Add CPartialMerkleTree

This adds a compact representation for a subset of a merkle tree's
nodes.

src/main.cpp

@@ -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)
 {
     uint64 nFreeBytesAvailable = filesystem::space(GetDataDir()).available;

src/main.h

@@ -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,

src/test/pmt_tests.cpp

@@ -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()