = z // 2**382`
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* `lowflag = (z % 2**382) // 2**381`
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If `highflag == 3`, the point is the point at infinity and we require `lowflag = x = 0`. Otherwise, we require `highflag == 2`, in which case the point is `(x, y)` where `y` is the valid coordinate such that `(y * 2) // q == lowflag`.
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We represent a point in G2 as a pair of 384-bit integers `(z1, z2)` that are each decomposed into `x1`, `highflag1`, `lowflag1`, `x2`, `highflag2`, `lowflag2` as above. We require `lowflag2 == highflag2 == 0`. If `highflag1 == 3`, the point is the point at infinity and we require `lowflag1 == x1 == x2 == 0`. Otherwise, we require `highflag == 2`, in which case the point is `(x1 * i + x2, y)` where `y` is the valid coordinate such that the imaginary part of `y` satisfies `(y_im * 2) // q == lowflag1`.
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`BLSVerify(pubkey: uint384, msg: bytes32, sig: [uint384], domain: uint64)` is done as follows:
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* Verify that `pubkey` is a valid G1 point and `sig` is a valid G2 point.
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* Convert `msg` to a G2 point using `hash_to_G2` defined below.
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* Do the pairing check: verify `e(pubkey, hash_to_G2(msg, domain)) == e(G1, sig)` (where `e` is the BLS pairing function)
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Here is the `hash_to_G2` definition:
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```python
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G2_cofactor = 305502333931268344200999753193121504214466019254188142667664032982267604182971884026507427359259977847832272839041616661285803823378372096355777062779109
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field_modulus = 4002409555221667393417789825735904156556882819939007885332058136124031650490837864442687629129015664037894272559787
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def hash_to_G2(m, domain):
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x1 = hash(bytes8(domain) + b'\x01' + m)
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x2 = hash(bytes8(domain) + b'\x02' + m)
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x_coord = FQ2([x1, x2]) # x1 + x2 * i
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while 1:
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x_cubed_plus_b2 = x_coord ** 3 + FQ2([4,4])
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y_coord = mod_sqrt(x_cubed_plus_b2)
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if y_coord is not None:
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break
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x_coord += FQ2([1, 0]) # Add one until we get a quadratic residue
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assert is_on_curve((x_coord, y_coord))
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return multiply((x_coord, y_coord), G2_cofactor)
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```
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Here is a sample implementation of `mod_sqrt`:
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```python
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qmod = field_modulus ** 2 - 1
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eighth_roots_of_unity = [FQ2([1,1]) ** ((qmod * k) // 8) for k in range(8)]
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def mod_sqrt(val):
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candidate_sqrt = val ** ((qmod + 8) // 16)
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check = candidate_sqrt ** 2 / val
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if check in eighth_roots_of_unity[::2]:
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return candidate_sqrt / eighth_roots_of_unity[eighth_roots_of_unity.index(check) // 2]
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return None
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```
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`BLSMultiVerify(pubkeys: [uint384], msgs: [bytes32], sig: [uint384], domain: uint64)` is done as follows:
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* Verify that each element of `pubkeys` is a valid G1 point and `sig` is a valid G2 point.
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* Convert each element of `msg` to a G2 point using `hash_to_G2` defined above, using the specified `domain`.
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* Check that the length of `pubkeys` and `msgs` is the same, call the length `L`
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* Do the pairing check: verify `e(pubkeys[0], hash_to_G2(msgs[0], domain)) * ... * e(pubkeys[L-1], hash_to_G2(msgs[L-1], domain)) == e(G1, sig)`
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@ -43,14 +43,15 @@ The primary source of load on the beacon chain are "attestations". Attestations
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| `MIN_VALIDATOR_SET_CHANGE_INTERVAL` | 2**8 (= 256) | slots | ~25 minutes |
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| `SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD` | 2**17 (= 131,072) | slots | ~9 days |
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| `MIN_ATTESTATION_INCLUSION_DELAY` | 2**2 (= 4) | slots | ~24 seconds |
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| `SQRT_E_DROP_TIME` | 2**18 (= 262,144) | slots | ~18 days |
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| `SQRT_E_DROP_TIME` | 2**11 (= 1,024) | cycles | ~9 days |
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| `WITHDRAWALS_PER_CYCLE` | 2**2 (=4) | validators | 5.2m ETH in ~6 months |
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| `MIN_WITHDRAWAL_PERIOD` | 2**13 (= 8,192) | slots | ~14 hours |
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| `DELETION_PERIOD` | 2**22 (= 4,194,304) | slots | ~290 days |
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| `COLLECTIVE_PENALTY_CALCULATION_PERIOD` | 2**20 (= 1,048,576) | slots | ~2.4 months |
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| `POW_RECEIPT_ROOT_VOTING_PERIOD` | 2**10 (= 1,024) | slots | ~1.7 hours |
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| `SLASHING_WHISTLEBLOWER_REWARD_DENOMINATOR` | 2**9 (= 512) |
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| `BASE_REWARD_QUOTIENT` | 2**15 (= 32,768) | — |
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| `BASE_REWARD_QUOTIENT` | 2**11 (= 2,048) | — |
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| `INCLUDER_REWARD_SHARE_QUOTIENT` | 2**3 (= 8) | — |
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| `MAX_VALIDATOR_CHURN_QUOTIENT` | 2**5 (= 32) | — |
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| `POW_CONTRACT_MERKLE_TREE_DEPTH` | 2**5 (= 32) | - |
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| `MAX_ATTESTATION_COUNT` | 2**7 (= 128) | - |
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@ -61,7 +62,7 @@ The primary source of load on the beacon chain are "attestations". Attestations
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* 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.
