bmt: Binary Merkle Tree Hash (#14334)

bmt is a new package that provides hashers for binary merkle tree hashes on
size-limited chunks. the main motivation is that using BMT hash as the chunk
hash of the swarm hash offers logsize inclusion proofs for arbitrary files on a
32-byte resolution completely viable to use in challenges on the blockchain.

3 files changed, 1128 insertions, 0 deletions

diff --git a/bmt/bmt.go b/bmt/bmt.go
new file mode 100644
index 000000000..d62365bb1
--- /dev/null
+++ b/bmt/bmt.go
@@ -0,0 +1,562 @@
+// Copyright 2017 The go-ethereum Authors
+// This file is part of the go-ethereum library.
+//
+// The go-ethereum library is free software: you can redistribute it and/or modify
+// it under the terms of the GNU Lesser General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// The go-ethereum library 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 Lesser General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public License
+// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
+
+// Package bmt provides a binary merkle tree implementation
+package bmt
+
+import (
+	"fmt"
+	"hash"
+	"io"
+	"strings"
+	"sync"
+	"sync/atomic"
+)
+
+/*
+Binary Merkle Tree Hash is a hash function over arbitrary datachunks of limited size
+It is defined as the root hash of the binary merkle tree built over fixed size segments
+of the underlying chunk using any base hash function (e.g keccak 256 SHA3)
+
+It is used as the chunk hash function in swarm which in turn is the basis for the
+128 branching swarm hash http://swarm-guide.readthedocs.io/en/latest/architecture.html#swarm-hash
+
+The BMT is optimal for providing compact inclusion proofs, i.e. prove that a
+segment is a substring of a chunk starting at a particular offset
+The size of the underlying segments is fixed at 32 bytes (called the resolution
+of the BMT hash), the EVM word size to optimize for on-chain BMT verification
+as well as the hash size optimal for inclusion proofs in the merkle tree of the swarm hash.
+
+Two implementations are provided:
+
+* RefHasher is optimized for code simplicity and meant as a reference implementation
+* Hasher is optimized for speed taking advantage of concurrency with minimalistic
+  control structure to coordinate the concurrent routines
+  It implements the ChunkHash interface as well as the go standard hash.Hash interface
+
+*/
+
+const (
+	// DefaultSegmentCount is the maximum number of segments of the underlying chunk
+	DefaultSegmentCount = 128 // Should be equal to storage.DefaultBranches
+	// DefaultPoolSize is the maximum number of bmt trees used by the hashers, i.e,
+	// the maximum number of concurrent BMT hashing operations performed by the same hasher
+	DefaultPoolSize = 8
+)
+
+// BaseHasher is a hash.Hash constructor function used for the base hash of the  BMT.
+type BaseHasher func() hash.Hash
+
+// Hasher a reusable hasher for fixed maximum size chunks representing a BMT
+// implements the hash.Hash interface
+// reuse pool of Tree-s for amortised memory allocation and resource control
+// supports order-agnostic concurrent segment writes
+// as well as sequential read and write
+// can not be called concurrently on more than one chunk
+// can be further appended after Sum
+// Reset gives back the Tree to the pool and guaranteed to leave
+// the tree and itself in a state reusable for hashing a new chunk
+type Hasher struct {
+	pool        *TreePool   // BMT resource pool
+	bmt         *Tree       // prebuilt BMT resource for flowcontrol and proofs
+	blocksize   int         // segment size (size of hash) also for hash.Hash
+	count       int         // segment count
+	size        int         // for hash.Hash same as hashsize
+	cur         int         // cursor position for righmost currently open chunk
+	segment     []byte      // the rightmost open segment (not complete)
+	depth       int         // index of last level
+	result      chan []byte // result channel
+	hash        []byte      // to record the result
+	max         int32       // max segments for SegmentWriter interface
+	blockLength []byte      // The block length that needes to be added in Sum
+}
+
+// New creates a reusable Hasher
+// implements the hash.Hash interface
+// pulls a new Tree from a resource pool for hashing each chunk
