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// Copyright 2018 Parity Technologies (UK) Ltd.
// This file is part of Polkadot.
// Polkadot is free software: you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation, either version 3 of the License, or
// (at your option) any later version.
// Polkadot is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
// You should have received a copy of the GNU General Public License
// along with Polkadot. If not, see <http://www.gnu.org/licenses/>.
//! As part of Polkadot's availability system, certain pieces of data
//! for each block are required to be kept available.
//!
//! The way we accomplish this is by erasure coding the data into n pieces
//! and constructing a merkle root of the data.
//!
//! Each of n validators stores their piece of data. We assume n=3f+k, k < 3.
//! f is the maximum number of faulty validators in the system.
//! The data is coded so any f+1 chunks can be used to reconstruct the full data.
use reed_solomon::galois_16::{self, ReedSolomon};
use primitives::{Hash as H256, BlakeTwo256, HashT};
use primitives::parachain::{BlockData, OutgoingMessages};
use sp_core::Blake2Hasher;
use trie::{EMPTY_PREFIX, MemoryDB, Trie, TrieMut, trie_types::{TrieDBMut, TrieDB}};
use self::wrapped_shard::WrappedShard;
mod wrapped_shard;
// we are limited to the field order of GF(2^16), which is 65536
const MAX_VALIDATORS: usize = <galois_16::Field as reed_solomon::Field>::ORDER;
/// Errors in erasure coding.
pub enum Error {
/// Returned when there are too many validators.
TooManyValidators,
/// Cannot encode something for no validators
EmptyValidators,
/// Cannot reconstruct: wrong number of validators.
WrongValidatorCount,
/// Not enough chunks present.
NotEnoughChunks,
/// Too many chunks present.
TooManyChunks,
/// Chunks not of uniform length or the chunks are empty.
NonUniformChunks,
/// An uneven byte-length of a shard is not valid for GF(2^16) encoding.
UnevenLength,
/// Chunk index out of bounds.
ChunkIndexOutOfBounds(usize, usize),
/// Bad payload in reconstructed bytes.
BadPayload,
/// Invalid branch proof.
InvalidBranchProof,
/// Branch out of bounds.
BranchOutOfBounds,
}
struct CodeParams {
data_shards: usize,
parity_shards: usize,
}
impl CodeParams {
// the shard length needed for a payload with initial size `base_len`.
fn shard_len(&self, base_len: usize) -> usize {
// how many bytes we actually need.
let needed_shard_len = base_len / self.data_shards
+ (base_len % self.data_shards != 0) as usize;
// round up to next even number
// (no actual space overhead since we are working in GF(2^16)).
needed_shard_len + needed_shard_len % 2
}
fn make_shards_for(&self, payload: &[u8]) -> Vec<WrappedShard> {
let shard_len = self.shard_len(payload.len());
let mut shards = vec![
WrappedShard::new(vec![0; shard_len]);
self.data_shards + self.parity_shards
];
for (data_chunk, blank_shard) in payload.chunks(shard_len).zip(&mut shards) {
// fill the empty shards with the corresponding piece of the payload,
// zero-padded to fit in the shards.
let len = std::cmp::min(shard_len, data_chunk.len());
let blank_shard: &mut [u8] = blank_shard.as_mut();
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blank_shard[..len].copy_from_slice(&data_chunk[..len]);
}
shards
}
// make a reed-solomon instance.
fn make_encoder(&self) -> ReedSolomon {
ReedSolomon::new(self.data_shards, self.parity_shards)
.expect("this struct is not created with invalid shard number; qed")
}
}
fn code_params(n_validators: usize) -> Result<CodeParams, Error> {
if n_validators > MAX_VALIDATORS { return Err(Error::TooManyValidators) }
if n_validators == 0 { return Err(Error::EmptyValidators) }
let n_faulty = n_validators.saturating_sub(1) / 3;
let n_good = n_validators - n_faulty;
Ok(CodeParams {
data_shards: n_faulty + 1,
parity_shards: n_good - 1,
})
}
/// Obtain erasure-coded chunks, one for each validator.
///
/// Works only up to 65536 validators, and `n_validators` must be non-zero.
pub fn obtain_chunks(n_validators: usize, block_data: &BlockData, outgoing: &OutgoingMessages)
-> Result<Vec<Vec<u8>>, Error>
{
let params = code_params(n_validators)?;
let encoded = (block_data, outgoing).encode();
if encoded.is_empty() {
return Err(Error::BadPayload);
}
let mut shards = params.make_shards_for(&encoded[..]);
params.make_encoder().encode(&mut shards[..])
.expect("Payload non-empty, shard sizes are uniform, and validator numbers checked; qed");
Ok(shards.into_iter().map(|w| w.into_inner()).collect())
}
/// Reconstruct the block data from a set of chunks.
