1390 lines
64 KiB
Markdown
1390 lines
64 KiB
Markdown
# Ethereum 2.0 Phase 0 -- The Beacon Chain
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**NOTICE**: This document is a work-in-progress for researchers and implementers. It reflects recent spec changes and takes precedence over the [Python proof-of-concept implementation](https://github.com/ethereum/beacon_chain).
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## Table of contents
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* [Ethereum 2.0 Phase 0 -- The Beacon Chain](#ethereum-20-phase-0----the-beacon-chain)
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* [Table of contents](#table-of-contents)
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* [Introduction](#introduction)
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* [Notation](#notation)
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* [Terminology](#terminology)
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* [Constants](#constants)
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* [PoW chain registration contract](#pow-chain-registration-contract)
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* [Contract code in Vyper](#contract-code-in-vyper)
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* [Data structures](#data-structures)
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* [Beacon chain blocks](#beacon-chain-blocks)
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* [Beacon chain state](#beacon-chain-state)
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* [Beacon chain processing](#beacon-chain-processing)
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* [Beacon chain fork choice rule](#beacon-chain-fork-choice-rule)
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* [Beacon chain state transition function](#beacon-chain-state-transition-function)
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* [Helper functions](#helper-functions)
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* [On startup](#on-startup)
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* [Routine for adding a validator](#routine-for-adding-a-validator)
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* [Routine for removing a validator](#routine-for-removing-a-validator)
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* [Per-block processing](#per-block-processing)
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* [Verify attestations](#verify-attestations)
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* [Verify proposer signature](#verify-proposer-signature)
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* [Verify and process RANDAO reveal](#verify-and-process-randao-reveal)
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* [Process PoW receipt root](#process-pow-receipt-root)
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* [Process penalties, logouts and other special objects](#process-penalties-logouts-and-other-special-objects)
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* [LOGOUT](#logout)
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* [CASPER_SLASHING](#casper_slashing)
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* [PROPOSER_SLASHING](#proposer_slashing)
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* [DEPOSIT_PROOF](#deposit_proof)
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* [Cycle boundary processing](#cycle-boundary-processing)
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* [Precomputation](#precomputation)
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* [Adjust justified slots and crosslink status](#adjust-justified-slots-and-crosslink-status)
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* [Balance recalculations related to FFG rewards](#balance-recalculations-related-to-ffg-rewards)
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* [Balance recalculations related to crosslink rewards](#balance-recalculations-related-to-crosslink-rewards)
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* [PoW chain related rules](#pow-chain-related-rules)
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* [Validator set change](#validator-set-change)
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* [If a validator set change does NOT happen](#if-a-validator-set-change-does-not-happen)
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* [Proposer reshuffling](#proposer-reshuffling)
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* [Finally...](#finally)
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* [Appendix](#appendix)
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* [Appendix A - Hash function](#appendix-a---hash-function)
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* [Copyright](#copyright)
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## Introduction
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This document represents the specification for Phase 0 of Ethereum 2.0 -- The Beacon Chain.
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At the core of Ethereum 2.0 is a system chain called the "beacon chain". The beacon chain stores and manages the set of active proof-of-stake validators. In the initial deployment phases of Ethereum 2.0 the only mechanism to become a validator is to make a fixed-size one-way ETH deposit to a registration contract on the Ethereum 1.0 PoW chain. Induction as a validator happens after registration transaction receipts are processed by the beacon chain and after a queuing process. Deregistration is either voluntary or done forcibly as a penalty for misbehavior.
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The primary source of load on the beacon chain are "attestations". Attestations simultaneously attest to a shard block and a corresponding beacon chain block. A sufficient number of attestations for the same shard block create a "crosslink", confirming the shard segment up to that shard block into the beacon chain. Crosslinks also serve as infrastructure for asynchronous cross-shard communication.
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## Notation
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Unless otherwise indicated, code appearing in `this style` is to be interpreted as an algorithm defined in Python. Implementations may implement such algorithms using any code and programming language desired as long as the behavior is identical to that of the algorithm provided.
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## Terminology
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* **Validator** - a participant in the Casper/sharding consensus system. You can become one by depositing 32 ETH into the Casper mechanism.
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* **Active validator set** - those validators who are currently participating, and which the Casper mechanism looks to produce and attest to blocks, crosslinks and other consensus objects.
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* **Committee** - a (pseudo-) randomly sampled subset of the active validator set. When a committee is referred to collectively, as in "this committee attests to X", this is assumed to mean "some subset of that committee that contains enough validators that the protocol recognizes it as representing the committee".
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* **Proposer** - the validator that creates a beacon chain block
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* **Attester** - a validator that is part of a committee that needs to sign off on a beacon chain block while simultaneously creating a link (crosslink) to a recent shard block on a particular shard chain.
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* **Beacon chain** - the central PoS chain that is the base of the sharding system.
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* **Shard chain** - one of the chains on which user transactions take place and account data is stored.
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* **Crosslink** - a set of signatures from a committee attesting to a block in a shard chain, which can be included into the beacon chain. Crosslinks are the main means by which the beacon chain "learns about" the updated state of shard chains.