+func New(p *TreePool) *Hasher {
+	return &Hasher{
+		pool:      p,
+		depth:     depth(p.SegmentCount),
+		size:      p.SegmentSize,
+		blocksize: p.SegmentSize,
+		count:     p.SegmentCount,
+		result:    make(chan []byte),
+	}
+}
+
+// Node is a reuseable segment hasher representing a node in a BMT
+// it allows for continued writes after a Sum
+// and is left in completely reusable state after Reset
+type Node struct {
+	level, index int   // position of node for information/logging only
+	initial      bool  // first and last node
+	root         bool  // whether the node is root to a smaller BMT
+	isLeft       bool  // whether it is left side of the parent double segment
+	unbalanced   bool  // indicates if a node has only the left segment
+	parent       *Node // BMT connections
+	state        int32 // atomic increment impl concurrent boolean toggle
+	left, right  []byte
+}
+
+// NewNode constructor for segment hasher nodes in the BMT
+func NewNode(level, index int, parent *Node) *Node {
+	return &Node{
+		parent:  parent,
+		level:   level,
+		index:   index,
+		initial: index == 0,
+		isLeft:  index%2 == 0,
+	}
+}
+
+// TreePool provides a pool of Trees used as resources by Hasher
+// a Tree popped from the pool is guaranteed to have clean state
+// for hashing a new chunk
+// Hasher Reset releases the Tree to the pool
+type TreePool struct {
+	lock         sync.Mutex
+	c            chan *Tree
+	hasher       BaseHasher
+	SegmentSize  int
+	SegmentCount int
+	Capacity     int
+	count        int
+}
+
+// NewTreePool creates a Tree pool with hasher, segment size, segment count and capacity
+// on GetTree it reuses free Trees or creates a new one if size is not reached
+func NewTreePool(hasher BaseHasher, segmentCount, capacity int) *TreePool {
+	return &TreePool{
+		c:            make(chan *Tree, capacity),
+		hasher:       hasher,
+		SegmentSize:  hasher().Size(),
+		SegmentCount: segmentCount,
+		Capacity:     capacity,
+	}
+}
+
+// Drain drains the pool uptil it has no more than n resources
+func (self *TreePool) Drain(n int) {
+	self.lock.Lock()
+	defer self.lock.Unlock()
+	for len(self.c) > n {
+		<-self.c
+		self.count--
+	}
+}
+
+// Reserve is blocking until it returns an available Tree
+// it reuses free Trees or creates a new one if size is not reached
+func (self *TreePool) Reserve() *Tree {
+	self.lock.Lock()
+	defer self.lock.Unlock()
+	var t *Tree
+	if self.count == self.Capacity {
+		return <-self.c
+	}
+	select {
+	case t = <-self.c:
+	default:
+		t = NewTree(self.hasher, self.SegmentSize, self.SegmentCount)
+		self.count++
+	}
+	return t
+}
+
+// Release gives back a Tree to the pool.
+// This Tree is guaranteed to be in reusable state
+// does not need locking
+func (self *TreePool) Release(t *Tree) {
+	self.c <- t // can never fail but...
+}
+
+// Tree is a reusable control structure representing a BMT
+// organised in a binary tree
+// Hasher uses a TreePool to pick one for each chunk hash
+// the Tree is 'locked' while not in the pool
+type Tree struct {
+	leaves []*Node
+}
+
+// Draw draws the BMT (badly)
+func (self *Tree) Draw(hash []byte, d int) string {
+	var left, right []string
+	var anc []*Node
+	for i, n := range self.leaves {
+		left = append(left, fmt.Sprintf("%v", hashstr(n.left)))
+		if i%2 == 0 {
+			anc = append(anc, n.parent)
+		}
+		right = append(right, fmt.Sprintf("%v", hashstr(n.right)))
+	}
+	anc = self.leaves
+	var hashes [][]string
+	for l := 0; len(anc) > 0; l++ {
+		var nodes []*Node
+		hash := []string{""}
+		for i, n := range anc {
+			hash = append(hash, fmt.Sprintf("%v|%v", hashstr(n.left), hashstr(n.right)))
+			if i%2 == 0 && n.parent != nil {
+				nodes = append(nodes, n.parent)
+			}
+		}
+		hash = append(hash, "")
+		hashes = append(hashes, hash)
+		anc = nodes
+	}
+	hashes = append(hashes, []string{"", fmt.Sprintf("%v", hashstr(hash)), ""})
+	total := 60
+	del := "                             "
+	var rows []string
+	for i := len(hashes) - 1; i >= 0; i-- {
+		var textlen int
+		hash := hashes[i]
+		for _, s := range hash {
+			textlen += len(s)
+		}
+		if total < textlen {
+			total = textlen + len(hash)
+		}
+		delsize := (total - textlen) / (len(hash) - 1)
+		if delsize > len(del) {
+			delsize = len(del)
+		}
+		row := fmt.Sprintf("%v: %v", len(hashes)-i-1, strings.Join(hash, del[:delsize]))