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* 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%.
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* 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.
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* The `BASE_REWARD_QUOTIENT` constant dictates the per-cycle interest rate assuming all validators are participating, assuming total deposits of 1 ETH. It corresponds to ~2.57% annual interest assuming 10 million participating ETH.
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* At most `1/MAX_VALIDATOR_CHURN_QUOTIENT` of the validators can change during each validator set change.
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**Validator status codes**
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@ -135,28 +136,38 @@ A `BeaconBlock` has the following fields:
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An `AttestationRecord` has the following fields:
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```python
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{
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'data': AttestationSignedData,
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# Attester participation bitfield
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'attester_bitfield': 'bytes',
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# Proof of custody bitfield
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'poc_bitfield': 'bytes',
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# BLS aggregate signature
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'aggregate_sig': ['uint384']
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}
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```
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`AttestationSignedData`:
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```python
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{
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# Slot number
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'slot': 'uint64',
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# Shard number
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'shard': 'uint64',
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# Beacon block hashes not part of the current chain, oldest to newest
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'oblique_parent_hashes': ['hash32'],
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# Hash of the block we're signing
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'block_hash': 'hash32',
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# Hash of the ancestor at the cycle boundary
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'cycle_boundary_hash': 'hash32',
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# Shard block hash being attested to
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'shard_block_hash': 'hash32',
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# Last crosslink hash
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'last_crosslink_hash': 'hash32',
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# Root of data between last hash and this one
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'shard_block_combined_data_root': 'hash32',
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# Attester participation bitfield (1 bit per attester)
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'attester_bitfield': 'bytes',
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# Slot of last justified beacon block
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'justified_slot': 'uint64',
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# Hash of last justified beacon block
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'justified_block_hash': 'hash32',
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# BLS aggregate signature
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'aggregate_sig': ['uint384']
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}
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```
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@ -173,27 +184,6 @@ A `ProposalSignedData` has the following fields:
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}
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```
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An `AttestationSignedData` has the following fields:
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```python
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{
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# Slot number
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'slot': 'uint64',
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# Shard number
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'shard': 'uint64',
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# CYCLE_LENGTH parent hashes
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'parent_hashes': ['hash32'],
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# Shard block hash
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'shard_block_hash': 'hash32',
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# Last crosslink hash
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'last_crosslink_hash': 'hash32',
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# Root of data between last hash and this one
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'shard_block_combined_data_root': 'hash32',
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# Slot of last justified beacon block referenced in the attestation
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'justified_slot': 'uint64'
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}
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```
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A `SpecialRecord` has the following fields:
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```python
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@ -221,10 +211,11 @@ The `BeaconState` has the following fields:
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'last_state_recalculation_slot': 'uint64',
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# Last finalized slot
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'last_finalized_slot': 'uint64',
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# Last justified slot
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'last_justified_slot': 'uint64',
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# Number of consecutive justified slots
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'justified_streak': 'uint64',
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# Justification source
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'justification_source': 'uint64',
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'prev_cycle_justification_source': 'uint64',
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# Recent justified slot bitmask
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'justified_slot_bitfield': 'uint64',
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# Committee members and their assigned shard, per slot
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'shard_and_committee_for_slots': [[ShardAndCommittee]],
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# Persistent shard committees
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@ -247,7 +238,7 @@ The `BeaconState` has the following fields:
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# Should be updated only by hard forks.
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'fork_data': ForkData,
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# Attestations not yet processed
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'pending_attestations': [AttestationRecord],
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'pending_attestations': [ProcessedAttestations],
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# recent beacon block hashes needed to process attestations, older to newer
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'recent_block_hashes': ['hash32'],
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# RANDAO state
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@ -333,6 +324,19 @@ A `ForkData` object contains the following fields:
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'post_fork_version': 'uint64',
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# Fork slot number
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'fork_slot_number': 'uint64'
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```
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A `ProcessedAttestation` object has the following fields:
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```python
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{
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# Signed data
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'data': AttestationSignedData,
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# Attester participation bitfield (2 bits per attester)
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'attester_bitfield': 'bytes',
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# Proof of custody bitfield
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'poc_bitfield': 'bytes',
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# Slot in which it was included
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'slot_included': 'uint64'
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}
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```
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@ -363,7 +367,7 @@ The beacon chain fork choice rule is a hybrid that combines justification and fi
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* Let `store` be the set of attestations and blocks that the validator `v` has observed and verified (in particular, block ancestors must be recursively verified). Attestations not part of any chain are still included in `store`.
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* Let `finalized_head` be the finalized block with the highest slot number. (A block `B` is finalized if there is a descendant of `B` in `store` the processing of which sets `B` as finalized.)
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* Let `justified_head` be the descendant of `finalized_head` with the highest slot number that has been justified for at least `CYCLE_LENGTH` slots. (A block `B` is justified is there is a descendant of `B` in `store` the processing of which sets `B` as justified.) If no such descendant exists set `justified_head` to `finalized_head`.
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* Let `justified_head` be the descendant of `finalized_head` with the highest slot number that has been justified for at least `CYCLE_LENGTH` slots. (A block `B` is justified if there is a descendant of `B` in `store` the processing of which sets `B` as justified.) If no such descendant exists set `justified_head` to `finalized_head`.
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* Let `get_ancestor(store, block, slot)` be the ancestor of `block` with slot number `slot`. The `get_ancestor` function can be defined recursively as `def get_ancestor(store, block, slot): return block if block.slot == slot else get_ancestor(store, store.get_parent(block), slot)`.
