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Add CPartialMerkleTree

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This adds a compact representation for a subset of a merkle tree's
nodes.
This commit is contained in:
Pieter Wuille 2012-10-27 21:08:45 +02:00 committed by Matt Corallo
parent b1f99bed6f
commit 4bedfa9223
3 changed files with 309 additions and 0 deletions
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121
src/main.cpp
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@ -2262,6 +2262,127 @@ CMerkleBlock::CMerkleBlock(const CBlock& block, CBloomFilter& filter)
uint256 CPartialMerkleTree::CalcHash(int height, unsigned int pos, const std::vector<uint256> &vTxid) {
if (height == 0) {
// hash at height 0 is the txids themself
return vTxid[pos];
} else {
// calculate left hash
uint256 left = CalcHash(height-1, pos*2, vTxid), right;
// calculate right hash if not beyong the end of the array - copy left hash otherwise1
if (pos*2+1 < CalcTreeWidth(height-1))
right = CalcHash(height-1, pos*2+1, vTxid);
else
right = left;
// combine subhashes
return Hash(BEGIN(left), END(left), BEGIN(right), END(right));
}
}
void CPartialMerkleTree::TraverseAndBuild(int height, unsigned int pos, const std::vector<uint256> &vTxid, const std::vector<bool> &vMatch) {
// determine whether this node is the parent of at least one matched txid
bool fParentOfMatch = false;
for (unsigned int p = pos << height; p < (pos+1) << height && p < nTransactions; p++)
fParentOfMatch |= vMatch[p];
// store as flag bit
vBits.push_back(fParentOfMatch);
if (height==0 || !fParentOfMatch) {
// if at height 0, or nothing interesting below, store hash and stop
vHash.push_back(CalcHash(height, pos, vTxid));
} else {
// otherwise, don't store any hash, but descend into the subtrees
TraverseAndBuild(height-1, pos*2, vTxid, vMatch);
if (pos*2+1 < CalcTreeWidth(height-1))
TraverseAndBuild(height-1, pos*2+1, vTxid, vMatch);
}
}
uint256 CPartialMerkleTree::TraverseAndExtract(int height, unsigned int pos, unsigned int &nBitsUsed, unsigned int &nHashUsed, std::vector<uint256> &vMatch) {
if (nBitsUsed >= vBits.size()) {
// overflowed the bits array - failure
fBad = true;
return 0;
}
bool fParentOfMatch = vBits[nBitsUsed++];
if (height==0 || !fParentOfMatch) {
// if at height 0, or nothing interesting below, use stored hash and do not descend
if (nHashUsed >= vHash.size()) {
// overflowed the hash array - failure
fBad = true;
return 0;
}
const uint256 &hash = vHash[nHashUsed++];
if (height==0 && fParentOfMatch) // in case of height 0, we have a matched txid
vMatch.push_back(hash);
return hash;
} else {
// otherwise, descend into the subtrees to extract matched txids and hashes
uint256 left = TraverseAndExtract(height-1, pos*2, nBitsUsed, nHashUsed, vMatch), right;
if (pos*2+1 < CalcTreeWidth(height-1))
right = TraverseAndExtract(height-1, pos*2+1, nBitsUsed, nHashUsed, vMatch);
else
right = left;
// and combine them before returning
return Hash(BEGIN(left), END(left), BEGIN(right), END(right));
}
}
CPartialMerkleTree::CPartialMerkleTree(const std::vector<uint256> &vTxid, const std::vector<bool> &vMatch) : nTransactions(vTxid.size()), fBad(false) {
// reset state
vBits.clear();
vHash.clear();
// calculate height of tree
int nHeight = 0;
while (CalcTreeWidth(nHeight) > 1)
nHeight++;
// traverse the partial tree
TraverseAndBuild(nHeight, 0, vTxid, vMatch);
}
CPartialMerkleTree::CPartialMerkleTree() : nTransactions(0), fBad(true) {}
uint256 CPartialMerkleTree::ExtractMatches(std::vector<uint256> &vMatch) {
vMatch.clear();
// An empty set will not work
if (nTransactions == 0)
return 0;
// check for excessively high numbers of transactions
if (nTransactions > MAX_BLOCK_SIZE / 60) // 60 is the lower bound for the size of a serialized CTransaction
return 0;
// there can never be more hashes provided than one for every txid
if (vHash.size() > nTransactions)
return 0;
// there must be at least one bit per node in the partial tree, and at least one node per hash
if (vBits.size() < vHash.size())
return 0;
// calculate height of tree
int nHeight = 0;
while (CalcTreeWidth(nHeight) > 1)
nHeight++;
// traverse the partial tree
unsigned int nBitsUsed = 0, nHashUsed = 0;