+		rows = append(rows, row)
+
+	}
+	rows = append(rows, strings.Join(left, "  "))
+	rows = append(rows, strings.Join(right, "  "))
+	return strings.Join(rows, "\n") + "\n"
+}
+
+// NewTree initialises the Tree by building up the nodes of a BMT
+// segment size is stipulated to be the size of the hash
+// segmentCount needs to be positive integer and does not need to be
+// a power of two and can even be an odd number
+// segmentSize * segmentCount determines the maximum chunk size
+// hashed using the tree
+func NewTree(hasher BaseHasher, segmentSize, segmentCount int) *Tree {
+	n := NewNode(0, 0, nil)
+	n.root = true
+	prevlevel := []*Node{n}
+	// iterate over levels and creates 2^level nodes
+	level := 1
+	count := 2
+	for d := 1; d <= depth(segmentCount); d++ {
+		nodes := make([]*Node, count)
+		for i := 0; i < len(nodes); i++ {
+			var parent *Node
+			parent = prevlevel[i/2]
+			t := NewNode(level, i, parent)
+			nodes[i] = t
+		}
+		prevlevel = nodes
+		level++
+		count *= 2
+	}
+	// the datanode level is the nodes on the last level where
+	return &Tree{
+		leaves: prevlevel,
+	}
+}
+
+// methods needed by hash.Hash
+
+// Size returns the size
+func (self *Hasher) Size() int {
+	return self.size
+}
+
+// BlockSize returns the block size
+func (self *Hasher) BlockSize() int {
+	return self.blocksize
+}
+
+// Sum returns the hash of the buffer
+// hash.Hash interface Sum method appends the byte slice to the underlying
+// data before it calculates and returns the hash of the chunk
+func (self *Hasher) Sum(b []byte) (r []byte) {
+	t := self.bmt
+	i := self.cur
+	n := t.leaves[i]
+	j := i
+	// must run strictly before all nodes calculate
+	// datanodes are guaranteed to have a parent
+	if len(self.segment) > self.size && i > 0 && n.parent != nil {
+		n = n.parent
+	} else {
+		i *= 2
+	}
+	d := self.finalise(n, i)
+	self.writeSegment(j, self.segment, d)
+	c := <-self.result
+	self.releaseTree()
+
+	// sha3(length + BMT(pure_chunk))
+	if self.blockLength == nil {
+		return c
+	}
+	res := self.pool.hasher()
+	res.Reset()
+	res.Write(self.blockLength)
+	res.Write(c)
+	return res.Sum(nil)
+}
+
+// Hasher implements the SwarmHash interface
+
+// Hash waits for the hasher result and returns it
+// caller must call this on a BMT Hasher being written to
+func (self *Hasher) Hash() []byte {
+	return <-self.result
+}
+
+// Hasher implements the io.Writer interface
+
+// Write fills the buffer to hash
+// with every full segment complete launches a hasher go routine
+// that shoots up the BMT
+func (self *Hasher) Write(b []byte) (int, error) {
+	l := len(b)
+	if l <= 0 {
+		return 0, nil
+	}
+	s := self.segment
+	i := self.cur
+	count := (self.count + 1) / 2
+	need := self.count*self.size - self.cur*2*self.size
+	size := self.size
+	if need > size {
+		size *= 2
+	}
+	if l < need {
+		need = l
+	}
+	// calculate missing bit to complete current open segment
+	rest := size - len(s)
+	if need < rest {
+		rest = need
+	}
+	s = append(s, b[:rest]...)
+	need -= rest
+	// read full segments and the last possibly partial segment
+	for need > 0 && i < count-1 {
+		// push all finished chunks we read
+		self.writeSegment(i, s, self.depth)
+		need -= size
+		if need < 0 {
+			size += need
+		}
+		s = b[rest : rest+size]
+		rest += size
+		i++
+	}
+	self.segment = s
+	self.cur = i
+	// otherwise, we can assume len(s) == 0, so all buffer is read and chunk is not yet full
+	return l, nil
+}
+
+// Hasher implements the io.ReaderFrom interface
+
+// ReadFrom reads from io.Reader and appends to the data to hash using Write
+// it reads so that chunk to hash is maximum length or reader reaches EOF
+// caller must Reset the hasher prior to call
+func (self *Hasher) ReadFrom(r io.Reader) (m int64, err error) {
+	bufsize := self.size*self.count - self.size*self.cur - len(self.segment)
+	buf := make([]byte, bufsize)
+	var read int
+	for {
+		var n int
+		n, err = r.Read(buf)
+		read += n
+		if err == io.EOF || read == len(buf) {
+			hash := self.Sum(buf[:n])
+			if read == len(buf) {
+				err = NewEOC(hash)
+			}
+			break
+		}
+		if err != nil {
+			break
+		}
+		n, err = self.Write(buf[:n])
+		if err != nil {
+			break
+		}
+	}
+	return int64(read), err
+}
+
+// Reset needs to be called before writing to the hasher