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* Let `get_latest_attestation(store, validator)` be the attestation with the highest slot number in `store` from `validator`. If several such attestations exist use the one the validator `v` observed first.
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* Let `get_latest_attestation_target(store, validator)` be the target block in the attestation `get_latest_attestation(store, validator)`.
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@ -407,7 +411,7 @@ def get_active_validator_indices(validators)
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return [i for i, v in enumerate(validators) if v.status == ACTIVE]
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```
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The following is a function that shuffles the validator list:
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The following is a function that shuffles any list; we primarily use it for the validator list:
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```python
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def shuffle(values: List[Any],
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@ -555,14 +559,38 @@ def get_block_hash(state: BeaconState,
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The following is a function that determines the proposer of a beacon block:
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```python
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def get_beacon_proposer(state:BeaconState, slot: int) -> ValidatorRecord:
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def get_beacon_proposer_index(state:BeaconState, slot: int) -> int:
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first_committee = get_shards_and_committees_for_slot(state, slot)[0].committee
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index = first_committee[slot % len(first_committee)]
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return state.validators[index]
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return index
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```
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The following is a function that determines the validators that participated in an attestation:
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```python
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def get_attestation_participants(state: State,
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attestation_data: AttestationSignedData,
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attester_bitfield: bytes) -> List[int]:
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sncs_for_slot = get_shards_and_committees_for_slot(state, attestation_data.slot)
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snc = [x for x in sncs_for_slot if x.shard == attestation_data.shard][0]
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assert len(attester_bitfield) == ceil_div8(len(snc.committee))
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participants = []
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for i, vindex in enumerate(snc.committee):
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bit = (attester_bitfield[i//8] >> (7 - (i % 8))) % 2
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if bit == 1:
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participants.append(vindex)
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return participants
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```
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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.
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We define a function to determine the balance of a validator used for determining punishments and calculating stake:
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```python
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def balance_at_stake(validator: ValidatorRecord) -> int:
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return min(validator.balance, DEPOSIT_SIZE)
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```
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We define a function to "add a link" to the validator hash chain, used when a validator is added or removed:
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```python
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@ -706,8 +734,9 @@ def on_startup(current_validators: List[ValidatorRecord],
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crosslinks=crosslinks,
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last_state_recalculation_slot=0,
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last_finalized_slot=0,
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last_justified_slot=0,
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justified_streak=0,
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justification_source=0,
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prev_cycle_justification_source=0,
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justified_slot_bitfield=0,
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shard_and_committee_for_slots=x + x,
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persistent_committees=split(shuffle(validators, bytes([0] * 32)), SHARD_COUNT),
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persistent_committee_reassignments=[],
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@ -739,7 +768,7 @@ This routine should be run for every validator that is inducted as part of a log
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First, some helper functions:
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||||
```python
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def min_empty_validator(validators: List[ValidatorRecord], current_slot: int):
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||||
def min_empty_validator_index(validators: List[ValidatorRecord], current_slot: int) -> int:
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for i, v in enumerate(validators):
|
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if v.status == WITHDRAWN and v.last_status_change_slot + DELETION_PERIOD <= current_slot:
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return i
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|
@ -796,12 +825,14 @@ def get_new_validators(current_validators: List[ValidatorRecord],
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last_status_change_slot=current_slot,
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||||
exit_seq=0
|
||||
)
|
||||
index = min_empty_validator(current_validators)
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||||
# Add the validator
|
||||
index = min_empty_validator_index(current_validators)
|
||||
if index is None:
|
||||
new_validators.append(rec)
|
||||
return new_validators, len(new_validators.validators) - 1
|
||||
index = len(new_validators) - 1
|
||||
else:
|
||||
new_validators[index] = rec
|
||||
|
||||
return new_validators, index
|
||||
```
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||||
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||||
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|
@ -829,6 +860,7 @@ def add_validator(state: BeaconState,
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|||
status=status,
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||||
current_slot=current_slot,
|
||||
)
|
||||
|
||||
return index
|
||||
```
|
||||
|
||||
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|
@ -846,12 +878,17 @@ def exit_validator(index: int,
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|||
validator.last_status_change_slot = current_slot
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||||
validator.exit_seq = state.current_exit_seq
|
||||
state.current_exit_seq += 1
|
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for committee in state.persistent_committees:
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for i, vindex in committee:
|
||||
if vindex == index:
|
||||
committee.pop(i)
|
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break
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||||
if penalize:
|
||||
state.deposits_penalized_in_period[current_slot // COLLECTIVE_PENALTY_CALCULATION_PERIOD] += balance_at_stake(validator)
|
||||
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.validators[get_beacon_proposer_index(state, block.slot)].deposit += whistleblower_xfer_amount
|
||||
else:
|
||||
validator.status = PENDING_EXIT
|
||||
state.validator_set_delta_hash_chain = get_new_validator_set_delta_hash_chain(
|
||||
|
|
@ -895,26 +932,26 @@ def update_ancestor_hashes(parent_ancestor_hashes: List[Hash32],
|
|||
|
||||
### Verify attestations
|
||||
|
||||
Verify that there are at most `MAX_ATTESTATION_COUNT` `AttestationRecord` objects. For each `AttestationRecord` object:
|
||||
Verify that there are at most `MAX_ATTESTATION_COUNT` `AttestationRecord` objects.
|
||||
|
||||
* 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_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`.
|
||||
* 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.
|
||||
* 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.