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* **Slot** - a period of `SLOT_DURATION` seconds, during which one proposer has the ability to create a beacon chain block and some attesters have the ability to make attestations
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* **Cycle** - a span of slots during which all validators get exactly one chance to make an attestation
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* **Finalized**, **justified** - see Casper FFG finalization here: https://arxiv.org/abs/1710.09437
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* **Withdrawal period** - number of slots between a validator exit and the validator balance being withdrawable
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* **Genesis time** - the Unix time of the genesis beacon chain block at slot 0
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## Constants
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| Constant | Value | Unit | Approximation |
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| --- | --- | :---: | - |
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| `SHARD_COUNT` | 2**10 (= 1,024)| shards |
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| `DEPOSIT_SIZE` | 2**5 (= 32) | ETH |
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| `MIN_TOPUP_SIZE` | 1 | ETH |
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| `MIN_ONLINE_DEPOSIT_SIZE` | 2**4 (= 16) | ETH |
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| `GWEI_PER_ETH` | 10**9 | Gwei/ETH |
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| `DEPOSIT_CONTRACT_ADDRESS` | **TBD** | - |
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| `DEPOSITS_FOR_CHAIN_START` | 2**14 (= 16,384) | deposits |
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| `TARGET_COMMITTEE_SIZE` | 2**8 (= 256) | validators |
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| `SLOT_DURATION` | 6 | seconds |
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| `CYCLE_LENGTH` | 2**6 (= 64) | slots | ~6 minutes |
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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**11 (= 2,048) | 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**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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| `INITIAL_FORK_VERSION` | 0 | - |
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**Notes**
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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 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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| Name | Value |
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| - | :-: |
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| `PENDING_ACTIVATION` | `0` |
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| `ACTIVE` | `1` |
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| `PENDING_EXIT` | `2` |
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| `PENDING_WITHDRAW` | `3` |
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| `WITHDRAWN` | `4` |
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| `PENALIZED` | `127` |
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**Special record types**
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| Name | Value | Maximum count |
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| - | :-: | :-: |
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| `LOGOUT` | `0` | `16` |
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| `CASPER_SLASHING` | `1` | `16` |
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| `PROPOSER_SLASHING` | `2` | `16` |
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| `DEPOSIT_PROOF` | `3` | `16` |
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**Validator set delta flags**
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| Name | Value |
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| - | :-: |
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| `ENTRY` | `0` |
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| `EXIT` | `1` |
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**Domains for BLS signatures**
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| Name | Value |
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| - | :-: |
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| `DOMAIN_DEPOSIT` | `0` |
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| `DOMAIN_ATTESTATION` | `1` |
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| `DOMAIN_PROPOSAL` | `2` |
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| `DOMAIN_LOGOUT` | `3` |
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## PoW chain registration contract
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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.
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The registration contract emits a log with the various arguments for consumption by the beacon chain. It does not do validation, pushing the registration logic to the beacon chain. In particular, the proof of possession (based on the BLS12-381 curve) is not verified by the registration contract.
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### Contract code in Vyper
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The beacon chain is initialized when a condition is met inside a contract on the existing PoW chain. This contract's code in Vyper is as follows:
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```python
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DEPOSITS_FOR_CHAIN_START: constant(uint256) = 2**14
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DEPOSIT_SIZE: constant(uint256) = 32 # ETH
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MIN_TOPUP_SIZE: constant(uint256) = 1 # ETH
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GWEI_PER_ETH: constant(uint256) = 10**9
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POW_CONTRACT_MERKLE_TREE_DEPTH: constant(uint256) = 32
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SECONDS_PER_DAY: constant(uint256) = 86400
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HashChainValue: event({previous_receipt_root: bytes32, data: bytes[2064], total_deposit_count: uint256})
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ChainStart: event({receipt_root: bytes32, time: bytes[8]})
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receipt_tree: bytes32[uint256]
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total_deposit_count: uint256
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@payable
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@public
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def deposit(deposit_params: bytes[2048]):
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index: uint256 = self.total_deposit_count + 2**POW_CONTRACT_MERKLE_TREE_DEPTH
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msg_gwei_bytes8: bytes[8] = slice(concat("", convert(msg.value / GWEI_PER_ETH, bytes32)), start=24, len=8)
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timestamp_bytes8: bytes[8] = slice(concat("", convert(block.timestamp, bytes32)), start=24, len=8)
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deposit_data: bytes[2064] = concat(msg_gwei_bytes8, timestamp_bytes8, deposit_params)
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log.HashChainValue(self.receipt_tree[1], deposit_data, self.total_deposit_count)
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self.receipt_tree[index] = sha3(deposit_data)
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for i in range(32): # POW_CONTRACT_MERKLE_TREE_DEPTH (range of constant var not yet supported)
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index /= 2
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self.receipt_tree[index] = sha3(concat(self.receipt_tree[index * 2], self.receipt_tree[index * 2 + 1]))
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assert msg.value >= as_wei_value(MIN_TOPUP_SIZE, "ether")
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assert msg.value <= as_wei_value(DEPOSIT_SIZE, "ether")
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if msg.value == as_wei_value(DEPOSIT_SIZE, "ether"):
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self.total_deposit_count += 1
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if self.total_deposit_count == DEPOSITS_FOR_CHAIN_START:
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timestamp_day_boundary: uint256 = as_unitless_number(block.timestamp) - as_unitless_number(block.timestamp) % SECONDS_PER_DAY + SECONDS_PER_DAY
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timestamp_day_boundary_bytes8: bytes[8] = slice(concat("", convert(timestamp_day_boundary, bytes32)), start=24, len=8)
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log.ChainStart(self.receipt_tree[1], timestamp_day_boundary_bytes8)
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@public
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@constant
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def get_receipt_root() -> bytes32:
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return self.receipt_tree[1]
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```
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The contract is at address `DEPOSIT_CONTRACT_ADDRESS`. When a user wishes to become a validator by moving their ETH from the 1.0 chain to the 2.0 chain, they should call the `deposit` function, sending along `DEPOSIT_SIZE` ETH and providing as `deposit_params` a SimpleSerialize'd `DepositParams` object of the form:
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```python
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{
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'pubkey': 'int256',
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'proof_of_possession': ['int256'],
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'withdrawal_credentials`: 'hash32',
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'randao_commitment`: 'hash32'
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}
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```
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If the user wishes to deposit more than `DEPOSIT_SIZE` ETH, they would need to make multiple calls. When the contract publishes a `ChainStart` log, this initializes the chain, calling `on_startup` with:
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* `initial_validator_entries` equal to the list of data records published as HashChainValue logs so far, in the order in which they were published (oldest to newest).