+func (self *Hasher) Reset() {
+	self.getTree()
+	self.blockLength = nil
+}
+
+// Hasher implements the SwarmHash interface
+
+// ResetWithLength needs to be called before writing to the hasher
+// the argument is supposed to be the byte slice binary representation of
+// the legth of the data subsumed under the hash
+func (self *Hasher) ResetWithLength(l []byte) {
+	self.Reset()
+	self.blockLength = l
+
+}
+
+// Release gives back the Tree to the pool whereby it unlocks
+// it resets tree, segment and index
+func (self *Hasher) releaseTree() {
+	if self.bmt != nil {
+		n := self.bmt.leaves[self.cur]
+		for ; n != nil; n = n.parent {
+			n.unbalanced = false
+			if n.parent != nil {
+				n.root = false
+			}
+		}
+		self.pool.Release(self.bmt)
+		self.bmt = nil
+
+	}
+	self.cur = 0
+	self.segment = nil
+}
+
+func (self *Hasher) writeSegment(i int, s []byte, d int) {
+	h := self.pool.hasher()
+	n := self.bmt.leaves[i]
+
+	if len(s) > self.size && n.parent != nil {
+		go func() {
+			h.Reset()
+			h.Write(s)
+			s = h.Sum(nil)
+
+			if n.root {
+				self.result <- s
+				return
+			}
+			self.run(n.parent, h, d, n.index, s)
+		}()
+		return
+	}
+	go self.run(n, h, d, i*2, s)
+}
+
+func (self *Hasher) run(n *Node, h hash.Hash, d int, i int, s []byte) {
+	isLeft := i%2 == 0
+	for {
+		if isLeft {
+			n.left = s
+		} else {
+			n.right = s
+		}
+		if !n.unbalanced && n.toggle() {
+			return
+		}
+		if !n.unbalanced || !isLeft || i == 0 && d == 0 {
+			h.Reset()
+			h.Write(n.left)
+			h.Write(n.right)
+			s = h.Sum(nil)
+
+		} else {
+			s = append(n.left, n.right...)
+		}
+
+		self.hash = s
+		if n.root {
+			self.result <- s
+			return
+		}
+
+		isLeft = n.isLeft
+		n = n.parent
+		i++
+	}
+}
+
+// getTree obtains a BMT resource by reserving one from the pool
+func (self *Hasher) getTree() *Tree {
+	if self.bmt != nil {
+		return self.bmt
+	}
+	t := self.pool.Reserve()
+	self.bmt = t
+	return t
+}
+
+// atomic bool toggle implementing a concurrent reusable 2-state object
+// atomic addint with %2 implements atomic bool toggle
+// it returns true if the toggler just put it in the active/waiting state
+func (self *Node) toggle() bool {
+	return atomic.AddInt32(&self.state, 1)%2 == 1
+}
+
+func hashstr(b []byte) string {
+	end := len(b)
+	if end > 4 {
+		end = 4
+	}
+	return fmt.Sprintf("%x", b[:end])
+}
+
+func depth(n int) (d int) {
+	for l := (n - 1) / 2; l > 0; l /= 2 {
+		d++
+	}
+	return d
+}
+
+// finalise is following the zigzags on the tree belonging
+// to the final datasegment
+func (self *Hasher) finalise(n *Node, i int) (d int) {
+	isLeft := i%2 == 0
+	for {
+		// when the final segment's path is going via left segments
+		// the incoming data is pushed to the parent upon pulling the left
+		// we do not need toogle the state since this condition is
+		// detectable
+		n.unbalanced = isLeft
+		n.right = nil
+		if n.initial {
+			n.root = true
+			return d
+		}
+		isLeft = n.isLeft
+		n = n.parent
+		d++
+	}
+}
+
+// EOC (end of chunk) implements the error interface
+type EOC struct {
+	Hash []byte // read the hash of the chunk off the error
+}
+
+// Error returns the error string
+func (self *EOC) Error() string {
+	return fmt.Sprintf("hasher limit reached, chunk hash: %x", self.Hash)
+}
+
+// NewEOC creates new end of chunk error with the hash
+func NewEOC(hash []byte) *EOC {
+	return &EOC{hash}
+}
diff --git a/bmt/bmt_r.go b/bmt/bmt_r.go
new file mode 100644
index 000000000..649093ee3
--- /dev/null
+++ b/bmt/bmt_r.go
@@ -0,0 +1,85 @@
+// Copyright 2017 The go-ethereum Authors
+// This file is part of the go-ethereum library.
+//
+// The go-ethereum library is free software: you can redistribute it and/or modify
+// it under the terms of the GNU Lesser General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// The go-ethereum library 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 Lesser General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public License
+// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
+
+// simple nonconcurrent reference implementation for hashsize segment based
+// Binary Merkle tree hash on arbitrary but fixed maximum chunksize
+//
+// This implementation does not take advantage of any paralellisms and uses
+// far more memory than necessary, but it is easy to see that it is correct.