|
||||
* Let `data = AttestationSignedData(slot, shard, parent_hashes, shard_block_hash, last_crosslinked_hash, shard_block_combined_data_root, justified_slot)`.
|
||||
* Check `BLSVerify(pubkey=group_public_key, msg=data, sig=aggregate_sig, domain=get_domain(state.fork_data, slot, DOMAIN_ATTESTATION))`.
|
||||
For each `AttestationRecord` object `obj`:
|
||||
|
||||
* Verify that `obj.data.slot <= block.slot - MIN_ATTESTATION_INCLUSION_DELAY` and `obj.data.slot >= max(parent.slot - CYCLE_LENGTH + 1, 0)`.
|
||||
* Verify that `obj.data.justified_slot` is equal to `justification_source if obj.data.slot >= state.last_state_recalculation_slot else prev_cycle_justification_source`
|
||||
* Verify that `obj.data.justified_block_hash` is equal to `get_block_hash(state, block, obj.data.justified_slot)`.
|
||||
* Verify that either `obj.data.last_crosslink_hash` or `obj.data.shard_block_hash` equals `state.crosslinks[shard].shard_block_hash`.
|
||||
* `aggregate_sig` verification:
|
||||
* Let `participants = get_attestation_participants(state, obj.data, obj.attester_bitfield)`
|
||||
* Let `group_public_key = BLSAddPubkeys([state.validators[v].pubkey for v in participants])`
|
||||
* Check `BLSVerify(pubkey=group_public_key, msg=obj.data, sig=aggregate_sig, domain=get_domain(state.fork_data, slot, DOMAIN_ATTESTATION))`.
|
||||
* [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.
|
||||
* Append `ProcessedAttestation(data=obj.data, attester_bitfield=obj.attester_bitfield, poc_bitfield=obj.poc_bitfield, slot_included=block.slot)` to `state.pending_attestations`.
|
||||
|
||||
### Verify proposer signature
|
||||
|
||||
* 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, domain=get_domain(state.fork_data, block.slot, DOMAIN_PROPOSAL))` passes.
|
||||
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=state.validators[get_beacon_proposer_index(state, block.slot)].pubkey, data=proposal_hash, sig=block.proposer_signature, domain=get_domain(state.fork_data, block.slot, DOMAIN_PROPOSAL))` passes.
|
||||
|
||||
### Verify and process RANDAO reveal
|
||||
|
||||
|
|
@ -922,16 +959,16 @@ First run the following state transition to update `randao_skips` variables for
|
|||
|
||||
```python
|
||||
for slot in range(parent.slot + 1, block.slot):
|
||||
proposer = get_beacon_proposer(state, slot)
|
||||
proposer.randao_skips += 1
|
||||
proposer_index = get_beacon_proposer_index(state, slot)
|
||||
state.validators[proposer_index].randao_skips += 1
|
||||
```
|
||||
|
||||
Then:
|
||||
|
||||
* Let `repeat_hash(x, n) = x if n == 0 else repeat_hash(hash(x), n-1)`.
|
||||
* Let `V = get_beacon_proposer(state, block.slot)`.
|
||||
* Verify that `repeat_hash(block.randao_reveal, V.randao_skips + 1) == V.randao_commitment`
|
||||
* Set `state.randao_mix = xor(state.randao_mix, block.randao_reveal)`, `V.randao_commitment = block.randao_reveal`, `V.randao_skips = 0`
|
||||
* Let `proposer = state.validators[get_beacon_proposer_index(state, block.slot)]`.
|
||||
* Verify that `repeat_hash(block.randao_reveal, proposer.randao_skips + 1) == proposer.randao_commitment`
|
||||
* Set `state.randao_mix = xor(state.randao_mix, block.randao_reveal)`, `proposer.randao_commitment = block.randao_reveal`, `proposer.randao_skips = 0`
|
||||
|
||||
### Process PoW receipt root
|
||||
|
||||
|
|
@ -1026,60 +1063,91 @@ Verify that `deposit_data.msg_value == DEPOSIT_SIZE` and `block.slot - (deposit_
|
|||
|
||||
Run `add_validator(state, pubkey=deposit_data.deposit_params.pubkey, proof_of_possession=deposit_data.deposit_params.proof_of_possession, withdrawal_credentials=deposit_data.deposit_params.withdrawal_credentials, randao_commitment=deposit_data.deposit_params.randao_commitment, status=PENDING_ACTIVATION, current_slot=block.slot)`.
|
||||
|
||||
## State recalculations (every `CYCLE_LENGTH` slots)
|
||||
## Cycle boundary processing
|
||||
|
||||
Repeat while `slot - last_state_recalculation_slot >= CYCLE_LENGTH`:
|
||||
Repeat the steps in this section while `block.slot - last_state_recalculation_slot >= CYCLE_LENGTH`. For simplicity, we'll use `s` as `last_state_recalculation_slot`.
|
||||
|
||||
_Note: `last_state_recalculation_slot` will always be a multiple of `CYCLE_LENGTH`. In the "happy case", this process will trigger, and loop once, every time `block.slot` passes a new exact multiple of `CYCLE_LENGTH`, but if a chain skips more than an entire cycle then the loop may run multiple times, incrementing `last_state_recalculation_slot` by `CYCLE_LENGTH` with each iteration._
|
||||
|
||||
#### Precomputation
|
||||
|
||||
All validators:
|
||||
|
||||
* Let `active_validators = [state.validators[i] for i in get_active_validator_indices(state.validators)]`.