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* `genesis_time` equal to the `time` value published in the log
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* `processed_pow_receipt_root` equal to the `receipt_root` value published in the log
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## Data structures
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### Beacon chain blocks
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A `BeaconBlock` 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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# Proposer RANDAO reveal
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'randao_reveal': 'hash32',
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# Recent PoW receipt root
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'candidate_pow_receipt_root': 'hash32',
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# Skip list of previous beacon block hashes
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# i'th item is the most recent ancestor whose slot is a multiple of 2**i for i = 0, ..., 31
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'ancestor_hashes': ['hash32'],
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# State root
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'state_root': 'hash32',
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# Attestations
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'attestations': [AttestationRecord],
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# Specials (e.g. logouts, penalties)
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'specials': [SpecialRecord],
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# Proposer signature
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'proposer_signature': ['uint384'],
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}
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```
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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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# 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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# 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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}
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```
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A `ProposalSignedData` 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 (or `2**64 - 1` for beacon chain)
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'shard': 'uint64',
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# Block hash
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'block_hash': 'hash32',
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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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{
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# Kind
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'kind': 'uint64',
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# Data
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'data': 'bytes'
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}
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```
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### Beacon chain state
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The `BeaconState` has the following fields:
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```python
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{
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# Slot of last validator set change
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'validator_set_change_slot': 'uint64',
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# List of validators
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'validators': [ValidatorRecord],
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# Most recent crosslink for each shard
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'crosslinks': [CrosslinkRecord],
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# Last cycle-boundary state recalculation
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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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# 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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'persistent_committees': [['uint24']],
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'persistent_committee_reassignments': [ShardReassignmentRecord],
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# Randao seed used for next shuffling
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'next_shuffling_seed': 'hash32',
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# Total deposits penalized in the given withdrawal period
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'deposits_penalized_in_period': ['uint64'],
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# Hash chain of validator set changes (for light clients to easily track deltas)
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'validator_set_delta_hash_chain': 'hash32'
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# Current sequence number for withdrawals
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'current_exit_seq': 'uint64',
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# Genesis time
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'genesis_time': 'uint64',
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# PoW receipt root
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'processed_pow_receipt_root': 'hash32',
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'candidate_pow_receipt_roots': [CandidatePoWReceiptRootRecord],
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# Parameters relevant to hard forks / versioning.
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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': [ProcessedAttestation],
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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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'randao_mix': 'hash32'
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}
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```
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A `ValidatorRecord` has the following fields:
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```python
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{
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# BLS public key
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'pubkey': 'uint384',
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# Withdrawal credentials
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'withdrawal_credentials': 'hash32',
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# RANDAO commitment
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'randao_commitment': 'hash32',
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# Slot the proposer has skipped (ie. layers of RANDAO expected)
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'randao_skips': 'uint64',
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# Balance in Gwei
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'balance': 'uint64',
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# Status code
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'status': 'uint64',
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# Slot when validator last changed status (or 0)
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'last_status_change_slot': 'uint64'
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# Sequence number when validator exited (or 0)
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'exit_seq': 'uint64'
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}
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```
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A `CrosslinkRecord` 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 chain block hash
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'shard_block_hash': 'hash32'
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}
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```
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A `ShardAndCommittee` object has the following fields:
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```python
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{
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# Shard number
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'shard': 'uint64',
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# Validator indices
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'committee': ['uint24']
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}
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```
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A `ShardReassignmentRecord` object has the following fields:
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```python
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{
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# Which validator to reassign
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'validator_index': 'uint24',
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|
# To which shard
|
|
'shard': 'uint64',
|
|
# When
|
|
'slot': 'uint64'
|
|
}
|
|
```
|
|
|
|
A `CandidatePoWReceiptRootRecord` object contains the following fields:
|
|
|
|
```python
|
|
{
|
|
# Candidate PoW receipt root
|
|
'candidate_pow_receipt_root': 'hash32',
|
|
# Vote count
|
|
'votes': 'uint64'
|
|
}
|
|
```
|
|
|
|
A `ForkData` object contains the following fields:
|
|
```python
|
|
{
|
|
# Previous fork version
|
|
'pre_fork_version': 'uint64',
|
|
# Post fork version
|
|
'post_fork_version': 'uint64',
|
|
# Fork slot number
|
|
'fork_slot_number': 'uint64'
|
|
```
|
|
|
|
A `ProcessedAttestation` object has the following fields:
|
|
```python
|
|
{
|
|
# Signed data
|
|
'data': AttestationSignedData,
|
|
# Attester participation bitfield
|
|
'attester_bitfield': 'bytes',
|
|
# Proof of custody bitfield
|
|
'poc_bitfield': 'bytes',
|
|
# Slot in which it was included
|
|
'slot_included': 'uint64'
|
|
}
|
|
```
|
|
|
|
## Beacon chain processing
|
|
|
|
The beacon chain is the "main chain" of the PoS system. The beacon chain's main responsibilities are:
|
|
|
|
* Store and maintain the set of active, queued and exited validators
|
|
* Process crosslinks (see above)
|
|
* Process its own block-by-block consensus, as well as the finality gadget
|
|
|
|
Processing the beacon chain is fundamentally similar to processing a PoW chain in many respects. Clients download and process blocks, and maintain a view of what is the current "canonical chain", terminating at the current "head". However, because of the beacon chain's relationship with the existing PoW chain, and because it is a PoS chain, there are differences.
|
|
|
|
For a block on the beacon chain to be processed by a node, four conditions have to be met:
|
|
|
|
* 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
|
|
* 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 `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.
|
|
|
|
Beacon block production is significantly different because of the proof of stake mechanism. A client simply checks what it thinks is the canonical chain when it should create a block, and looks up what its slot number is; when the slot arrives, it either proposes or attests to a block as required. Note that this requires each node to have a clock that is roughly (ie. within `SLOT_DURATION` seconds) synchronized with the other nodes.
|
|
|
|
### Beacon chain fork choice rule
|
|
|
|
The beacon chain fork choice rule is a hybrid that combines justification and finality with Latest Message Driven (LMD) Greediest Heaviest Observed SubTree (GHOST). At any point in time a validator `v` subjectively calculates the beacon chain head as follows.
|
|
|
|
* 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`.
|
|
* 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.)
|
|
* 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`.
|
|
* 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)`.
|
|
* 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.
|
|
* Let `get_latest_attestation_target(store, validator)` be the target block in the attestation `get_latest_attestation(store, validator)`.
|
|
* The head is `lmd_ghost(store, justified_head)` where the function `lmd_ghost` is defined below. Note that the implementation below is suboptimal; there are implementations that compute the head in time logarithmic in slot count.
|
|
|
|
```python
|
|
def lmd_ghost(store, start):
|
|
validators = start.state.validators
|
|
active_validators = [validators[i] for i in
|
|
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):
|
|
return len([target for target in attestation_targets if
|
|
get_ancestor(store, target, block.slot) == block])
|
|
|
|
head = start
|
|
while 1:
|
|
children = get_children(head)
|
|
if len(children) == 0:
|
|
return head
|
|
head = max(children, key=get_vote_count)
|
|
```
|
|
|
|
## Beacon chain state transition function
|
|
|
|
We now define the state transition function. At the high level, the state transition is made up of two parts:
|
|
|
|
1. The per-block processing, which happens every block, and only affects a few parts of the `state`.
|
|
2. The inter-cycle state recalculation, which happens only if `block.slot >= last_state_recalculation_slot + CYCLE_LENGTH`, and affects the entire `state`.
|
|
|
|
The inter-cycle state recalculation generally focuses on changes to the validator set, including adjusting balances and adding and removing validators, as well as processing crosslinks and managing block justification/finalization, while the per-block processing generally focuses on verifying aggregate signatures and saving temporary records relating to the per-block activity in the `BeaconState`.
|
|
|
|
### Helper functions
|
|
|
|
Below are various helper functions.
|
|
|
|
The following is a function that gets active validator indices from the validator list:
|
|
```python
|
|
def get_active_validator_indices(validators: [ValidatorRecords]) -> List[int]:
|
|
return [i for i, v in enumerate(validators) if v.status == ACTIVE]
|
|
```
|
|
|
|
The following is a function that shuffles any list; we primarily use it for the validator list:
|
|
|
|
```python
|
|
def shuffle(values: List[Any],
|
|
seed: Hash32) -> List[Any]:
|
|
"""
|
|
Returns the shuffled ``values`` with seed as entropy.
|
|
"""
|
|
values_count = len(values)
|
|
|
|
# Entropy is consumed from the seed in 3-byte (24 bit) chunks.
|
|
rand_bytes = 3
|
|
# The highest possible result of the RNG.
|
|
rand_max = 2 ** (rand_bytes * 8) - 1
|
|
|
|
# The range of the RNG places an upper-bound on the size of the list that
|
|
# may be shuffled. It is a logic error to supply an oversized list.
|
|
assert values_count < rand_max
|
|
|
|
output = [x for x in values]
|
|
source = seed
|
|
index = 0
|
|
while index < values_count - 1:
|
|
# Re-hash the `source` to obtain a new pattern of bytes.
|
|
source = hash(source)
|
|
# Iterate through the `source` bytes in 3-byte chunks.
|
|
for position in range(0, 32 - (32 % rand_bytes), rand_bytes):
|
|
# Determine the number of indices remaining in `values` and exit
|
|
# once the last index is reached.
|
|
remaining = values_count - index
|
|
if remaining == 1:
|
|
break
|
|
|
|
# Read 3-bytes of `source` as a 24-bit big-endian integer.
|
|
sample_from_source = int.from_bytes(
|
|
source[position:position + rand_bytes], 'big'
|
|
)
|
|
|
|
# Sample values greater than or equal to `sample_max` will cause
|
|
# modulo bias when mapped into the `remaining` range.
|
|
sample_max = rand_max - rand_max % remaining
|
|
|
|
# Perform a swap if the consumed entropy will not cause modulo bias.
|
|
if sample_from_source < sample_max:
|
|
# Select a replacement index for the current index.
|
|
replacement_position = (sample_from_source % remaining) + index
|
|
# Swap the current index with the replacement index.
|
|
output[index], output[replacement_position] = output[replacement_position], output[index]
|
|
index += 1
|
|
else:
|
|
# The sample causes modulo bias. A new sample should be read.
|
|
pass
|
|
|
|
return output
|
|
```
|
|
|
|
Here's a function that splits a list into `split_count` pieces:
|
|
|
|
```python
|
|
def split(seq: List[Any], split_count: int) -> List[Any]:
|
|
"""
|
|
Returns the split ``seq`` in ``split_count`` pieces in protocol.
|
|
"""
|
|
list_length = len(seq)
|
|
return [
|
|
seq[(list_length * i // split_count): (list_length * (i + 1) // split_count)]
|
|
for i in range(split_count)
|
|
]
|
|
```
|
|
|
|
A helper method for readability:
|
|
|
|
```python
|
|
def clamp(minval: int, maxval: int, x: int) -> int:
|
|
if x <= minval:
|
|
return minval
|
|
elif x >= maxval:
|
|
return maxval
|
|
else:
|
|
return x
|
|
```
|
|
|
|
Now, our combined helper method:
|
|
|
|
```python
|
|
def get_new_shuffling(seed: Hash32,
|
|
validators: List[ValidatorRecord],
|
|
crosslinking_start_shard: int) -> List[List[ShardAndCommittee]]:
|
|
active_validator_indices = get_active_validator_indices(validators)
|
|
|
|
committees_per_slot = clamp(
|
|
1,
|
|
SHARD_COUNT // CYCLE_LENGTH,
|
|
len(active_validator_indices) // CYCLE_LENGTH // TARGET_COMMITTEE_SIZE,
|
|
)
|
|
|
|
output = []
|
|
|
|
# Shuffle with seed
|
|
shuffled_active_validator_indices = shuffle(active_validator_indices, seed)
|
|
|
|
# Split the shuffled list into cycle_length pieces
|
|
validators_per_slot = split(shuffled_active_validator_indices, CYCLE_LENGTH)
|
|
|
|
for slot, slot_indices in enumerate(validators_per_slot):
|
|
# Split the shuffled list into committees_per_slot pieces
|
|
shard_indices = split(slot_indices, committees_per_slot)
|
|
|
|
shard_id_start = crosslinking_start_shard + slot * committees_per_slot
|
|
|
|
shards_and_committees_for_slot = [
|
|
ShardAndCommittee(
|
|
shard=(shard_id_start + shard_position) % SHARD_COUNT,
|
|
committee=indices
|
|
)
|
|
for shard_position, indices in enumerate(shard_indices)
|
|
]
|
|
output.append(shards_and_committees_for_slot)
|
|
|
|
return output
|
|
```
|
|
|
|
Here's a diagram of what's going on:
|
|
|
|
|
|
|
|
We also define two functions for retrieving data from the state:
|
|
|
|
```python
|
|
def get_shards_and_committees_for_slot(state: BeaconState,
|
|
slot: int) -> List[ShardAndCommittee]:
|
|
earliest_slot_in_array = state.last_state_recalculation_slot - CYCLE_LENGTH
|
|
assert earliest_slot_in_array <= slot < earliest_slot_in_array + CYCLE_LENGTH * 2
|
|
return state.shard_and_committee_for_slots[slot - earliest_slot_in_array]
|
|
|
|
def get_block_hash(state: BeaconState,
|
|
current_block: BeaconBlock,
|
|
slot: int) -> Hash32:
|
|
earliest_slot_in_array = current_block.slot - len(state.recent_block_hashes)
|
|
assert earliest_slot_in_array <= slot < current_block.slot
|
|
return state.recent_block_hashes[slot - earliest_slot_in_array]
|
|
```
|
|
|
|
`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_index(state:BeaconState, slot: int) -> int:
|
|
first_committee = get_shards_and_committees_for_slot(state, slot)[0].committee
|
|
index = first_committee[slot % len(first_committee)]
|
|
return index
|
|
```
|
|
|
|
The following is a function that determines the validators that participated in an attestation:
|
|
|
|
```python
|
|
def get_attestation_participants(state: State,
|
|
attestation_data: AttestationSignedData,
|
|
attester_bitfield: bytes) -> List[int]:
|
|
sncs_for_slot = get_shards_and_committees_for_slot(state, attestation_data.slot)
|
|
snc = [x for x in sncs_for_slot if x.shard == attestation_data.shard][0]
|
|
assert len(attester_bitfield) == ceil_div8(len(snc.committee))
|
|
participants = []
|
|
for i, vindex in enumerate(snc.committee):
|
|
bit = (attester_bitfield[i//8] >> (7 - (i % 8))) % 2
|
|
if bit == 1:
|
|
participants.append(vindex)
|
|
return participants
|
|
```
|
|
|
|
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 determine the balance of a validator used for determining punishments and calculating stake:
|
|
|
|
```python
|
|
def balance_at_stake(validator: ValidatorRecord) -> int:
|
|
return min(validator.balance, DEPOSIT_SIZE)
|
|
```
|
|
|
|
We define a function to "add a link" to the validator hash chain, used when a validator is added or removed:
|
|
|
|
```python
|
|
def get_new_validator_set_delta_hash_chain(current_validator_set_delta_hash_chain: Hash32,
|
|
index: int,
|
|
pubkey: int,
|
|
flag: int) -> Hash32:
|
|
new_validator_set_delta_hash_chain = hash(
|
|
current_validator_set_delta_hash_chain +
|
|
bytes1(flag) +
|
|
bytes3(index) +
|
|
bytes32(pubkey)
|
|
)
|
|
return new_validator_set_delta_hash_chain
|
|
```
|
|
|
|
Finally, we abstractly define `int_sqrt(n)` for use in reward/penalty calculations as the largest integer `k` such that `k**2 <= n`. Here is one possible implementation, though clients are free to use their own including standard libraries for [integer square root](https://en.wikipedia.org/wiki/Integer_square_root) if available and meet the specification.
|
|
|
|
```python
|
|
def int_sqrt(n: int) -> int:
|
|
x = n
|
|
y = (x + 1) // 2
|
|
while y < x:
|
|
x = y
|
|
y = (x + n // x) // 2
|
|
return x
|
|
```
|
|
|
|
### On startup
|
|
|
|
A valid block with slot `0` (the "genesis block") has the following values. Other validity rules (eg. requiring a signature) do not apply.
|
|
|
|
```python
|
|
{
|
|
'slot': 0,
|
|
'randao_reveal': bytes32(0),
|
|
'candidate_pow_receipt_roots': [],
|
|
'ancestor_hashes': [bytes32(0) for i in range(32)],
|
|
'state_root': STARTUP_STATE_ROOT,
|
|
'attestations': [],
|
|
'specials': [],
|
|
'proposer_signature': [0, 0]
|
|
}
|
|
```
|
|
|
|
`STARTUP_STATE_ROOT` is the root of the initial state, computed by running the following code:
|
|
|
|
```python
|
|
def on_startup(initial_validator_entries: List[Any],
|
|
genesis_time: int,
|
|
processed_pow_receipt_root: Hash32) -> BeaconState:
|
|
# Induct validators
|
|
validators = []
|
|
for pubkey, deposit_size, proof_of_possession, withdrawal_credentials, \
|
|
randao_commitment in initial_validator_entries:
|
|
validators, _ = get_new_validators(
|
|
current_validators=validators,
|
|
fork_data=ForkData(
|
|
pre_fork_version=INITIAL_FORK_VERSION,
|
|
post_fork_version=INITIAL_FORK_VERSION,
|
|
fork_slot_number=2**64 - 1,
|
|
),
|
|
pubkey=pubkey,
|
|
deposit_size=deposit_size,
|
|
proof_of_possession=proof_of_possession,
|
|
withdrawal_credentials=withdrawal_credentials,
|
|
randao_commitment=randao_commitment,
|
|
current_slot=0,
|
|
status=ACTIVE,
|
|
)
|
|
# Setup state
|
|
x = get_new_shuffling(bytes([0] * 32), validators, 0)
|
|
crosslinks = [
|
|
CrosslinkRecord(
|
|
slot=0,
|
|
hash=bytes([0] * 32)
|
|
)
|
|
for i in range(SHARD_COUNT)
|
|
]
|
|
state = BeaconState(
|
|
validator_set_change_slot=0,
|
|
validators=validators,
|
|
crosslinks=crosslinks,
|
|
last_state_recalculation_slot=0,
|
|
last_finalized_slot=0,
|
|
justification_source=0,
|
|
prev_cycle_justification_source=0,
|
|
justified_slot_bitfield=0,
|
|
shard_and_committee_for_slots=x + x,
|
|
persistent_committees=split(shuffle(validators, bytes([0] * 32)), SHARD_COUNT),
|
|
persistent_committee_reassignments=[],
|
|
deposits_penalized_in_period=[],
|
|
next_shuffling_seed=bytes([0] * 32),
|
|
validator_set_delta_hash_chain=bytes([0] * 32), # stub
|
|
current_exit_seq=0,
|
|
genesis_time=genesis_time,
|
|
processed_pow_receipt_root=processed_pow_receipt_root,
|
|
candidate_pow_receipt_roots=[],
|
|
pre_fork_version=INITIAL_FORK_VERSION,
|
|
post_fork_version=INITIAL_FORK_VERSION,
|
|
fork_slot_number=0,
|
|
pending_attestations=[],
|
|
pending_specials=[],
|
|
recent_block_hashes=[bytes([0] * 32) for _ in range(CYCLE_LENGTH * 2)],
|
|
randao_mix=bytes([0] * 32) # stub
|
|
)
|
|
|
|
return state
|
|
```
|
|
|
|
|
|
### Routine for adding a validator
|
|
|
|
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, some helper functions:
|
|
|
|
```python
|
|
def min_empty_validator_index(validators: List[ValidatorRecord], current_slot: int) -> int:
|
|
for i, v in enumerate(validators):
|
|
if v.status == WITHDRAWN and v.last_status_change_slot + DELETION_PERIOD <= current_slot:
|
|
return i
|
|
return None
|
|
|
|
|
|
def get_fork_version(fork_data: ForkData,
|
|
slot: int) -> int:
|
|
if slot < fork_data.fork_slot_number:
|
|
return fork_data.pre_fork_version
|
|
else:
|
|
return fork_data.post_fork_version
|
|
|
|
|
|
def get_domain(fork_data: ForkData,
|
|
slot: int,
|
|
base_domain: int) -> int:
|
|
return get_fork_version(
|
|
fork_data,
|
|
slot
|
|
) * 2**32 + base_domain
|
|
|
|
|
|
def get_new_validators(current_validators: List[ValidatorRecord],
|
|
fork_data: ForkData,
|
|
pubkey: int,
|
|
deposit_size: int,
|
|
proof_of_possession: bytes,
|
|
withdrawal_credentials: Hash32,
|
|
randao_commitment: Hash32,
|
|
status: int,
|
|
current_slot: int) -> Tuple[List[ValidatorRecord], int]:
|
|
# if any asserts fail, validator induction/topup failed
|
|
# move on to next validator deposit log
|
|
signed_message = bytes32(pubkey) + withdrawal_credentials + randao_commitment
|
|
assert BLSVerify(
|
|
pub=pubkey,
|
|
msg=hash(signed_message),
|
|
sig=proof_of_possession,
|
|
domain=get_domain(
|
|
fork_data,
|
|
current_slot,
|
|
DOMAIN_DEPOSIT
|
|
)
|
|
)
|
|
new_validators = copy.deepcopy(current_validators)
|
|
validator_pubkeys = [v.pubkey for v in new_validators]
|
|
|
|
# add new validator
|
|
if pubkey not in validator_pubkeys:
|
|
assert deposit_size == DEPOSIT_SIZE
|
|
|
|
rec = ValidatorRecord(
|
|
pubkey=pubkey,
|
|
withdrawal_credentials=withdrawal_credentials,
|
|
randao_commitment=randao_commitment,
|
|
randao_skips=0,
|
|
balance=DEPOSIT_SIZE * GWEI_PER_ETH,
|
|
status=status,
|
|
last_status_change_slot=current_slot,
|
|
exit_seq=0
|
|
)
|
|
|
|
index = min_empty_validator(new_validators)
|
|
if index is None:
|
|
new_validators.append(rec)
|
|
index = len(new_validators) - 1
|
|
else:
|
|
new_validators[index] = rec
|
|
return new_validators, index
|
|
|
|
# topup existing validator
|
|
else:
|
|
index = validator_pubkeys.index(pubkey)
|
|
val = new_validators[index]
|
|
assert deposit_size >= MIN_TOPUP_SIZE
|
|
assert val.status != WITHDRAWN
|
|
assert val.withdrawal_credentials == withdrawal_credentials
|
|
|
|
val.balance += deposit_size
|
|
return new_validators, index
|
|
```
|
|
|
|
Now, to add a validator or top up an existing validator's balance:
|
|
|
|
```python
|
|
def add_or_topup_validator(state: BeaconState,
|
|
pubkey: int,
|
|
deposit_size: int,
|
|
proof_of_possession: bytes,
|
|
withdrawal_credentials: Hash32,
|
|
randao_commitment: Hash32,
|
|
status: int,
|
|
current_slot: int) -> int:
|
|
"""
|
|
Add the validator into the given `state`.
|
|
Note that this function mutates `state`.
|
|
"""
|
|
state.validators, index = get_new_validators(
|
|
current_validators=state.validators,
|
|
fork_data=ForkData(
|
|
pre_fork_version=state.pre_fork_version,
|
|
post_fork_version=state.post_fork_version,
|
|
fork_slot_number=state.fork_slot_number,
|
|
),
|
|
pubkey=pubkey,
|
|
deposit_size=deposit_size,
|
|
proof_of_possession=proof_of_possession,
|
|
withdrawal_credentials=withdrawal_credentials,
|
|
randao_commitment=randao_commitment,
|
|
status=status,
|
|
current_slot=current_slot,
|
|
)
|
|
|
|
return index
|
|
```
|
|
|
|
`BLSVerify` is a function for verifying a BLS12-381 signature, defined in the BLS12-381 spec.
|
|
|
|
### Routine for removing a validator
|
|
|
|
```python
|
|
def exit_validator(index: int,
|
|
state: BeaconState,
|
|
block: BeaconBlock,
|
|
penalize: bool,
|
|
current_slot: int) -> None:
|
|
"""
|
|
Remove the validator with the given `index` from `state`.
|
|
Note that this function mutates `state`.
|
|
"""
|
|
validator = state.validators[index]
|
|
validator.last_status_change_slot = current_slot
|
|
validator.exit_seq = state.current_exit_seq
|
|
state.current_exit_seq += 1
|
|
for committee in state.persistent_committees:
|
|
for i, vindex in committee:
|
|
if vindex == index:
|
|
committee.pop(i)
|
|
break
|
|
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
|
|
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(
|
|
validator_set_delta_hash_chain=state.validator_set_delta_hash_chain,
|
|
index=index,
|
|
pubkey=validator.pubkey,
|
|
flag=EXIT,
|
|
)
|
|
```
|
|
|
|
## Per-block processing
|
|
|
|
This procedure should be carried out every beacon block.
|
|
|
|
* Let `parent_hash` be the hash of the immediate previous beacon block (ie. equal to `ancestor_hashes[0]`).
|
|
* Let `parent` be the beacon block with the hash `parent_hash`.
|
|
|
|
First, set `recent_block_hashes` to the output of the following:
|
|
|
|
```python
|
|
def append_to_recent_block_hashes(old_block_hashes: List[Hash32],
|
|
parent_slot: int,
|
|
current_slot: int,
|
|
parent_hash: Hash32) -> List[Hash32]:
|
|
d = current_slot - parent_slot
|
|
return old_block_hashes + [parent_hash] * d
|
|
```
|
|
|
|
The output of `get_block_hash` should not change, except that it will no longer throw for `current_slot - 1`. Also, check that the block's `ancestor_hashes` array was correctly updated, using the following algorithm:
|
|
|
|
```python
|
|
def update_ancestor_hashes(parent_ancestor_hashes: List[Hash32],
|
|
parent_slot_number: int,
|
|
parent_hash: Hash32) -> List[Hash32]:
|
|
new_ancestor_hashes = copy.copy(parent_ancestor_hashes)
|
|
for i in range(32):
|
|
if parent_slot_number % 2**i == 0:
|
|
new_ancestor_hashes[i] = parent_hash
|
|
return new_ancestor_hashes
|
|
```
|
|
|
|
### Verify attestations
|
|
|
|
Verify that there are at most `MAX_ATTESTATION_COUNT` `AttestationRecord` objects.
|
|
|
|
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)`.
|
|
* 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=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
|
|
|
|
First run the following state transition to update `randao_skips` variables for the missing slots.
|
|
|
|
```python
|
|
for slot in range(parent.slot + 1, block.slot):
|
|
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 `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
|
|
|
|
If `block.candidate_pow_receipt_root` is `x.candidate_pow_receipt_root` for some `x` in `state.candidate_pow_receipt_roots`, set `x.votes += 1`. Otherwise, append to `state.candidate_pow_receipt_roots` a new `CandidatePoWReceiptRootRecord(candidate_pow_receipt_root=block.candidate_pow_receipt_root, votes=1)`.
|
|
|
|
### Process penalties, logouts and other special objects
|
|
|
|
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.
|
|
|
|
#### LOGOUT
|
|
|
|
```python
|
|
{
|
|
'validator_index': 'uint64',
|
|
'signature': '[uint384]'
|
|
}
|
|
```
|
|
Perform the following checks:
|
|
* Verify that `BLSVerify(pubkey=validators[data.validator_index].pubkey, msg=bytes([0] * 32), sig=data.signature, domain=get_domain(state.fork_data, current_slot, DOMAIN_LOGOUT))`.
|
|
* Verify that `validators[validator_index].status == ACTIVE`.
|
|
* Verify that `block.slot >= last_status_change_slot + SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD`.
|
|
|
|
Run `exit_validator(data.validator_index, state, block, penalize=False, current_slot=block.slot)`.
|
|
|
|
#### CASPER_SLASHING
|
|
|
|
```python
|
|
{
|
|
'vote1_aggregate_sig_indices': '[uint24]',
|
|
'vote1_data': AttestationSignedData,
|
|
'vote1_aggregate_sig': '[uint384]',
|
|
'vote2_aggregate_sig_indices': '[uint24]',
|
|
'vote2_data': AttestationSignedData,
|
|
'vote2_aggregate_sig': '[uint384]',
|
|
}
|
|
```
|
|
|
|
Perform the following checks:
|
|
|
|
* 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.fork_data, vote_data.slot, DOMAIN_ATTESTATION))` passes.
|
|
* 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`.
|
|
* 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, block, penalize=True, current_slot=block.slot)`
|
|
|
|
#### PROPOSER_SLASHING
|
|
|
|
```python
|
|
{
|
|
'proposer_index': 'uint24',
|
|
'proposal1_data': ProposalSignedData,
|
|
'proposal1_signature': '[uint384]',
|
|
'proposal2_data': ProposalSignedData,
|
|
'proposal1_signature': '[uint384]',
|
|
}
|
|
```
|
|
For each `proposal_signature`, verify that `BLSVerify(pubkey=validators[proposer_index].pubkey, msg=hash(proposal_data), sig=proposal_signature, domain=get_domain(state.fork_data, 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
|
|
|
|
```python
|
|
{
|
|
'merkle_branch': '[hash32]',
|
|
'merkle_tree_index': 'uint64',
|
|
'deposit_data': {
|
|
'deposit_params': DepositParams,
|
|
'msg_value': 'uint64',
|
|
'timestamp': 'uint64'
|
|
}
|
|
}
|
|
```
|
|
|
|
Note that `deposit_data` in serialized form should be the `DepositParams` followed by 8 bytes for the `msg_value` and 8 bytes for the `timestamp`, or exactly the `deposit_data` in the [PoW chain registration contract](#pow-chain-registration-contract) of which the hash was placed into the Merkle tree.
|
|
|
|
Use the following procedure to verify the `merkle_branch`, setting `leaf=serialized_deposit_data`, `depth=POW_CONTRACT_MERKLE_TREE_DEPTH` and `root=state.processed_pow_receipt_root`:
|
|
|
|
```python
|
|
def verify_merkle_branch(leaf: Hash32, branch: [Hash32], depth: int, index: int, root: Hash32) -> bool:
|
|
value = leaf
|
|
for i in range(depth):
|
|
if index % 2:
|
|
value = hash(branch[i], value)
|
|
else:
|
|
value = hash(value, branch[i])
|
|
return value == root
|
|
```
|
|
|
|
Verify that `block.slot - (deposit_data.timestamp - state.genesis_time) // SLOT_DURATION < DELETION_PERIOD`.
|
|
|
|
Run `add_or_topup_validator(state, pupkey=deposit_data.deposit_params.pubkey, deposit_size=deposit_data.msg_value, 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)`.
|
|
|
|
## Cycle boundary processing
|
|
|
|
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
|
|
|
|
* 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`.
|
|
|
|
For every `ShardAndCommittee` object `obj`:
|
|
|
|
* 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 `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`.
|
|
|
|
Case 1: `time_since_finality <= 4 * CYCLE_LENGTH`:
|
|
|
|
* 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)`.
|
|
|
|
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 `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:
|
|
|
|
* 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
|
|
|
|
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`.
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* Set `state.candidate_pow_receipt_roots = []`.
|
|
|
|
### Validator set change
|
|
|
|
A validator set change can happen if all of the following criteria are satisfied:
|
|
|
|
* `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`
|
|
|
|
A helper function is defined as:
|
|
|
|
```python
|
|
def get_changed_validators(validators: List[ValidatorRecord],
|
|
deposits_penalized_in_period: List[int],
|
|
validator_set_delta_hash_chain: int,
|
|
current_slot: int) -> Tuple[List[ValidatorRecord], List[int], int]:
|
|
"""
|
|
Return changed validator set and `deposits_penalized_in_period`, `validator_set_delta_hash_chain`.
|
|
"""
|
|
# The active validator set
|
|
active_validator_indices = get_active_validator_indices(validators)
|
|
# The total balance of active validators
|
|
total_balance = sum([balance_at_stake(v) for i, v in enumerate(validators) if i in active_validator_indices])
|
|
# The maximum total wei that can deposit+withdraw
|
|
max_allowable_change = max(
|
|
2 * DEPOSIT_SIZE * GWEI_PER_ETH,
|
|
total_balance // MAX_VALIDATOR_CHURN_QUOTIENT
|
|
)
|
|
# Go through the list start to end depositing+withdrawing as many as possible
|
|
total_changed = 0
|
|
for i in range(len(validators)):
|
|
if validators[i].status == PENDING_ACTIVATION:
|
|
validators[i].status = ACTIVE
|
|
total_changed += DEPOSIT_SIZE * GWEI_PER_ETH
|
|
validator_set_delta_hash_chain = get_new_validator_set_delta_hash_chain(
|
|
validator_set_delta_hash_chain=validator_set_delta_hash_chain,
|
|
index=i,
|
|
pubkey=validators[i].pubkey,
|
|
flag=ENTRY,
|
|
)
|
|
if validators[i].status == PENDING_EXIT:
|
|
validators[i].status = PENDING_WITHDRAW
|
|
validators[i].last_status_change_slot = current_slot
|
|
total_changed += balance_at_stake(validators[i])
|
|
validator_set_delta_hash_chain = get_new_validator_set_delta_hash_chain(
|
|
validator_set_delta_hash_chain=validator_set_delta_hash_chain,
|
|
index=i,
|
|
pubkey=validators[i].pubkey,
|
|
flag=EXIT,
|
|
)
|
|
if total_changed >= max_allowable_change:
|
|
break
|
|
|
|
# Calculate the total ETH that has been penalized in the last ~2-3 withdrawal periods
|
|
period_index = current_slot // COLLECTIVE_PENALTY_CALCULATION_PERIOD
|
|
total_penalties = (
|
|
(deposits_penalized_in_period[period_index]) +
|
|
(deposits_penalized_in_period[period_index - 1] if period_index >= 1 else 0) +
|
|
(deposits_penalized_in_period[period_index - 2] if period_index >= 2 else 0)
|
|
)
|
|
# Separate loop to withdraw validators that have been logged out for long enough, and
|
|
# calculate their penalties if they were slashed
|
|
|
|
def withdrawable(v):
|
|
return v.status in (PENDING_WITHDRAW, PENALIZED) and current_slot >= v.last_status_change_slot + MIN_WITHDRAWAL_PERIOD
|
|
|
|
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 -= 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
|
|
|
|
return validators, deposits_penalized_in_period, validator_set_delta_hash_chain
|
|
```
|
|
|
|
Then, run the following algorithm to update the validator set:
|
|
|
|
```python
|
|
def change_validators(state: BeaconState,
|
|
current_slot: int) -> None:
|
|
"""
|
|
Change validator set.
|
|
Note that this function mutates `state`.
|
|
"""
|
|
state.validators, state.deposits_penalized_in_period = get_changed_validators(
|
|
copy.deepcopy(state.validators),
|
|
copy.deepcopy(state.deposits_penalized_in_period),
|
|
state.validator_set_delta_hash_chain,
|
|
current_slot
|
|
)
|
|
```
|
|
|
|
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
|
|
|
|
* 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 = 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.
|
|
|
|
### Proposer reshuffling
|
|
|
|
Run the following code to update the shard proposer set:
|
|
|
|
```python
|
|
active_validator_indices = get_active_validator_indices(validators)
|
|
num_validators_to_reshuffle = len(active_validator_indices) // SHARD_PERSISTENT_COMMITTEE_CHANGE_PERIOD
|
|
for i in range(num_validators_to_reshuffle):
|
|
# Multiplying i to 2 to ensure we have different input to all the required hashes in the shuffling
|
|
# and none of the hashes used for entropy in this loop will be the same
|
|
vid = active_validator_indices[hash(state.randao_mix + bytes8(i * 2)) % len(active_validator_indices)]
|
|
new_shard = hash(state.randao_mix + bytes8(i * 2 + 1)) % SHARD_COUNT
|
|
shard_reassignment_record = ShardReassignmentRecord(
|
|
validator_index=vid,
|
|
shard=new_shard,
|
|
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 <= s:
|
|
rec = state.persistent_committee_reassignments.pop(0)
|
|
for committee in state.persistent_committees:
|
|
if rec.validator_index in committee:
|
|
committee.pop(
|
|
committee.index(rec.validator_index)
|
|
)
|
|
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
|
|
|
|
We aim to have a STARK-friendly hash function `hash(x)` for the production launch of the beacon chain. While the standardisation process for a STARK-friendly hash function takes place—led by STARKware, who will produce a detailed report with recommendations—we use `BLAKE2b-512` as a placeholder. Specifically, we set `hash(x) := BLAKE2b-512(x)[0:32]` where the `BLAKE2b-512` algorithm is defined in [RFC 7693](https://tools.ietf.org/html/rfc7693) and the input `x` is of type `bytes`.
|
|
|
|
# Copyright
|
|
Copyright and related rights waived via [CC0](https://creativecommons.org/publicdomain/zero/1.0/).
|