+// It can be used for generating test cases for optimized implementations.
+// see testBMTHasherCorrectness function in bmt_test.go
+package bmt
+
+import (
+	"hash"
+)
+
+// RefHasher is the non-optimized easy to read reference implementation of BMT
+type RefHasher struct {
+	span    int
+	section int
+	cap     int
+	h       hash.Hash
+}
+
+// NewRefHasher returns a new RefHasher
+func NewRefHasher(hasher BaseHasher, count int) *RefHasher {
+	h := hasher()
+	hashsize := h.Size()
+	maxsize := hashsize * count
+	c := 2
+	for ; c < count; c *= 2 {
+	}
+	if c > 2 {
+		c /= 2
+	}
+	return &RefHasher{
+		section: 2 * hashsize,
+		span:    c * hashsize,
+		cap:     maxsize,
+		h:       h,
+	}
+}
+
+// Hash returns the BMT hash of the byte slice
+// implements the SwarmHash interface
+func (rh *RefHasher) Hash(d []byte) []byte {
+	if len(d) > rh.cap {
+		d = d[:rh.cap]
+	}
+
+	return rh.hash(d, rh.span)
+}
+
+func (rh *RefHasher) hash(d []byte, s int) []byte {
+	l := len(d)
+	left := d
+	var right []byte
+	if l > rh.section {
+		for ; s >= l; s /= 2 {
+		}
+		left = rh.hash(d[:s], s)
+		right = d[s:]
+		if l-s > rh.section/2 {
+			right = rh.hash(right, s)
+		}
+	}
+	defer rh.h.Reset()
+	rh.h.Write(left)
+	rh.h.Write(right)
+	h := rh.h.Sum(nil)
+	return h
+}
diff --git a/bmt/bmt_test.go b/bmt/bmt_test.go
new file mode 100644
index 000000000..57df83060
--- /dev/null
+++ b/bmt/bmt_test.go
@@ -0,0 +1,481 @@
+// Copyright 2017 The go-ethereum Authors
+// This file is part of the go-ethereum library.
+//
+// The go-ethereum library is free software: you can redistribute it and/or modify
+// it under the terms of the GNU Lesser General Public License as published by
+// the Free Software Foundation, either version 3 of the License, or
+// (at your option) any later version.
+//
+// The go-ethereum library 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 Lesser General Public License for more details.
+//
+// You should have received a copy of the GNU Lesser General Public License
+// along with the go-ethereum library. If not, see <http://www.gnu.org/licenses/>.
+
+package bmt
+
+import (
+	"bytes"
+	crand "crypto/rand"
+	"fmt"
+	"hash"
+	"io"
+	"math/rand"
+	"sync"
+	"sync/atomic"
+	"testing"
+	"time"
+
+	"github.com/ethereum/go-ethereum/crypto/sha3"
+)
+
+const (
+	maxproccnt = 8
+)
+
+// TestRefHasher tests that the RefHasher computes the expected BMT hash for
+// all data lengths between 0 and 256 bytes
+func TestRefHasher(t *testing.T) {
+	hashFunc := sha3.NewKeccak256
+
+	sha3 := func(data ...[]byte) []byte {
+		h := hashFunc()
+		for _, v := range data {
+			h.Write(v)
+		}
+		return h.Sum(nil)
+	}
+
+	// the test struct is used to specify the expected BMT hash for data
+	// lengths between "from" and "to"
+	type test struct {
+		from     int64
+		to       int64
+		expected func([]byte) []byte
+	}
+
+	var tests []*test
+
+	// all lengths in [0,64] should be:
+	//
+	//   sha3(data)
+	//
+	tests = append(tests, &test{
+		from: 0,
+		to:   64,
+		expected: func(data []byte) []byte {
+			return sha3(data)
+		},
+	})
+
+	// all lengths in [65,96] should be:
+	//
+	//   sha3(
+	//     sha3(data[:64])
+	//     data[64:]
+	//   )
+	//
+	tests = append(tests, &test{
+		from: 65,
+		to:   96,
+		expected: func(data []byte) []byte {
+			return sha3(sha3(data[:64]), data[64:])
+		},
+	})
+
+	// all lengths in [97,128] should be:
+	//
+	//   sha3(
+	//     sha3(data[:64])
+	//     sha3(data[64:])
+	//   )
+	//
+	tests = append(tests, &test{