|
||||
* Let `total_balance = sum([balance_at_stake(v) for v in active_validators])`. Let `total_balance_in_eth = total_balance // GWEI_PER_ETH`.
|
||||
* Let `reward_quotient = BASE_REWARD_QUOTIENT * int_sqrt(total_balance_in_eth)`. (The per-slot maximum interest rate is `2/reward_quotient`.)
|
||||
|
||||
Validators justifying the cycle boundary block at the start of the current cycle:
|
||||
|
||||
* Let `this_cycle_attestations = [a for a in state.pending_attestations if s <= a.data.slot < s + CYCLE_LENGTH]`. (note: this is the set of attestations _of slots in the cycle `s...s+CYCLE_LENGTH-1`_, not attestations _that got included in the chain during the cycle `s...s+CYCLE_LENGTH-1`_)
|
||||
* Let `this_cycle_boundary_attestations = [a for a in this_cycle_attestations if a.data.cycle_boundary_hash == get_block_hash(state, block, s) and a.justified_slot == state.justification_source]`.
|
||||
* Let `this_cycle_boundary_attesters` be the union of the validator index sets given by `[get_attestation_participants(state, a.data, a.attester_bitfield) for a in this_cycle_boundary_attestations]`.
|
||||
* Let `this_cycle_boundary_attesting_balance = sum([balance_at_stake(v) for v in this_cycle_boundary_attesters])`.
|
||||
|
||||
Validators justifying the cycle boundary block at the start of the previous cycle:
|
||||
|
||||
* Let `prev_cycle_attestations = [a for a in state.pending_attestations if s - CYCLE_LENGTH <= a.slot < s]`.
|
||||
* Let `prev_cycle_boundary_attestations = [a for a in this_cycle_attestations + prev_cycle_attestations if a.cycle_boundary_hash == get_block_hash(state, block, s - CYCLE_LENGTH) and a.justified_slot == state.prev_cycle_justification_source]`.
|
||||
* Let `prev_cycle_boundary_attesters` be the union of the validator index sets given by `[get_attestation_participants(state, a.data, a.attester_bitfield) for a in prev_cycle_boundary_attestations]`.
|
||||
* Let `prev_cycle_boundary_attesting_balance = sum([balance_at_stake(v) for v in prev_cycle_boundary_attesters])`.
|
||||
|
||||
For every `ShardAndCommittee` object `obj` in `shard_and_committee_for_slots`, let:
|
||||
|
||||
|
||||
* `attesting_validators(obj, shard_block_hash)` be the union of the validator index sets given by `[get_attestation_participants(state, a.data, a.attester_bitfield) for a in this_cycle_attestations + prev_cycle_attestations if a.shard == obj.shard and a.shard_block_hash == shard_block_hash]`
|
||||
* `attesting_validators(obj)` be equal to `attesting_validators(obj, shard_block_hash)` for the value of `shard_block_hash` such that `sum([balance_at_stake(v) for v in attesting_validators(obj, shard_block_hash)])` is maximized (ties broken by favoring lower `shard_block_hash` values)
|
||||
* `total_attesting_balance(obj)` be the sum of the balances-at-stake of `attesting_validators(obj)`
|
||||
* `winning_hash(obj)` be the winning `shard_block_hash` value
|
||||
* `total_balance(obj) = sum([balance_at_stake(v) for v in obj.committee])`
|
||||
|
||||
Let `inclusion_slot(v)` equal `a.slot_included` for the attestation `a` where `v` is in `get_attestation_participants(state, a.data, a.attester_bitfield)`, and `inclusion_distance(v) = a.slot_included - a.data.slot` for the same attestation. We define a function `adjust_for_inclusion_distance(magnitude, dist)` which adjusts the reward of an attestation based on how long it took to get included (the longer, the lower the reward). Returns a value between 0 and `magnitude`
|
||||
|
||||
```python
|
||||
def adjust_for_inclusion_distance(magnitude: int, dist: int) -> int:
|
||||
return magnitude // 2 + (magnitude // 2) * MIN_ATTESTATION_INCLUSION_DELAY // dist
|
||||
```
|
||||
|
||||
For any validator `v`, `base_reward(v) = balance_at_stake(v) // reward_quotient`
|
||||
|
||||
#### Adjust justified slots and crosslink status
|
||||
|
||||
For every slot `s` in the range `last_state_recalculation_slot - CYCLE_LENGTH ... last_state_recalculation_slot - 1`:
|
||||
* Set `state.justified_slot_bitfield = (state.justified_slot_bitfield * 2) % 2**64`.
|
||||
* If `3 * prev_cycle_boundary_attesting_balance >= 2 * total_balance` then set `state.justified_slot_bitfield &= 2` (ie. flip the second lowest bit to 1) and `new_justification_source = s - CYCLE_LENGTH`.
|
||||
* If `3 * this_cycle_boundary_attesting_balance >= 2 * total_balance` then set `state.justified_slot_bitfield &= 1` (ie. flip the lowest bit to 1) and `new_justification_source = s`.
|
||||
* If `state.justification_source == s - CYCLE_LENGTH and state.justified_slot_bitfield % 4 == 3`, set `last_finalized_slot = justification_source`.
|
||||
* If `state.justification_source == s - CYCLE_LENGTH - CYCLE_LENGTH and state.justified_slot_bitfield % 8 == 7`, set `state.last_finalized_slot = state.justification_source`.
|
||||
* If `state.justification_source == s - CYCLE_LENGTH - 2 * CYCLE_LENGTH and state.justified_slot_bitfield % 16 in (15, 14)`, set `last_finalized_slot = justification_source`.
