# Ethereum 2.0 Phase 0 -- Weak Subjectivity Guide

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

## Table of contents
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- [Introduction](#introduction)
- [Prerequisites](#prerequisites)
- [Constants](#constants)
- [Weak Subjectivity Checkpoint](#weak-subjectivity-checkpoint)
- [Weak Subjectivity Period](#weak-subjectivity-period)
  - [Calculating the Weak Subjectivity Period](#calculating-the-weak-subjectivity-period)
- [Weak Subjectivity Sync](#weak-subjectivity-sync)
  - [Weak Subjectivity Sync Procedure](#weak-subjectivity-sync-procedure)
  - [Checking for Stale Weak Subjectivity Checkpoint](#checking-for-stale-weak-subjectivity-checkpoint)
- [Distributing Weak Subjectivity Checkpoints](#distributing-weak-subjectivity-checkpoints)

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## Introduction
This document is a guide for implementing the Weak Subjectivity protections in Phase 0 of Ethereum 2.0. For more information about weak subjectivity and why it is required, please refer to:
- [Weak Subjectivity in Eth2.0](https://notes.ethereum.org/@adiasg/weak-subjectvity-eth2)
- [Proof of Stake: How I Learned to Love Weak Subjectivity](https://blog.ethereum.org/2014/11/25/proof-stake-learned-love-weak-subjectivity/)

## Prerequisites
This document uses data structures, constants, functions, and terminology from [Phase 0 -- The Beacon Chain](https://github.com/ethereum/eth2.0-specs/blob/dev/specs/phase0/beacon-chain.md) and [Phase 0 -- Beacon Chain Fork Choice](https://github.com/ethereum/eth2.0-specs/blob/dev/specs/phase0/fork-choice.md).

## Constants
| Name           | Value        |
|----------------|--------------|
| `SAFETY_DECAY` | `uint64(10)` |


## Weak Subjectivity Checkpoint
Any `Checkpoint` can used be a Weak Subjectivity Checkpoint. These Weak Subjectivity Checkpoints are distributed by providers, downloaded by users and/or distributed as a part of clients, and used as input while syncing a client.

## Weak Subjectivity Period
The Weak Subjectivity Period is the number of recent epochs within which there must be a Weak Subjectivity Checkpoint so that an attacker who takes control of the validator set at the beginning of the period is slashed at least a threshold amount in case a conflicting `Checkpoint` is finalized. `SAFETY_DECAY` is defined as the maximum percentage tolerable loss in the 1/3rd safety margin of FFG finality, which makes our threshold amount of slashing to be 1/3 - `SAFETY_DECAY/100`.

### Calculating the Weak Subjectivity Period
For more information about this calculation, refer to [Weak Subjectivity in Eth2.0](https://notes.ethereum.org/@adiasg/weak-subjectvity-eth2).

Note: `compute_weak_subjectivity_period()` is planned to be updated when a more accurate calculation is made.
```python
  def compute_weak_subjectivity_period(state):
    weak_subjectivity_period = MIN_VALIDATOR_WITHDRAWABILITY_DELAY
    val_count = len(get_active_validator_indices(state, get_current_epoch(state)))
    if val_count >= MIN_PER_EPOCH_CHURN_LIMIT * CHURN_LIMIT_QUOTIENT:
        weak_subjectivity_period += SAFETY_DECAY*CHURN_LIMIT_QUOTIENT/(2*100)
    else:
        weak_subjectivity_period += SAFETY_DECAY*val_count/(2*100*MIN_PER_EPOCH_CHURN_LIMIT)
    return weak_subjectivity_period
```

A brief reference for what these values look like in practice:

| `val_count` | `weak_subjectivity_period` |
| ----  | ---- |
| 1024  | 268 |
| 2048  | 281 |
| 4096  | 307 |
| 8192  | 358 |
| 16384 | 460 |
| 32768 | 665 |
| 65536 | 1075 |
| 131072  | 1894 |
| 262144  | 3532 |
| 524288  | 3532 |

## Weak Subjectivity Sync
Clients should allow users to input a Weak Subjectivity Checkpoint at startup, and guarantee that any successful sync leads to the given Weak Subjectivity Checkpoint being in the canonical chain. If such a sync is not possible, the client should treat this as a critical and irrecoverable failure.

### Weak Subjectivity Sync Procedure
1. Take a Weak Subjectivity Checkpoint as a CLI parameter input in `block_root:epoch_number` format, where `block_root` and `epoch_number` represent a valid `Checkpoint`. Example of the format:
```
0x8584188b86a9296932785cc2827b925f9deebacce6d72ad8d53171fa046b43d9:9544
```
2.  - *IF* `epoch_number > store.finalized_checkpoint.epoch`, then *ASSERT* during block sync that block with root `block_root` is in the sync path at epoch `epoch_number`. Emit descriptive critical error if this assert fails, then exit client process.
    - *IF* `epoch_number <= store.finalized_checkpoint.epoch`, then *ASSERT* that the block in the canonical chain at epoch `epoch_number` has root `block_root`. Emit descriptive critical error if this assert fails, then exit client process.

### Checking for Stale Weak Subjectivity Checkpoint
Clients may choose to validate that the input Weak Subjectivity Checkpoint is not stale at the time of startup. To support this mechanism, the client needs to take the state at the Weak Subjectivity Checkpoint as a CLI parameter input (or fetch the state associated with the input Weak Subjectivity Checkpoint from some source). The check can be implemented in the following way:
```python
  def is_within_weak_subjectivity_period(store, ws_state, ws_checkpoint):
    # Clients may choose to validate the input state against the input Weak Subjectivity Checkpoint
    assert ws_state.latest_block_header.state_root == ws_checkpoint.root
    assert compute_epoch_at_slot(ws_state.slot) == ws_checkpoint.epoch
    ws_period = compute_weak_subjectivity_period(ws_state)
    ws_state_epoch = compute_epoch_at_slot(ws_state.slot)
    current_epoch = compute_epoch_at_slot(get_current_slot(store))
    assert current_epoch <= ws_state_epoch + ws_period, "The input Weak Subjectivity Checkpoint is stale"
```

## Distributing Weak Subjectivity Checkpoints
This section will be updated soon.