///
/// Provide an iterator containing chunk data and the corresponding index.
/// The indices of the present chunks must be indicated. If too few chunks
/// are provided, recovery is not possible.
///
/// Works only up to 65536 validators, and `n_validators` must be non-zero.
pub fn reconstruct<'a, I: 'a>(n_validators: usize, chunks: I)
-> Result<(BlockData, OutgoingMessages), Error>
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where I: IntoIterator<Item=(&'a [u8], usize)>
{
let params = code_params(n_validators)?;
let mut shards: Vec<Option<WrappedShard>> = vec![None; n_validators];
let mut shard_len = None;
for (chunk_data, chunk_idx) in chunks.into_iter().take(n_validators) {
if chunk_idx >= n_validators {
return Err(Error::ChunkIndexOutOfBounds(chunk_idx, n_validators));
}
let shard_len = shard_len.get_or_insert_with(|| chunk_data.len());
if *shard_len % 2 != 0 {
return Err(Error::UnevenLength);
}
if *shard_len != chunk_data.len() || *shard_len == 0 {
return Err(Error::NonUniformChunks);
}
shards[chunk_idx] = Some(WrappedShard::new(chunk_data.to_vec()));
}
if let Err(e) = params.make_encoder().reconstruct(&mut shards[..]) {
match e {
reed_solomon::Error::TooFewShardsPresent => Err(Error::NotEnoughChunks)?,
reed_solomon::Error::InvalidShardFlags => Err(Error::WrongValidatorCount)?,
reed_solomon::Error::TooManyShards => Err(Error::TooManyChunks)?,
reed_solomon::Error::EmptyShard => panic!("chunks are all non-empty; this is checked above; qed"),
reed_solomon::Error::IncorrectShardSize => panic!("chunks are all same len; this is checked above; qed"),
_ => panic!("reed_solomon encoder returns no more variants for this function; qed"),
}
}
// lazily decode from the data shards.
Decode::decode(&mut ShardInput {
remaining_len: shard_len.map(|s| s * params.data_shards).unwrap_or(0),
shards: shards.iter()
.map(|x| x.as_ref())
.take(params.data_shards)
.map(|x| x.expect("all data shards have been recovered; qed"))
}).or_else(|_| Err(Error::BadPayload))
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}
/// An iterator that yields merkle branches and chunk data for all chunks to
/// be sent to other validators.
pub struct Branches<'a> {
trie_storage: MemoryDB<Blake2Hasher>,
root: H256,
chunks: Vec<&'a [u8]>,
current_pos: usize,
}
impl<'a> Branches<'a> {
/// Get the trie root.
pub fn root(&self) -> H256 { self.root.clone() }
}
impl<'a> Iterator for Branches<'a> {
type Item = (Vec<Vec<u8>>, &'a [u8]);
fn next(&mut self) -> Option<Self::Item> {
use trie::Recorder;
let trie = TrieDB::new(&self.trie_storage, &self.root)
.expect("`Branches` is only created with a valid memorydb that contains all nodes for the trie with given root; qed");
let mut recorder = Recorder::new();
let res = (self.current_pos as u32).using_encoded(|s|
trie.get_with(s, &mut recorder)
);
match res.expect("all nodes in trie present; qed") {
Some(_) => {
let nodes = recorder.drain().into_iter().map(|r| r.data).collect();
let chunk = &self.chunks.get(self.current_pos)
.expect("there is a one-to-one mapping of chunks to valid merkle branches; qed");
self.current_pos += 1;
Some((nodes, chunk))
}
None => None,
}
}
}
/// Construct a trie from chunks of an erasure-coded value. This returns the root hash and an
/// iterator of merkle proofs, one for each validator.
pub fn branches<'a>(chunks: Vec<&'a [u8]>) -> Branches<'a> {
let mut trie_storage: MemoryDB<Blake2Hasher> = MemoryDB::default();
let mut root = H256::default();
// construct trie mapping each chunk's index to its hash.
{
let mut trie = TrieDBMut::new(&mut trie_storage, &mut root);
for (i, &chunk) in chunks.iter().enumerate() {
(i as u32).using_encoded(|encoded_index| {
let chunk_hash = BlakeTwo256::hash(chunk);
trie.insert(encoded_index, chunk_hash.as_ref())
.expect("a fresh trie stored in memory cannot have errors loading nodes; qed");
})
}
}
Branches {
trie_storage,
root,
chunks,
current_pos: 0,
}
}
/// Verify a merkle branch, yielding the chunk hash meant to be present at that
/// index.
pub fn branch_hash(root: &H256, branch_nodes: &[Vec<u8>], index: usize) -> Result<H256, Error> {
let mut trie_storage: MemoryDB<Blake2Hasher> = MemoryDB::default();
for node in branch_nodes.iter() {
(&mut trie_storage as &mut trie::HashDB<_>).insert(EMPTY_PREFIX, node.as_slice());
}
let trie = TrieDB::new(&trie_storage, &root).map_err(|_| Error::InvalidBranchProof)?;
let res = (index as u32).using_encoded(|key|
trie.get_with(key, |raw_hash: &[u8]| H256::decode(&mut &raw_hash[..]))
);
match res {
Ok(Some(Ok(hash))) => Ok(hash),
Ok(Some(Err(_))) => Err(Error::InvalidBranchProof), // hash failed to decode
Ok(None) => Err(Error::BranchOutOfBounds),
Err(_) => Err(Error::InvalidBranchProof),
}
}
// input for `codec` which draws data from the data shards
struct ShardInput<'a, I> {
shards: I,
cur_shard: Option<(&'a [u8], usize)>,
}
impl<'a, I: Iterator<Item=&'a [u8]>> codec::Input for ShardInput<'a, I> {
fn remaining_len(&mut self) -> Result<Option<usize>, codec::Error> {
Ok(Some(self.remaining_len))
}
fn read(&mut self, into: &mut [u8]) -> Result<(), codec::Error> {
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let mut read_bytes = 0;
loop {
if read_bytes == into.len() { break }
let cur_shard = self.cur_shard.take().or_else(|| self.shards.next().map(|s| (s, 0)));
let (active_shard, mut in_shard) = match cur_shard {
Some((s, i)) => (s, i),
None => break,
};
if in_shard >= active_shard.len() {
continue;
}
let remaining_len_out = into.len() - read_bytes;
let remaining_len_shard = active_shard.len() - in_shard;
let write_len = std::cmp::min(remaining_len_out, remaining_len_shard);
into[read_bytes..][..write_len]
.copy_from_slice(&active_shard[in_shard..][..write_len]);
in_shard += write_len;
read_bytes += write_len;
self.cur_shard = Some((active_shard, in_shard))
}
self.remaining_len -= read_bytes;
if read_bytes == into.len() {
Ok(())
} else {
Err("slice provided too big for input".into())
}
}
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn field_order_is_right_size() {
assert_eq!(MAX_VALIDATORS, 65536);
}
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#[test]
fn test_code_params() {
assert_eq!(code_params(0), Err(Error::EmptyValidators));
assert_eq!(code_params(1), Ok(CodeParams {
data_shards: 1,
parity_shards: 0,
}));
assert_eq!(code_params(2), Ok(CodeParams {
data_shards: 1,
parity_shards: 1,
}));
assert_eq!(code_params(3), Ok(CodeParams {
data_shards: 1,
parity_shards: 2,
}));
assert_eq!(code_params(4), Ok(CodeParams {
data_shards: 2,
parity_shards: 2,
}));
assert_eq!(code_params(100), Ok(CodeParams {
data_shards: 34,
parity_shards: 66,
}));
}
#[test]
fn shard_len_is_reasonable() {
let mut params = CodeParams {
data_shards: 5,
parity_shards: 0, // doesn't affect calculation.
};
assert_eq!(params.shard_len(100), 20);
assert_eq!(params.shard_len(99), 20);
// see if it rounds up to 2.
assert_eq!(params.shard_len(95), 20);
assert_eq!(params.shard_len(94), 20);
assert_eq!(params.shard_len(89), 18);
params.data_shards = 7;
// needs 3 bytes to fit, rounded up to next even number.
assert_eq!(params.shard_len(19), 4);
}
#[test]
fn round_trip_block_data() {
let block_data = BlockData((0..255).collect());
let ex = OutgoingMessages { outgoing_messages: Vec::new() };
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let chunks = obtain_chunks(
10,
&block_data,
&ex,
).unwrap();
assert_eq!(chunks.len(), 10);
// any 4 chunks should work.
let reconstructed = reconstruct(
10,
[
(&*chunks[1], 1),
(&*chunks[4], 4),
(&*chunks[6], 6),
(&*chunks[9], 9),
].iter().cloned(),
).unwrap();
assert_eq!(reconstructed, (block_data, ex));
}
#[test]
fn construct_valid_branches() {
let block_data = BlockData(vec![2; 256]);
let chunks = obtain_chunks(
10,
&block_data,
&OutgoingMessages { outgoing_messages: Vec::new() },
).unwrap();
let chunks: Vec<_> = chunks.iter().map(|c| &c[..]).collect();
assert_eq!(chunks.len(), 10);
let branches = branches(chunks.clone());
let root = branches.root();
let proofs: Vec<_> = branches.map(|(proof, _)| proof).collect();
assert_eq!(proofs.len(), 10);
for (i, proof) in proofs.into_iter().enumerate() {
assert_eq!(branch_hash(&root, &proof, i).unwrap(), BlakeTwo256::hash(chunks[i]));
}
}
}