|
||||
* Set `state.prev_cycle_justification_source = state.justification_source` and if `new_justification_source` has been set, set `state.justification_source = new_justification_source`.
|
||||
|
||||
* Let `total_balance` be the total balance of active validators.
|
||||
* Let `total_balance_attesting_at_s` be the total balance of validators that attested to the beacon block at slot `s`.
|
||||
* If `3 * total_balance_attesting_at_s >= 2 * total_balance` set `last_justified_slot = max(last_justified_slot, s)` and `justified_streak += 1`. Otherwise set `justified_streak = 0`.
|
||||
* If `justified_streak >= CYCLE_LENGTH + 1` set `last_finalized_slot = max(last_finalized_slot, s - CYCLE_LENGTH - 1)`.
|
||||
For every `ShardAndCommittee` object `obj`:
|
||||
|
||||
For every `(shard, shard_block_hash)` tuple:
|
||||
|
||||
* Let `total_balance_attesting_to_h` be the total balance of validators that attested to the shard block with hash `shard_block_hash`.
|
||||
* Let `total_committee_balance` be the total balance in the committee of validators that could have attested to the shard block with hash `shard_block_hash`.
|
||||
* If `3 * total_balance_attesting_to_h >= 2 * total_committee_balance`, set `crosslinks[shard] = CrosslinkRecord(slot=last_state_recalculation_slot + CYCLE_LENGTH, hash=shard_block_hash)`.
|
||||
* If `3 * total_attesting_balance(obj) >= 2 * total_balance(obj)`, set `crosslinks[shard] = CrosslinkRecord(slot=last_state_recalculation_slot + CYCLE_LENGTH, hash=winning_hash(obj))`.
|
||||
|
||||
#### Balance recalculations related to FFG rewards
|
||||
|
||||
Note: When applying penalties in the following balance recalculations implementers should make sure the `uint64` does not underflow.
|
||||
|
||||
* Let `total_balance` be the total balance of active validators.
|
||||
* Let `total_balance_in_eth = total_balance // GWEI_PER_ETH`.
|
||||
* Let `reward_quotient = BASE_REWARD_QUOTIENT * int_sqrt(total_balance_in_eth)`. (The per-slot maximum interest rate is `1/reward_quotient`.)
|
||||
* Let `quadratic_penalty_quotient = SQRT_E_DROP_TIME**2`. (The portion lost by offline validators after `D` slots is about `D*D/2/quadratic_penalty_quotient`.)
|
||||
* Let `time_since_finality = block.slot - last_finalized_slot`.
|
||||
* Let `quadratic_penalty_quotient = SQRT_E_DROP_TIME**2`. (The portion lost by offline validators after `D` cycles is about `D*D/2/quadratic_penalty_quotient`.)
|
||||
* Let `time_since_finality = block.slot - state.last_finalized_slot`.
|
||||
|
||||
For every slot `s` in the range `last_state_recalculation_slot - CYCLE_LENGTH ... last_state_recalculation_slot - 1`:
|
||||
Case 1: `time_since_finality <= 4 * CYCLE_LENGTH`:
|
||||
|
||||
* Let `total_balance_participating` be the total balance of validators that voted for the canonical beacon block at slot `s`. In the normal case every validator will be in one of the `CYCLE_LENGTH` slots following slot `s` and so can vote for a block at slot `s`.
|
||||
* Let `B` be the balance of any given validator whose balance we are adjusting, not including any balance changes from this round of state recalculation.
|
||||
* If `time_since_finality <= 3 * CYCLE_LENGTH` adjust the balance of participating and non-participating validators as follows:
|
||||
* Participating validators gain `B // reward_quotient * (2 * total_balance_participating - total_balance) // total_balance`. (Note that this value may be negative.)
|
||||
* Non-participating validators lose `B // reward_quotient`.
|
||||
* Otherwise:
|
||||
* Participating validators gain nothing.
|
||||
* Non-participating validators lose `B // reward_quotient + B * time_since_finality // quadratic_penalty_quotient`.
|
||||
* Any validator `v` in `prev_cycle_boundary_attesters` gains `adjust_for_inclusion_distance(base_reward(v) * prev_cycle_boundary_attesting_balance // total_balance, inclusion_distance(v))`.
|
||||
* Any active validator `v` not in `prev_cycle_boundary_attesters` loses `base_reward(v)`.
|
||||
|
||||
In addition, validators with `status == PENALIZED` lose `B // reward_quotient + B * time_since_finality // quadratic_penalty_quotient`.
|
||||
Case 2: `time_since_finality > 4 * CYCLE_LENGTH`:
|
||||
|
||||
* Any validator in `prev_cycle_boundary_attesters` sees their balance unchanged.
|
||||
* Any active validator `v` not in `prev_cycle_boundary_attesters`, and any validator with `status == PENALIZED`, loses `base_reward(v) + balance_at_stake(v) * time_since_finality // quadratic_penalty_quotient`.
|
||||
|
||||
For each `v` in `prev_cycle_boundary_attesters`, we determine the proposer `proposer_index = get_beacon_proposer_index(state, inclusion_slot(v))` and set `state.validators[proposer_index].balance += base_reward(v) // INCLUDER_REWARD_SHARE_QUOTIENT`.