+		from: 97,
+		to:   128,
+		expected: func(data []byte) []byte {
+			return sha3(sha3(data[:64]), sha3(data[64:]))
+		},
+	})
+
+	// all lengths in [129,160] should be:
+	//
+	//   sha3(
+	//     sha3(
+	//       sha3(data[:64])
+	//       sha3(data[64:128])
+	//     )
+	//     data[128:]
+	//   )
+	//
+	tests = append(tests, &test{
+		from: 129,
+		to:   160,
+		expected: func(data []byte) []byte {
+			return sha3(sha3(sha3(data[:64]), sha3(data[64:128])), data[128:])
+		},
+	})
+
+	// all lengths in [161,192] should be:
+	//
+	//   sha3(
+	//     sha3(
+	//       sha3(data[:64])
+	//       sha3(data[64:128])
+	//     )
+	//     sha3(data[128:])
+	//   )
+	//
+	tests = append(tests, &test{
+		from: 161,
+		to:   192,
+		expected: func(data []byte) []byte {
+			return sha3(sha3(sha3(data[:64]), sha3(data[64:128])), sha3(data[128:]))
+		},
+	})
+
+	// all lengths in [193,224] should be:
+	//
+	//   sha3(
+	//     sha3(
+	//       sha3(data[:64])
+	//       sha3(data[64:128])
+	//     )
+	//     sha3(
+	//       sha3(data[128:192])
+	//       data[192:]
+	//     )
+	//   )
+	//
+	tests = append(tests, &test{
+		from: 193,
+		to:   224,
+		expected: func(data []byte) []byte {
+			return sha3(sha3(sha3(data[:64]), sha3(data[64:128])), sha3(sha3(data[128:192]), data[192:]))
+		},
+	})
+
+	// all lengths in [225,256] should be:
+	//
+	//   sha3(
+	//     sha3(
+	//       sha3(data[:64])
+	//       sha3(data[64:128])
+	//     )
+	//     sha3(
+	//       sha3(data[128:192])
+	//       sha3(data[192:])
+	//     )
+	//   )
+	//
+	tests = append(tests, &test{
+		from: 225,
+		to:   256,
+		expected: func(data []byte) []byte {
+			return sha3(sha3(sha3(data[:64]), sha3(data[64:128])), sha3(sha3(data[128:192]), sha3(data[192:])))
+		},
+	})
+
+	// run the tests
+	for _, x := range tests {
+		for length := x.from; length <= x.to; length++ {
+			t.Run(fmt.Sprintf("%d_bytes", length), func(t *testing.T) {
+				data := make([]byte, length)
+				if _, err := io.ReadFull(crand.Reader, data); err != nil && err != io.EOF {
+					t.Fatal(err)
+				}
+				expected := x.expected(data)
+				actual := NewRefHasher(hashFunc, 128).Hash(data)
+				if !bytes.Equal(actual, expected) {
+					t.Fatalf("expected %x, got %x", expected, actual)
+				}
+			})
+		}
+	}
+}
+
+func testDataReader(l int) (r io.Reader) {
+	return io.LimitReader(crand.Reader, int64(l))
+}
+
+func TestHasherCorrectness(t *testing.T) {
+	err := testHasher(testBaseHasher)
+	if err != nil {
+		t.Fatal(err)
+	}
+}
+
+func testHasher(f func(BaseHasher, []byte, int, int) error) error {
+	tdata := testDataReader(4128)
+	data := make([]byte, 4128)
+	tdata.Read(data)
+	hasher := sha3.NewKeccak256
+	size := hasher().Size()
+	counts := []int{1, 2, 3, 4, 5, 8, 16, 32, 64, 128}
+
+	var err error
+	for _, count := range counts {
+		max := count * size
+		incr := 1
+		for n := 0; n <= max+incr; n += incr {
+			err = f(hasher, data, n, count)
+			if err != nil {
+				return err
+			}
+		}
+	}
+	return nil
+}
+
+func TestHasherReuseWithoutRelease(t *testing.T) {
+	testHasherReuse(1, t)
+}
+
+func TestHasherReuseWithRelease(t *testing.T) {
+	testHasherReuse(maxproccnt, t)
+}
+
+func testHasherReuse(i int, t *testing.T) {
+	hasher := sha3.NewKeccak256
+	pool := NewTreePool(hasher, 128, i)
+	defer pool.Drain(0)
+	bmt := New(pool)
+
+	for i := 0; i < 500; i++ {
+		n := rand.Intn(4096)
+		tdata := testDataReader(n)
+		data := make([]byte, n)
+		tdata.Read(data)
+
+		err := testHasherCorrectness(bmt, hasher, data, n, 128)
+		if err != nil {
+			t.Fatal(err)
+		}
+	}
+}
+
+func TestHasherConcurrency(t *testing.T) {
+	hasher := sha3.NewKeccak256
+	pool := NewTreePool(hasher, 128, maxproccnt)
+	defer pool.Drain(0)
+	wg := sync.WaitGroup{}
+	cycles := 100
+	wg.Add(maxproccnt * cycles)
+	errc := make(chan error)
+
+	for p := 0; p < maxproccnt; p++ {
+		for i := 0; i < cycles; i++ {
+			go func() {
+				bmt := New(pool)
+				n := rand.Intn(4096)
+				tdata := testDataReader(n)
+				data := make([]byte, n)
+				tdata.Read(data)
+				err := testHasherCorrectness(bmt, hasher, data, n, 128)
+				wg.Done()
+				if err != nil {
+					errc <- err
+				}
+			}()
+		}
+	}
+	go func() {
+		wg.Wait()
+		close(errc)
+	}()
+	var err error
+	select {
+	case <-time.NewTimer(5 * time.Second).C:
+		err = fmt.Errorf("timed out")
+	case err = <-errc:
+	}
+	if err != nil {
+		t.Fatal(err)
+	}
+}
+
+func testBaseHasher(hasher BaseHasher, d []byte, n, count int) error {
+	pool := NewTreePool(hasher, count, 1)
+	defer pool.Drain(0)
+	bmt := New(pool)
+	return testHasherCorrectness(bmt, hasher, d, n, count)
+}
+
+func testHasherCorrectness(bmt hash.Hash, hasher BaseHasher, d []byte, n, count int) (err error) {
+	data := d[:n]
+	rbmt := NewRefHasher(hasher, count)
+	exp := rbmt.Hash(data)
+	timeout := time.NewTimer(time.Second)
+	c := make(chan error)
+
+	go func() {
+		bmt.Reset()
+		bmt.Write(data)
+		got := bmt.Sum(nil)
+		if !bytes.Equal(got, exp) {
+			c <- fmt.Errorf("wrong hash: expected %x, got %x", exp, got)
+		}
+		close(c)
+	}()
+	select {
+	case <-timeout.C:
+		err = fmt.Errorf("BMT hash calculation timed out")
+	case err = <-c:
+	}
+	return err
+}
+
+func BenchmarkSHA3_4k(t *testing.B)   { benchmarkSHA3(4096, t) }
+func BenchmarkSHA3_2k(t *testing.B)   { benchmarkSHA3(4096/2, t) }
+func BenchmarkSHA3_1k(t *testing.B)   { benchmarkSHA3(4096/4, t) }
+func BenchmarkSHA3_512b(t *testing.B) { benchmarkSHA3(4096/8, t) }
+func BenchmarkSHA3_256b(t *testing.B) { benchmarkSHA3(4096/16, t) }
+func BenchmarkSHA3_128b(t *testing.B) { benchmarkSHA3(4096/32, t) }
+
+func BenchmarkBMTBaseline_4k(t *testing.B)   { benchmarkBMTBaseline(4096, t) }
+func BenchmarkBMTBaseline_2k(t *testing.B)   { benchmarkBMTBaseline(4096/2, t) }
+func BenchmarkBMTBaseline_1k(t *testing.B)   { benchmarkBMTBaseline(4096/4, t) }
+func BenchmarkBMTBaseline_512b(t *testing.B) { benchmarkBMTBaseline(4096/8, t) }
+func BenchmarkBMTBaseline_256b(t *testing.B) { benchmarkBMTBaseline(4096/16, t) }
+func BenchmarkBMTBaseline_128b(t *testing.B) { benchmarkBMTBaseline(4096/32, t) }
+
+func BenchmarkRefHasher_4k(t *testing.B)   { benchmarkRefHasher(4096, t) }
+func BenchmarkRefHasher_2k(t *testing.B)   { benchmarkRefHasher(4096/2, t) }
+func BenchmarkRefHasher_1k(t *testing.B)   { benchmarkRefHasher(4096/4, t) }
+func BenchmarkRefHasher_512b(t *testing.B) { benchmarkRefHasher(4096/8, t) }
+func BenchmarkRefHasher_256b(t *testing.B) { benchmarkRefHasher(4096/16, t) }
+func BenchmarkRefHasher_128b(t *testing.B) { benchmarkRefHasher(4096/32, t) }
+
+func BenchmarkHasher_4k(t *testing.B)   { benchmarkHasher(4096, t) }
+func BenchmarkHasher_2k(t *testing.B)   { benchmarkHasher(4096/2, t) }
+func BenchmarkHasher_1k(t *testing.B)   { benchmarkHasher(4096/4, t) }
+func BenchmarkHasher_512b(t *testing.B) { benchmarkHasher(4096/8, t) }
+func BenchmarkHasher_256b(t *testing.B) { benchmarkHasher(4096/16, t) }
+func BenchmarkHasher_128b(t *testing.B) { benchmarkHasher(4096/32, t) }
+
+func BenchmarkHasherNoReuse_4k(t *testing.B)   { benchmarkHasherReuse(1, 4096, t) }
+func BenchmarkHasherNoReuse_2k(t *testing.B)   { benchmarkHasherReuse(1, 4096/2, t) }
+func BenchmarkHasherNoReuse_1k(t *testing.B)   { benchmarkHasherReuse(1, 4096/4, t) }
+func BenchmarkHasherNoReuse_512b(t *testing.B) { benchmarkHasherReuse(1, 4096/8, t) }
+func BenchmarkHasherNoReuse_256b(t *testing.B) { benchmarkHasherReuse(1, 4096/16, t) }
+func BenchmarkHasherNoReuse_128b(t *testing.B) { benchmarkHasherReuse(1, 4096/32, t) }
+
+func BenchmarkHasherReuse_4k(t *testing.B)   { benchmarkHasherReuse(16, 4096, t) }
+func BenchmarkHasherReuse_2k(t *testing.B)   { benchmarkHasherReuse(16, 4096/2, t) }
+func BenchmarkHasherReuse_1k(t *testing.B)   { benchmarkHasherReuse(16, 4096/4, t) }
+func BenchmarkHasherReuse_512b(t *testing.B) { benchmarkHasherReuse(16, 4096/8, t) }
+func BenchmarkHasherReuse_256b(t *testing.B) { benchmarkHasherReuse(16, 4096/16, t) }
+func BenchmarkHasherReuse_128b(t *testing.B) { benchmarkHasherReuse(16, 4096/32, t) }
+
+// benchmarks the minimum hashing time for a balanced (for simplicity) BMT
+// by doing count/segmentsize parallel hashings of 2*segmentsize bytes
+// doing it on n maxproccnt each reusing the base hasher
+// the premise is that this is the minimum computation needed for a BMT
+// therefore this serves as a theoretical optimum for concurrent implementations
+func benchmarkBMTBaseline(n int, t *testing.B) {
+	tdata := testDataReader(64)
+	data := make([]byte, 64)
+	tdata.Read(data)
+	hasher := sha3.NewKeccak256
+
+	t.ReportAllocs()
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		count := int32((n-1)/hasher().Size() + 1)
+		wg := sync.WaitGroup{}
+		wg.Add(maxproccnt)
+		var i int32
+		for j := 0; j < maxproccnt; j++ {
+			go func() {
+				defer wg.Done()
+				h := hasher()
+				for atomic.AddInt32(&i, 1) < count {
+					h.Reset()
+					h.Write(data)
+					h.Sum(nil)
+				}
+			}()
+		}
+		wg.Wait()
+	}
+}
+
+func benchmarkHasher(n int, t *testing.B) {
+	tdata := testDataReader(n)
+	data := make([]byte, n)
+	tdata.Read(data)
+
+	size := 1
+	hasher := sha3.NewKeccak256
+	segmentCount := 128
+	pool := NewTreePool(hasher, segmentCount, size)
+	bmt := New(pool)
+
+	t.ReportAllocs()
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		bmt.Reset()
+		bmt.Write(data)
+		bmt.Sum(nil)
+	}
+}
+
+func benchmarkHasherReuse(poolsize, n int, t *testing.B) {
+	tdata := testDataReader(n)
+	data := make([]byte, n)
+	tdata.Read(data)
+
+	hasher := sha3.NewKeccak256
+	segmentCount := 128
+	pool := NewTreePool(hasher, segmentCount, poolsize)
+	cycles := 200
+
+	t.ReportAllocs()
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		wg := sync.WaitGroup{}
+		wg.Add(cycles)
+		for j := 0; j < cycles; j++ {
+			bmt := New(pool)
+			go func() {
+				defer wg.Done()
+				bmt.Reset()
+				bmt.Write(data)
+				bmt.Sum(nil)
+			}()
+		}
+		wg.Wait()
+	}
+}
+
+func benchmarkSHA3(n int, t *testing.B) {
+	data := make([]byte, n)
+	tdata := testDataReader(n)
+	tdata.Read(data)
+	hasher := sha3.NewKeccak256
+	h := hasher()
+
+	t.ReportAllocs()
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		h.Reset()
+		h.Write(data)
+		h.Sum(nil)
+	}
+}
+
+func benchmarkRefHasher(n int, t *testing.B) {
+	data := make([]byte, n)
+	tdata := testDataReader(n)
+	tdata.Read(data)
+	hasher := sha3.NewKeccak256
+	rbmt := NewRefHasher(hasher, 128)
+
+	t.ReportAllocs()
+	t.ResetTimer()
+	for i := 0; i < t.N; i++ {
+		rbmt.Hash(data)
+	}
+}