uint256 hashMerkleRoot = TraverseAndExtract(nHeight, 0, nBitsUsed, nHashUsed, vMatch);
// verify that no problems occured during the tree traversal
if (fBad)
return 0;
// verify that all bits were consumed (except for the padding caused by serializing it as a byte sequence)
if ((nBitsUsed+7)/8 != (vBits.size()+7)/8)
return 0;
// verify that all hashes were consumed
if (nHashUsed != vHash.size())
return 0;
return hashMerkleRoot;
}
bool CheckDiskSpace(uint64 nAdditionalBytes) bool CheckDiskSpace(uint64 nAdditionalBytes)
{ {
uint64 nFreeBytesAvailable = filesystem::space(GetDataDir()).available; uint64 nFreeBytesAvailable = filesystem::space(GetDataDir()).available;

90
src/main.h
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@ -1110,11 +1110,101 @@ public:
/** Data structure that represents a partial merkle tree.
*
* It respresents a subset of the txid's of a known block, in a way that
* allows recovery of the list of txid's and the merkle root, in an
* authenticated way.
*
* The encoding works as follows: we traverse the tree in depth-first order,
* storing a bit for each traversed node, signifying whether the node is the
* parent of at least one matched leaf txid (or a matched txid itself). In
* case we are at the leaf level, or this bit is 0, its merkle node hash is
* stored, and its children are not explorer further. Otherwise, no hash is
* stored, but we recurse into both (or the only) child branch. During
* decoding, the same depth-first traversal is performed, consuming bits and
* hashes as they written during encoding.
*
* The serialization is fixed and provides a hard guarantee about the
* encoded size:
*
* SIZE <= 10 + ceil(32.25*N)
*
* Where N represents the number of leaf nodes of the partial tree. N itself
* is bounded by:
*
* N <= total_transactions
* N <= 1 + matched_transactions*tree_height
*
* The serialization format:
* - uint32 total_transactions (4 bytes)
* - varint number of hashes (1-3 bytes)
* - uint256[] hashes in depth-first order (<= 32*N bytes)
* - varint number of bytes of flag bits (1-3 bytes)
* - byte[] flag bits, packed per 8 in a byte, least significant bit first (<= 2*N-1 bits)
* The size constraints follow from this.
*/
class CPartialMerkleTree
{
protected:
// the total number of transactions in the block
unsigned int nTransactions;
// node-is-parent-of-matched-txid bits
std::vector<bool> vBits;
// txids and internal hashes
std::vector<uint256> vHash;
// flag set when encountering invalid data
bool fBad;
// helper function to efficiently calculate the number of nodes at given height in the merkle tree
unsigned int CalcTreeWidth(int height) {
return (nTransactions+(1 << height)-1) >> height;
}
// calculate the hash of a node in the merkle tree (at leaf level: the txid's themself)
uint256 CalcHash(int height, unsigned int pos, const std::vector<uint256> &vTxid);
// recursive function that traverses tree nodes, storing the data as bits and hashes
void TraverseAndBuild(int height, unsigned int pos, const std::vector<uint256> &vTxid, const std::vector<bool> &vMatch);
// recursive function that traverses tree nodes, consuming the bits and hashes produced by TraverseAndBuild.
// it returns the hash of the respective node.
uint256 TraverseAndExtract(int height, unsigned int pos, unsigned int &nBitsUsed, unsigned int &nHashUsed, std::vector<uint256> &vMatch);
public:
// serialization implementation
IMPLEMENT_SERIALIZE(
READWRITE(nTransactions);
READWRITE(vHash);
std::vector<unsigned char> vBytes;
if (fRead) {
READWRITE(vBytes);
CPartialMerkleTree &us = *(const_cast<CPartialMerkleTree*>(this));
us.vBits.resize(vBytes.size() * 8);
for (unsigned int p = 0; p < us.vBits.size(); p++)
us.vBits[p] = (vBytes[p / 8] & (1 << (p % 8))) != 0;
us.fBad = false;
} else {
vBytes.resize((vBits.size()+7)/8);
for (unsigned int p = 0; p < vBits.size(); p++)
vBytes[p / 8] |= vBits[p] << (p % 8);
READWRITE(vBytes);
}
)
// Construct a partial merkle tree from a list of transaction id's, and a mask that selects a subset of them
CPartialMerkleTree(const std::vector<uint256> &vTxid, const std::vector<bool> &vMatch);
CPartialMerkleTree();
// extract the matching txid's represented by this partial merkle tree.
// returns the merkle root, or 0 in case of failure
uint256 ExtractMatches(std::vector<uint256> &vMatch);
};
/** Nodes collect new transactions into a block, hash them into a hash tree, /** Nodes collect new transactions into a block, hash them into a hash tree,

98
src/test/pmt_tests.cpp Normal file
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@ -0,0 +1,98 @@
#include <boost/test/unit_test.hpp>
#include "uint256.h"
#include "main.h"
using namespace std;
class CPartialMerkleTreeTester : public CPartialMerkleTree
{
public:
// flip one bit in one of the hashes - this should break the authentication
void Damage() {
unsigned int n = rand() % vHash.size();
int bit = rand() % 256;
uint256 &hash = vHash[n];
hash ^= ((uint256)1 << bit);
}
};
BOOST_AUTO_TEST_SUITE(pmt_tests)
BOOST_AUTO_TEST_CASE(pmt_test1)
{
static const unsigned int nTxCounts[] = {1, 4, 7, 17, 56, 100, 127, 256, 312, 513, 1000, 4095};
for (int n = 0; n < 12; n++) {
unsigned int nTx = nTxCounts[n];
// build a block with some dummy transactions
CBlock block;
for (unsigned int j=0; j<nTx; j++) {
CTransaction tx;
tx.nLockTime = rand(); // actual transaction data doesn't matter; just make the nLockTime's unique
block.vtx.push_back(tx);
}
// calculate actual merkle root and height
uint256 merkleRoot1 = block.BuildMerkleTree();
std::vector<uint256> vTxid(nTx, 0);
for (unsigned int j=0; j<nTx; j++)
vTxid[j] = block.vtx[j].GetHash();
int nHeight = 1, nTx_ = nTx;
while (nTx_ > 1) {
nTx_ = (nTx_+1)/2;
nHeight++;
}
// check with random subsets with inclusion chances 1, 1/2, 1/4, ..., 1/128
for (int att = 1; att < 15; att++) {
// build random subset of txid's
std::vector<bool> vMatch(nTx, false);
std::vector<uint256> vMatchTxid1;
for (unsigned int j=0; j<nTx; j++) {
bool fInclude = (rand() & ((1 << (att/2)) - 1)) == 0;
vMatch[j] = fInclude;
if (fInclude)
vMatchTxid1.push_back(vTxid[j]);
}
// build the partial merkle tree
CPartialMerkleTree pmt1(vTxid, vMatch);
// serialize
CDataStream ss(SER_NETWORK, PROTOCOL_VERSION);
ss << pmt1;
// verify CPartialMerkleTree's size guarantees
unsigned int n = std::min<unsigned int>(nTx, 1 + vMatchTxid1.size()*nHeight);
BOOST_CHECK(ss.size() <= 10 + (258*n+7)/8);
// deserialize into a tester copy
CPartialMerkleTreeTester pmt2;
ss >> pmt2;
// extract merkle root and matched txids from copy
std::vector<uint256> vMatchTxid2;
uint256 merkleRoot2 = pmt2.ExtractMatches(vMatchTxid2);
// check that it has the same merkle root as the original, and a valid one
BOOST_CHECK(merkleRoot1 == merkleRoot2);
BOOST_CHECK(merkleRoot2 != 0);
// check that it contains the matched transactions (in the same order!)
BOOST_CHECK(vMatchTxid1 == vMatchTxid2);
// check that random bit flips break the authentication
for (int j=0; j<4; j++) {
CPartialMerkleTreeTester pmt3(pmt2);
pmt3.Damage();
std::vector<uint256> vMatchTxid3;
uint256 merkleRoot3 = pmt3.ExtractMatches(vMatchTxid3);
BOOST_CHECK(merkleRoot3 != merkleRoot1);
}
}
}
}
BOOST_AUTO_TEST_SUITE_END()