|
||||
|
||||
#### Balance recalculations related to crosslink rewards
|
||||
|
||||
For every shard number `shard` for which a crosslink committee exists in the cycle prior to the most recent cycle (`last_state_recalculation_slot - CYCLE_LENGTH ... last_state_recalculation_slot - 1`), let `V` be the corresponding validator set. Let `B` be the balance of any given validator whose balance we are adjusting, not including any balance changes from this round of state recalculation. For each `shard`, `V`:
|
||||
For every `ShardAndCommittee` object `obj` in `shard_and_committee_for_slots[:CYCLE_LENGTH]` (ie. the objects corresponding to the cycle before the current one), for each `v` in `[state.validators[index] for index in obj.committee]`, adjust balances as follows:
|
||||
|
||||
* Let `total_balance_of_v` be the total balance of `V`.
|
||||
* Let `winning_shard_hash` be the hash that the largest total deposits signed for the `shard` during the cycle.
|
||||
* Define a "participating validator" as a member of `V` that signed a crosslink of `winning_shard_hash`.
|
||||
* Let `total_balance_of_v_participating` be the total balance of the subset of `V` that participated.
|
||||
* Let `time_since_last_confirmation = block.slot - crosslinks[shard].slot`.
|
||||
* Adjust balances as follows:
|
||||
* Participating validators gain `B // reward_quotient * (2 * total_balance_of_v_participating - total_balance_of_v) // total_balance_of_v`.
|
||||
* Non-participating validators lose `B // reward_quotient`.
|
||||
* If `v in attesting_validators(obj)`, `v.balance += adjust_for_inclusion_distance(base_reward(v) * total_attesting_balance(obj) // total_balance(obj)), inclusion_distance(v))`.
|
||||
* If `v not in attesting_validators(obj)`, `v.balance -= base_reward(v)`.
|
||||
|
||||
#### PoW chain related rules
|
||||
|
||||
|
|
@ -1088,11 +1156,10 @@ If `last_state_recalculation_slot % POW_RECEIPT_ROOT_VOTING_PERIOD == 0`, then:
|
|||
* If for any `x` in `state.candidate_pow_receipt_root`, `x.votes * 2 >= POW_RECEIPT_ROOT_VOTING_PERIOD` set `state.processed_pow_receipt_root = x.receipt_root`.
|
||||
* Set `state.candidate_pow_receipt_roots = []`.
|
||||
|
||||
### Validator set change
|
||||
#### Validator set change
|
||||
|
||||
A validator set change can happen after a state recalculation if all of the following criteria are satisfied:
|
||||
A validator set change can happen if all of the following criteria are satisfied:
|
||||
|
||||
* `block.slot - state.validator_set_change_slot >= MIN_VALIDATOR_SET_CHANGE_INTERVAL`
|
||||
* `last_finalized_slot > state.validator_set_change_slot`
|
||||
* For every shard number `shard` in `shard_and_committee_for_slots`, `crosslinks[shard].slot > state.validator_set_change_slot`
|
||||
|
||||
|
|
@ -1103,7 +1170,7 @@ def change_validators(validators: List[ValidatorRecord], current_slot: int) -> N
|
|||
# The active validator set
|
||||
active_validators = get_active_validator_indices(validators)
|
||||
# The total balance of active validators
|
||||
total_balance = sum([v.balance for i, v in enumerate(validators) if i in active_validators])
|
||||
total_balance = sum([balance_at_stake(v) for i, v in enumerate(validators) if i in active_validators])
|
||||
# The maximum total wei that can deposit+withdraw
|
||||
max_allowable_change = max(
|
||||
2 * DEPOSIT_SIZE * GWEI_PER_ETH,
|
||||
|
|
@ -1124,7 +1191,7 @@ def change_validators(validators: List[ValidatorRecord], current_slot: int) -> N
|
|||
if validators[i].status == PENDING_EXIT:
|
||||
validators[i].status = PENDING_WITHDRAW
|
||||
validators[i].last_status_change_slot = current_slot
|
||||
total_changed += validators[i].balance
|
||||
total_changed += balance_at_stake(validators[i])
|
||||
state.validator_set_delta_hash_chain = get_new_validator_set_delta_hash_chain(
|
||||
validator_set_delta_hash_chain=state.validator_set_delta_hash_chain,
|
||||
index=i,
|
||||
|
|
@ -1150,45 +1217,32 @@ def change_validators(validators: List[ValidatorRecord], current_slot: int) -> N
|
|||
withdrawable_validators = sorted(filter(withdrawable, validators), key=lambda v: v.exit_seq)
|
||||
for v in withdrawable_validators[:WITHDRAWALS_PER_CYCLE]:
|
||||
if v.status == PENALIZED:
|
||||
v.balance -= v.balance * min(total_penalties * 3, total_balance) // total_balance
|
||||
v.balance -= balance_at_stake(v) * min(total_penalties * 3, total_balance) // total_balance
|
||||
v.status = WITHDRAWN
|
||||
v.last_status_change_slot = current_slot
|
||||
|
||||
withdraw_amount = v.balance
|
||||
...
|
||||
# STUB: withdraw to shard chain
|
||||
```
|
||||
|
||||
* Set `state.validator_set_change_slot = state.last_state_recalculation_slot`
|
||||
* Set `shard_and_committee_for_slots[:CYCLE_LENGTH] = shard_and_committee_for_slots[CYCLE_LENGTH:]`
|
||||
* Let `next_start_shard = (shard_and_committee_for_slots[-1][-1].shard + 1) % SHARD_COUNT`
|
||||
* Set `shard_and_committee_for_slots[CYCLE_LENGTH:] = get_new_shuffling(state.next_shuffling_seed, validators, next_start_shard)`
|
||||
And perform the following updates to the `state`:
|
||||
|
||||
* Set `state.validator_set_change_slot = s + CYCLE_LENGTH`
|
||||
* Set `state.shard_and_committee_for_slots[:CYCLE_LENGTH] = state.shard_and_committee_for_slots[CYCLE_LENGTH:]`
|
||||
* Let `state.next_start_shard = (shard_and_committee_for_slots[-1][-1].shard + 1) % SHARD_COUNT`
|
||||
* Set `state.shard_and_committee_for_slots[CYCLE_LENGTH:] = get_new_shuffling(state.next_shuffling_seed, validators, next_start_shard)`
|
||||
* Set `state.next_shuffling_seed = state.randao_mix`
|
||||
|
||||
### If a validator set change does NOT happen
|
||||
#### If a validator set change does NOT happen
|
||||
|
||||
* Set `shard_and_committee_for_slots[:CYCLE_LENGTH] = shard_and_committee_for_slots[CYCLE_LENGTH:]`
|
||||
* Set `state.shard_and_committee_for_slots[:CYCLE_LENGTH] = state.shard_and_committee_for_slots[CYCLE_LENGTH:]`
|
||||
* Let `time_since_finality = block.slot - state.validator_set_change_slot`
|
||||
* Let `start_shard = shard_and_committee_for_slots[0][0].shard`
|
||||
* If `time_since_finality * CYCLE_LENGTH <= MIN_VALIDATOR_SET_CHANGE_INTERVAL` or `time_since_finality` is an exact power of 2, set `shard_and_committee_for_slots[CYCLE_LENGTH:] = get_new_shuffling(state.next_shuffling_seed, validators, start_shard)` and set `state.next_shuffling_seed = state.randao_mix`. Note that `start_shard` is not changed from last cycle.
|
||||
* Let `start_shard = state.shard_and_committee_for_slots[0][0].shard`
|
||||
* If `time_since_finality * CYCLE_LENGTH <= MIN_VALIDATOR_SET_CHANGE_INTERVAL` or `time_since_finality` is an exact power of 2, set `state.shard_and_committee_for_slots[CYCLE_LENGTH:] = get_new_shuffling(state.next_shuffling_seed, validators, start_shard)` and set `state.next_shuffling_seed = state.randao_mix`. Note that `start_shard` is not changed from last cycle.
|
||||
|
||||
#### Finally...
|
||||
#### Proposer reshuffling
|
||||
|
||||
* Remove all attestation records older than slot `state.last_state_recalculation_slot`
|
||||
* 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, block, penalize=False, current_slot=block.slot)`
|
||||
* Set `state.recent_block_hashes = state.recent_block_hashes[CYCLE_LENGTH:]`
|
||||
* Set `state.last_state_recalculation_slot += CYCLE_LENGTH`
|
||||
|
||||
For any validator that was added or removed from the active validator list during this state recalculation:
|
||||
|
||||
* If the validator was removed, remove their index from the `persistent_committees` and remove any `ShardReassignmentRecord`s containing their index from `persistent_committee_reassignments`.
|
||||
* If the validator was added with index `validator_index`:
|
||||
* let `assigned_shard = hash(state.randao_mix + bytes8(validator_index)) % SHARD_COUNT`
|
||||
* let `reassignment_record = ShardReassignmentRecord(validator_index=validator_index, shard=assigned_shard, slot=block.slot + SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD)`
|
||||
* Append `reassignment_record` to the end of `persistent_committee_reassignments`
|
||||
|
||||
Now run the following code to reshuffle a few proposers:
|
||||
Run the following code to update the shard proposer set:
|
||||
|
||||
```python
|
||||
active_validator_indices = get_active_validator_indices(validators)
|
||||
|
|
@ -1201,11 +1255,11 @@ for i in range(num_validators_to_reshuffle):
|
|||
shard_reassignment_record = ShardReassignmentRecord(
|
||||
validator_index=vid,
|
||||
shard=new_shard,
|
||||
slot=block.slot + SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD
|
||||
slot=s + SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD
|
||||
)
|
||||
state.persistent_committee_reassignments.append(shard_reassignment_record)
|
||||
|
||||
while len(state.persistent_committee_reassignments) > 0 and state.persistent_committee_reassignments[0].slot <= block.slot:
|
||||
while len(state.persistent_committee_reassignments) > 0 and state.persistent_committee_reassignments[0].slot <= s:
|
||||
rec = state.persistent_committee_reassignments.pop(0)
|
||||
for committee in state.persistent_committees:
|
||||
if rec.validator_index in committee:
|
||||
|
|
@ -1215,6 +1269,13 @@ while len(state.persistent_committee_reassignments) > 0 and state.persistent_com
|
|||
state.persistent_committees[rec.shard].append(rec.validator_index)
|
||||
```
|
||||
|
||||
#### Finally...
|
||||
|
||||
* Remove all attestation records older than slot `s`
|
||||
* 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.last_state_recalculation_slot += CYCLE_LENGTH`
|
||||
|
||||
# Appendix
|
||||
## Appendix A - Hash function
|
||||
|
||||
|
|
|
|||
|
|
@ -51,10 +51,10 @@ A `ShardBlock` object has the following fields:
|
|||
# State root (placeholder for now)
|
||||
'state_root': 'hash32',
|
||||
# Block signature
|
||||
'signature': ['uint256'],
|
||||
'signature': ['uint384'],
|
||||
# Attestation
|
||||
'attester_bitfield': 'bytes',
|
||||
'aggregate_sig': ['uint256'],
|
||||
'aggregate_sig': ['uint384'],
|
||||
}
|
||||
```
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue