diff --git a/sumdb/tlog/ct_test.go b/sumdb/tlog/ct_test.go
new file mode 100644
index 0000000..c2d9aeb
--- /dev/null
+++ b/sumdb/tlog/ct_test.go
@@ -0,0 +1,96 @@
+// Copyright 2019 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package tlog
+
+import (
+	"encoding/json"
+	"fmt"
+	"io/ioutil"
+	"net/http"
+	"net/url"
+	"os"
+	"testing"
+)
+
+func TestCertificateTransparency(t *testing.T) {
+	// Test that we can verify actual Certificate Transparency proofs.
+	// (The other tests check that we can verify our own proofs;
+	// this is a test that the two are compatible.)
+
+	if testing.Short() {
+		t.Skip("skipping in -short mode")
+	}
+
+	var root ctTree
+	httpGET(t, "http://ct.googleapis.com/logs/argon2020/ct/v1/get-sth", &root)
+
+	var leaf ctEntries
+	httpGET(t, "http://ct.googleapis.com/logs/argon2020/ct/v1/get-entries?start=10000&end=10000", &leaf)
+	hash := RecordHash(leaf.Entries[0].Data)
+
+	var rp ctRecordProof
+	httpGET(t, "http://ct.googleapis.com/logs/argon2020/ct/v1/get-proof-by-hash?tree_size="+fmt.Sprint(root.Size)+"&hash="+url.QueryEscape(hash.String()), &rp)
+
+	err := CheckRecord(rp.Proof, root.Size, root.Hash, 10000, hash)
+	if err != nil {
+		t.Fatal(err)
+	}
+
+	var tp ctTreeProof
+	httpGET(t, "http://ct.googleapis.com/logs/argon2020/ct/v1/get-sth-consistency?first=3654490&second="+fmt.Sprint(root.Size), &tp)
+
+	oh, _ := ParseHash("AuIZ5V6sDUj1vn3Y1K85oOaQ7y+FJJKtyRTl1edIKBQ=")
+	err = CheckTree(tp.Proof, root.Size, root.Hash, 3654490, oh)
+	if err != nil {
+		t.Fatal(err)
+	}
+}
+
+type ctTree struct {
+	Size int64 `json:"tree_size"`
+	Hash Hash  `json:"sha256_root_hash"`
+}
+
+type ctEntries struct {
+	Entries []*ctEntry
+}
+
+type ctEntry struct {
+	Data []byte `json:"leaf_input"`
+}
+
+type ctRecordProof struct {
+	Index int64       `json:"leaf_index"`
+	Proof RecordProof `json:"audit_path"`
+}
+
+type ctTreeProof struct {
+	Proof TreeProof `json:"consistency"`
+}
+
+func httpGET(t *testing.T, url string, targ interface{}) {
+	if testing.Verbose() {
+		println()
+		println(url)
+	}
+	resp, err := http.Get(url)
+	if err != nil {
+		t.Fatal(err)
+	}
+	defer resp.Body.Close()
+	data, err := ioutil.ReadAll(resp.Body)
+	if err != nil {
+		t.Fatal(err)
+	}
+	if testing.Verbose() {
+		os.Stdout.Write(data)
+	}
+	err = json.Unmarshal(data, targ)
+	if err != nil {
+		println(url)
+		os.Stdout.Write(data)
+		t.Fatal(err)
+	}
+}
diff --git a/sumdb/tlog/note.go b/sumdb/tlog/note.go
new file mode 100644
index 0000000..ce5353e
--- /dev/null
+++ b/sumdb/tlog/note.go
@@ -0,0 +1,135 @@
+// Copyright 2019 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package tlog
+
+import (
+	"bytes"
+	"encoding/base64"
+	"errors"
+	"fmt"
+	"strconv"
+	"strings"
+	"unicode/utf8"
+)
+
+// A Tree is a tree description, to be signed by a go.sum database server.
+type Tree struct {
+	N    int64
+	Hash Hash
+}
+
+// FormatTree formats a tree description for inclusion in a note.
+//
+// The encoded form is three lines, each ending in a newline (U+000A):
+//
+//	go.sum database tree
+//	N
+//	Hash
+//
+// where N is in decimal and Hash is in base64.
+//
+// A future backwards-compatible encoding may add additional lines,
+// which the parser can ignore.
+// A future backwards-incompatible encoding would use a different
+// first line (for example, "go.sum database tree v2").
+func FormatTree(tree Tree) []byte {
+	return []byte(fmt.Sprintf("go.sum database tree\n%d\n%s\n", tree.N, tree.Hash))
+}
+
+var errMalformedTree = errors.New("malformed tree note")
+var treePrefix = []byte("go.sum database tree\n")
+
+// ParseTree parses a formatted tree root description.
+func ParseTree(text []byte) (tree Tree, err error) {
+	// The message looks like:
+	//
+	//	go.sum database tree
+	//	2
+	//	nND/nri/U0xuHUrYSy0HtMeal2vzD9V4k/BO79C+QeI=
+	//
+	// For forwards compatibility, extra text lines after the encoding are ignored.
+	if !bytes.HasPrefix(text, treePrefix) || bytes.Count(text, []byte("\n")) < 3 || len(text) > 1e6 {
+		return Tree{}, errMalformedTree
+	}
+
+	lines := strings.SplitN(string(text), "\n", 4)
+	n, err := strconv.ParseInt(lines[1], 10, 64)
+	if err != nil || n < 0 || lines[1] != strconv.FormatInt(n, 10) {
+		return Tree{}, errMalformedTree
+	}
+
+	h, err := base64.StdEncoding.DecodeString(lines[2])
+	if err != nil || len(h) != HashSize {
+		return Tree{}, errMalformedTree
+	}
+
+	var hash Hash
+	copy(hash[:], h)
+	return Tree{n, hash}, nil
+}
+
+var errMalformedRecord = errors.New("malformed record data")
+
+// FormatRecord formats a record for serving to a client
+// in a lookup response or data tile.
+//
+// The encoded form is the record ID as a single number,
+// then the text of the record, and then a terminating blank line.
+// Record text must be valid UTF-8 and must not contain any ASCII control
+// characters (those below U+0020) other than newline (U+000A).
+// It must end in a terminating newline and not contain any blank lines.
+func FormatRecord(id int64, text []byte) (msg []byte, err error) {
+	if !isValidRecordText(text) {
+		return nil, errMalformedRecord
+	}
+	msg = []byte(fmt.Sprintf("%d\n", id))
+	msg = append(msg, text...)
+	msg = append(msg, '\n')
+	return msg, nil
+}
+
+// isValidRecordText reports whether text is syntactically valid record text.
+func isValidRecordText(text []byte) bool {
+	var last rune
+	for i := 0; i < len(text); {
+		r, size := utf8.DecodeRune(text[i:])
+		if r < 0x20 && r != '\n' || r == utf8.RuneError && size == 1 || last == '\n' && r == '\n' {
+			return false
+		}
+		i += size
+		last = r
+	}
+	if last != '\n' {
+		return false
+	}
+	return true
+}
+
+// ParseRecord parses a record description at the start of text,
+// stopping immediately after the terminating blank line.
+// It returns the record id, the record text, and the remainder of text.
+func ParseRecord(msg []byte) (id int64, text, rest []byte, err error) {
+	// Leading record id.
+	i := bytes.IndexByte(msg, '\n')
+	if i < 0 {
+		return 0, nil, nil, errMalformedRecord
+	}
+	id, err = strconv.ParseInt(string(msg[:i]), 10, 64)
+	if err != nil {
+		return 0, nil, nil, errMalformedRecord
+	}
+	msg = msg[i+1:]
+
+	// Record text.
+	i = bytes.Index(msg, []byte("\n\n"))
+	if i < 0 {
+		return 0, nil, nil, errMalformedRecord
+	}
+	text, rest = msg[:i+1], msg[i+2:]
+	if !isValidRecordText(text) {
+		return 0, nil, nil, errMalformedRecord
+	}
+	return id, text, rest, nil
+}
diff --git a/sumdb/tlog/note_test.go b/sumdb/tlog/note_test.go
new file mode 100644
index 0000000..a32d6d2
--- /dev/null
+++ b/sumdb/tlog/note_test.go
@@ -0,0 +1,117 @@
+// Copyright 2019 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package tlog
+
+import (
+	"strings"
+	"testing"
+)
+
+func TestFormatTree(t *testing.T) {
+	n := int64(123456789012)
+	h := RecordHash([]byte("hello world"))
+	golden := "go.sum database tree\n123456789012\nTszzRgjTG6xce+z2AG31kAXYKBgQVtCSCE40HmuwBb0=\n"
+	b := FormatTree(Tree{n, h})
+	if string(b) != golden {
+		t.Errorf("FormatTree(...) = %q, want %q", b, golden)
+	}
+}
+
+func TestParseTree(t *testing.T) {
+	in := "go.sum database tree\n123456789012\nTszzRgjTG6xce+z2AG31kAXYKBgQVtCSCE40HmuwBb0=\n"
+	goldH := RecordHash([]byte("hello world"))
+	goldN := int64(123456789012)
+	tree, err := ParseTree([]byte(in))
+	if tree.N != goldN || tree.Hash != goldH || err != nil {
+		t.Fatalf("ParseTree(...) = Tree{%d, %v}, %v, want Tree{%d, %v}, nil", tree.N, tree.Hash, err, goldN, goldH)
+	}
+
+	// Check invalid trees.
+	var badTrees = []string{
+		"not-" + in,
+		"go.sum database tree\n0xabcdef\nTszzRgjTG6xce+z2AG31kAXYKBgQVtCSCE40HmuwBb0=\n",
+		"go.sum database tree\n123456789012\nTszzRgjTG6xce+z2AG31kAXYKBgQVtCSCE40HmuwBTOOBIG=\n",
+	}
+	for _, bad := range badTrees {
+		_, err := ParseTree([]byte(bad))
+		if err == nil {
+			t.Fatalf("ParseTree(%q) succeeded, want failure", in)
+		}
+	}
+
+	// Check junk on end is ignored.
+	var goodTrees = []string{
+		in + "JOE",
+		in + "JOE\n",
+		in + strings.Repeat("JOE\n", 1000),
+	}
+	for _, good := range goodTrees {
+		_, err := ParseTree([]byte(good))
+		if tree.N != goldN || tree.Hash != goldH || err != nil {
+			t.Fatalf("ParseTree(...+%q) = Tree{%d, %v}, %v, want Tree{%d, %v}, nil", good[len(in):], tree.N, tree.Hash, err, goldN, goldH)
+		}
+	}
+}
+
+func TestFormatRecord(t *testing.T) {
+	id := int64(123456789012)
+	text := "hello, world\n"
+	golden := "123456789012\nhello, world\n\n"
+	msg, err := FormatRecord(id, []byte(text))
+	if err != nil {
+		t.Fatalf("FormatRecord: %v", err)
+	}
+	if string(msg) != golden {
+		t.Fatalf("FormatRecord(...) = %q, want %q", msg, golden)
+	}
+
+	var badTexts = []string{
+		"",
+		"hello\nworld",
+		"hello\n\nworld\n",
+		"hello\x01world\n",
+	}
+	for _, bad := range badTexts {
+		msg, err := FormatRecord(id, []byte(bad))
+		if err == nil {
+			t.Errorf("FormatRecord(id, %q) = %q, want error", bad, msg)
+		}
+	}
+}
+
+func TestParseRecord(t *testing.T) {
+	in := "123456789012\nhello, world\n\njunk on end\x01\xff"
+	goldID := int64(123456789012)
+	goldText := "hello, world\n"
+	goldRest := "junk on end\x01\xff"
+	id, text, rest, err := ParseRecord([]byte(in))
+	if id != goldID || string(text) != goldText || string(rest) != goldRest || err != nil {
+		t.Fatalf("ParseRecord(%q) = %d, %q, %q, %v, want %d, %q, %q, nil", in, id, text, rest, err, goldID, goldText, goldRest)
+	}
+
+	in = "123456789012\nhello, world\n\n"
+	id, text, rest, err = ParseRecord([]byte(in))
+	if id != goldID || string(text) != goldText || len(rest) != 0 || err != nil {
+		t.Fatalf("ParseRecord(%q) = %d, %q, %q, %v, want %d, %q, %q, nil", in, id, text, rest, err, goldID, goldText, "")
+	}
+	if rest == nil {
+		t.Fatalf("ParseRecord(%q): rest = []byte(nil), want []byte{}", in)
+	}
+
+	// Check invalid records.
+	var badRecords = []string{
+		"not-" + in,
+		"123\nhello\x01world\n\n",
+		"123\nhello\xffworld\n\n",
+		"123\nhello world\n",
+		"0x123\nhello world\n\n",
+	}
+	for _, bad := range badRecords {
+		id, text, rest, err := ParseRecord([]byte(bad))
+		if err == nil {
+			t.Fatalf("ParseRecord(%q) = %d, %q, %q, nil, want error", in, id, text, rest)
+		}
+	}
+}
diff --git a/sumdb/tlog/tile.go b/sumdb/tlog/tile.go
new file mode 100644
index 0000000..e4aeb14
--- /dev/null
+++ b/sumdb/tlog/tile.go
@@ -0,0 +1,435 @@
+// Copyright 2019 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package tlog
+
+import (
+	"fmt"
+	"strconv"
+	"strings"
+)
+
+// A Tile is a description of a transparency log tile.
+// A tile of height H at level L offset N lists W consecutive hashes
+// at level H*L of the tree starting at offset N*(2**H).
+// A complete tile lists 2**H hashes; a partial tile lists fewer.
+// Note that a tile represents the entire subtree of height H
+// with those hashes as the leaves. The levels above H*L
+// can be reconstructed by hashing the leaves.
+//
+// Each Tile can be encoded as a “tile coordinate path”
+// of the form tile/H/L/NNN[.p/W].
+// The .p/W suffix is present only for partial tiles, meaning W < 2**H.
+// The NNN element is an encoding of N into 3-digit path elements.
+// All but the last path element begins with an "x".
+// For example,
+// Tile{H: 3, L: 4, N: 1234067, W: 1}'s path
+// is tile/3/4/x001/x234/067.p/1, and
+// Tile{H: 3, L: 4, N: 1234067, W: 8}'s path
+// is tile/3/4/x001/x234/067.
+// See Tile's Path method and the ParseTilePath function.
+//
+// The special level L=-1 holds raw record data instead of hashes.
+// In this case, the level encodes into a tile path as the path element
+// "data" instead of "-1".
+//
+// See also https://golang.org/design/25530-sumdb#checksum-database
+// and https://research.swtch.com/tlog#tiling_a_log.
+type Tile struct {
+	H int   // height of tile (1 ≤ H ≤ 30)
+	L int   // level in tiling (-1 ≤ L ≤ 63)
+	N int64 // number within level (0 ≤ N, unbounded)
+	W int   // width of tile (1 ≤ W ≤ 2**H; 2**H is complete tile)
+}
+
+// TileForIndex returns the tile of fixed height h ≥ 1
+// and least width storing the given hash storage index.
+//
+// If h ≤ 0, TileForIndex panics.
+func TileForIndex(h int, index int64) Tile {
+	if h <= 0 {
+		panic(fmt.Sprintf("TileForIndex: invalid height %d", h))
+	}
+	t, _, _ := tileForIndex(h, index)
+	return t
+}
+
+// tileForIndex returns the tile of height h ≥ 1
+// storing the given hash index, which can be
+// reconstructed using tileHash(data[start:end]).
+func tileForIndex(h int, index int64) (t Tile, start, end int) {
+	level, n := SplitStoredHashIndex(index)
+	t.H = h
+	t.L = level / h
+	level -= t.L * h // now level within tile
+	t.N = n << uint(level) >> uint(t.H)
+	n -= t.N << uint(t.H) >> uint(level) // now n within tile at level
+	t.W = int((n + 1) << uint(level))
+	return t, int(n<<uint(level)) * HashSize, int((n+1)<<uint(level)) * HashSize
+}
+
+// HashFromTile returns the hash at the given storage index,
+// provided that t == TileForIndex(t.H, index) or a wider version,
+// and data is t's tile data (of length at least t.W*HashSize).
+func HashFromTile(t Tile, data []byte, index int64) (Hash, error) {
+	if t.H < 1 || t.H > 30 || t.L < 0 || t.L >= 64 || t.W < 1 || t.W > 1<<uint(t.H) {
+		return Hash{}, fmt.Errorf("invalid tile %v", t.Path())
+	}
+	if len(data) < t.W*HashSize {
+		return Hash{}, fmt.Errorf("data len %d too short for tile %v", len(data), t.Path())
+	}
+	t1, start, end := tileForIndex(t.H, index)
+	if t.L != t1.L || t.N != t1.N || t.W < t1.W {
+		return Hash{}, fmt.Errorf("index %v is in %v not %v", index, t1.Path(), t.Path())
+	}
+	return tileHash(data[start:end]), nil
+}
+
+// tileHash computes the subtree hash corresponding to the (2^K)-1 hashes in data.
+func tileHash(data []byte) Hash {
+	if len(data) == 0 {
+		panic("bad math in tileHash")
+	}
+	if len(data) == HashSize {
+		var h Hash
+		copy(h[:], data)
+		return h
+	}
+	n := len(data) / 2
+	return NodeHash(tileHash(data[:n]), tileHash(data[n:]))
+}
+
+// NewTiles returns the coordinates of the tiles of height h ≥ 1
+// that must be published when publishing from a tree of
+// size newTreeSize to replace a tree of size oldTreeSize.
+// (No tiles need to be published for a tree of size zero.)
+//
+// If h ≤ 0, TileForIndex panics.
+func NewTiles(h int, oldTreeSize, newTreeSize int64) []Tile {
+	if h <= 0 {
+		panic(fmt.Sprintf("NewTiles: invalid height %d", h))
+	}
+	H := uint(h)
+	var tiles []Tile
+	for level := uint(0); newTreeSize>>(H*level) > 0; level++ {
+		oldN := oldTreeSize >> (H * level)
+		newN := newTreeSize >> (H * level)
+		for n := oldN >> H; n < newN>>H; n++ {
+			tiles = append(tiles, Tile{H: h, L: int(level), N: n, W: 1 << H})
+		}
+		n := newN >> H
+		maxW := int(newN - n<<H)
+		minW := 1
+		if oldN > n<<H {
+			minW = int(oldN - n<<H)
+		}
+		for w := minW; w <= maxW; w++ {
+			tiles = append(tiles, Tile{H: h, L: int(level), N: n, W: w})
+		}
+	}
+	return tiles
+}
+
+// ReadTileData reads the hashes for tile t from r
+// and returns the corresponding tile data.
+func ReadTileData(t Tile, r HashReader) ([]byte, error) {
+	size := t.W
+	if size == 0 {
+		size = 1 << uint(t.H)
+	}
+	start := t.N << uint(t.H)
+	indexes := make([]int64, size)
+	for i := 0; i < size; i++ {
+		indexes[i] = StoredHashIndex(t.H*t.L, start+int64(i))
+	}
+
+	hashes, err := r.ReadHashes(indexes)
+	if err != nil {
+		return nil, err
+	}
+	if len(hashes) != len(indexes) {
+		return nil, fmt.Errorf("tlog: ReadHashes(%d indexes) = %d hashes", len(indexes), len(hashes))
+	}
+
+	tile := make([]byte, size*HashSize)
+	for i := 0; i < size; i++ {
+		copy(tile[i*HashSize:], hashes[i][:])
+	}
+	return tile, nil
+}
+
+// To limit the size of any particular directory listing,
+// we encode the (possibly very large) number N
+// by encoding three digits at a time.
+// For example, 123456789 encodes as x123/x456/789.
+// Each directory has at most 1000 each xNNN, NNN, and NNN.p children,
+// so there are at most 3000 entries in any one directory.
+const pathBase = 1000
+
+// Path returns a tile coordinate path describing t.
+func (t Tile) Path() string {
+	n := t.N
+	nStr := fmt.Sprintf("%03d", n%pathBase)
+	for n >= pathBase {
+		n /= pathBase
+		nStr = fmt.Sprintf("x%03d/%s", n%pathBase, nStr)
+	}
+	pStr := ""
+	if t.W != 1<<uint(t.H) {
+		pStr = fmt.Sprintf(".p/%d", t.W)
+	}
+	var L string
+	if t.L == -1 {
+		L = "data"
+	} else {
+		L = fmt.Sprintf("%d", t.L)
+	}
+	return fmt.Sprintf("tile/%d/%s/%s%s", t.H, L, nStr, pStr)
+}
+
+// ParseTilePath parses a tile coordinate path.
+func ParseTilePath(path string) (Tile, error) {
+	f := strings.Split(path, "/")
+	if len(f) < 4 || f[0] != "tile" {
+		return Tile{}, &badPathError{path}
+	}
+	h, err1 := strconv.Atoi(f[1])
+	isData := false
+	if f[2] == "data" {
+		isData = true
+		f[2] = "0"
+	}
+	l, err2 := strconv.Atoi(f[2])
+	if err1 != nil || err2 != nil || h < 1 || l < 0 || h > 30 {
+		return Tile{}, &badPathError{path}
+	}
+	w := 1 << uint(h)
+	if dotP := f[len(f)-2]; strings.HasSuffix(dotP, ".p") {
+		ww, err := strconv.Atoi(f[len(f)-1])
+		if err != nil || ww <= 0 || ww >= w {
+			return Tile{}, &badPathError{path}
+		}
+		w = ww
+		f[len(f)-2] = dotP[:len(dotP)-len(".p")]
+		f = f[:len(f)-1]
+	}
+	f = f[3:]
+	n := int64(0)
+	for _, s := range f {
+		nn, err := strconv.Atoi(strings.TrimPrefix(s, "x"))
+		if err != nil || nn < 0 || nn >= pathBase {
+			return Tile{}, &badPathError{path}
+		}
+		n = n*pathBase + int64(nn)
+	}
+	if isData {
+		l = -1
+	}
+	t := Tile{H: h, L: l, N: n, W: w}
+	if path != t.Path() {
+		return Tile{}, &badPathError{path}
+	}
+	return t, nil
+}
+
+type badPathError struct {
+	path string
+}
+
+func (e *badPathError) Error() string {
+	return fmt.Sprintf("malformed tile path %q", e.path)
+}
+
+// A TileReader reads tiles from a go.sum database log.
+type TileReader interface {
+	// Height returns the height of the available tiles.
+	Height() int
+
+	// ReadTiles returns the data for each requested tile.
+	// If ReadTiles returns err == nil, it must also return
+	// a data record for each tile (len(data) == len(tiles))
+	// and each data record must be the correct length
+	// (len(data[i]) == tiles[i].W*HashSize).
+	//
+	// An implementation of ReadTiles typically reads
+	// them from an on-disk cache or else from a remote
+	// tile server. Tile data downloaded from a server should
+	// be considered suspect and not saved into a persistent
+	// on-disk cache before returning from ReadTiles.
+	// When the client confirms the validity of the tile data,
+	// it will call SaveTiles to signal that they can be safely
+	// written to persistent storage.
+	// See also https://research.swtch.com/tlog#authenticating_tiles.
+	ReadTiles(tiles []Tile) (data [][]byte, err error)
+
+	// SaveTiles informs the TileReader that the tile data
+	// returned by ReadTiles has been confirmed as valid
+	// and can be saved in persistent storage (on disk).
+	SaveTiles(tiles []Tile, data [][]byte)
+}
+
+// TileHashReader returns a HashReader that satisfies requests
+// by loading tiles of the given tree.
+//
+// The returned HashReader checks that loaded tiles are
+// valid for the given tree. Therefore, any hashes returned
+// by the HashReader are already proven to be in the tree.
+func TileHashReader(tree Tree, tr TileReader) HashReader {
+	return &tileHashReader{tree: tree, tr: tr}
+}
+
+type tileHashReader struct {
+	tree Tree
+	tr   TileReader
+}
+
+// tileParent returns t's k'th tile parent in the tiles for a tree of size n.
+// If there is no such parent, tileParent returns Tile{}.
+func tileParent(t Tile, k int, n int64) Tile {
+	t.L += k
+	t.N >>= uint(k * t.H)
+	t.W = 1 << uint(t.H)
+	if max := n >> uint(t.L*t.H); t.N<<uint(t.H)+int64(t.W) >= max {
+		if t.N<<uint(t.H) >= max {
+			return Tile{}
+		}
+		t.W = int(max - t.N<<uint(t.H))
+	}
+	return t
+}
+
+func (r *tileHashReader) ReadHashes(indexes []int64) ([]Hash, error) {
+	h := r.tr.Height()
+
+	tileOrder := make(map[Tile]int) // tileOrder[tileKey(tiles[i])] = i
+	var tiles []Tile
+
+	// Plan to fetch tiles necessary to recompute tree hash.
+	// If it matches, those tiles are authenticated.
+	stx := subTreeIndex(0, r.tree.N, nil)
+	stxTileOrder := make([]int, len(stx))
+	for i, x := range stx {
+		tile, _, _ := tileForIndex(h, x)
+		tile = tileParent(tile, 0, r.tree.N)
+		if j, ok := tileOrder[tile]; ok {
+			stxTileOrder[i] = j
+			continue
+		}
+		stxTileOrder[i] = len(tiles)
+		tileOrder[tile] = len(tiles)
+		tiles = append(tiles, tile)
+	}
+
+	// Plan to fetch tiles containing the indexes,
+	// along with any parent tiles needed
+	// for authentication. For most calls,
+	// the parents are being fetched anyway.
+	indexTileOrder := make([]int, len(indexes))
+	for i, x := range indexes {
+		if x >= StoredHashIndex(0, r.tree.N) {
+			return nil, fmt.Errorf("indexes not in tree")
+		}
+
+		tile, _, _ := tileForIndex(h, x)
+
+		// Walk up parent tiles until we find one we've requested.
+		// That one will be authenticated.
+		k := 0
+		for ; ; k++ {
+			p := tileParent(tile, k, r.tree.N)
+			if j, ok := tileOrder[p]; ok {
+				if k == 0 {
+					indexTileOrder[i] = j
+				}
+				break
+			}
+		}
+
+		// Walk back down recording child tiles after parents.
+		// This loop ends by revisiting the tile for this index
+		// (tileParent(tile, 0, r.tree.N)) unless k == 0, in which
+		// case the previous loop did it.
+		for k--; k >= 0; k-- {
+			p := tileParent(tile, k, r.tree.N)
+			if p.W != 1<<uint(p.H) {
+				// Only full tiles have parents.
+				// This tile has a parent, so it must be full.
+				return nil, fmt.Errorf("bad math in tileHashReader: %d %d %v", r.tree.N, x, p)
+			}
+			tileOrder[p] = len(tiles)
+			if k == 0 {
+				indexTileOrder[i] = len(tiles)
+			}
+			tiles = append(tiles, p)
+		}
+	}
+
+	// Fetch all the tile data.
+	data, err := r.tr.ReadTiles(tiles)
+	if err != nil {
+		return nil, err
+	}
+	if len(data) != len(tiles) {
+		return nil, fmt.Errorf("TileReader returned bad result slice (len=%d, want %d)", len(data), len(tiles))
+	}
+	for i, tile := range tiles {
+		if len(data[i]) != tile.W*HashSize {
+			return nil, fmt.Errorf("TileReader returned bad result slice (%v len=%d, want %d)", tile.Path(), len(data[i]), tile.W*HashSize)
+		}
+	}
+
+	// Authenticate the initial tiles against the tree hash.
+	// They are arranged so that parents are authenticated before children.
+	// First the tiles needed for the tree hash.
+	th, err := HashFromTile(tiles[stxTileOrder[len(stx)-1]], data[stxTileOrder[len(stx)-1]], stx[len(stx)-1])
+	if err != nil {
+		return nil, err
+	}
+	for i := len(stx) - 2; i >= 0; i-- {
+		h, err := HashFromTile(tiles[stxTileOrder[i]], data[stxTileOrder[i]], stx[i])
+		if err != nil {
+			return nil, err
+		}
+		th = NodeHash(h, th)
+	}
+	if th != r.tree.Hash {
+		// The tiles do not support the tree hash.
+		// We know at least one is wrong, but not which one.
+		return nil, fmt.Errorf("downloaded inconsistent tile")
+	}
+
+	// Authenticate full tiles against their parents.
+	for i := len(stx); i < len(tiles); i++ {
+		tile := tiles[i]
+		p := tileParent(tile, 1, r.tree.N)
+		j, ok := tileOrder[p]
+		if !ok {
+			return nil, fmt.Errorf("bad math in tileHashReader %d %v: lost parent of %v", r.tree.N, indexes, tile)
+		}
+		h, err := HashFromTile(p, data[j], StoredHashIndex(p.L*p.H, tile.N))
+		if err != nil {
+			return nil, fmt.Errorf("bad math in tileHashReader %d %v: lost hash of %v: %v", r.tree.N, indexes, tile, err)
+		}
+		if h != tileHash(data[i]) {
+			return nil, fmt.Errorf("downloaded inconsistent tile")
+		}
+	}
+
+	// Now we have all the tiles needed for the requested hashes,
+	// and we've authenticated the full tile set against the trusted tree hash.
+	r.tr.SaveTiles(tiles, data)
+
+	// Pull out the requested hashes.
+	hashes := make([]Hash, len(indexes))
+	for i, x := range indexes {
+		j := indexTileOrder[i]
+		h, err := HashFromTile(tiles[j], data[j], x)
+		if err != nil {
+			return nil, fmt.Errorf("bad math in tileHashReader %d %v: lost hash %v: %v", r.tree.N, indexes, x, err)
+		}
+		hashes[i] = h
+	}
+
+	return hashes, nil
+}
diff --git a/sumdb/tlog/tlog.go b/sumdb/tlog/tlog.go
new file mode 100644
index 0000000..a5b3d03
--- /dev/null
+++ b/sumdb/tlog/tlog.go
@@ -0,0 +1,598 @@
+// Copyright 2019 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+// Package tlog implements a tamper-evident log
+// used in the Go module go.sum database server.
+//
+// This package follows the design of Certificate Transparency (RFC 6962)
+// and its proofs are compatible with that system.
+// See TestCertificateTransparency.
+//
+package tlog
+
+import (
+	"crypto/sha256"
+	"encoding/base64"
+	"errors"
+	"fmt"
+	"math/bits"
+)
+
+// A Hash is a hash identifying a log record or tree root.
+type Hash [HashSize]byte
+
+// HashSize is the size of a Hash in bytes.
+const HashSize = 32
+
+// String returns a base64 representation of the hash for printing.
+func (h Hash) String() string {
+	return base64.StdEncoding.EncodeToString(h[:])
+}
+
+// MarshalJSON marshals the hash as a JSON string containing the base64-encoded hash.
+func (h Hash) MarshalJSON() ([]byte, error) {
+	return []byte(`"` + h.String() + `"`), nil
+}
+
+// UnmarshalJSON unmarshals a hash from JSON string containing the a base64-encoded hash.
+func (h *Hash) UnmarshalJSON(data []byte) error {
+	if len(data) != 1+44+1 || data[0] != '"' || data[len(data)-2] != '=' || data[len(data)-1] != '"' {
+		return errors.New("cannot decode hash")
+	}
+
+	// As of Go 1.12, base64.StdEncoding.Decode insists on
+	// slicing into target[33:] even when it only writes 32 bytes.
+	// Since we already checked that the hash ends in = above,
+	// we can use base64.RawStdEncoding with the = removed;
+	// RawStdEncoding does not exhibit the same bug.
+	// We decode into a temporary to avoid writing anything to *h
+	// unless the entire input is well-formed.
+	var tmp Hash
+	n, err := base64.RawStdEncoding.Decode(tmp[:], data[1:len(data)-2])
+	if err != nil || n != HashSize {
+		return errors.New("cannot decode hash")
+	}
+	*h = tmp
+	return nil
+}
+
+// ParseHash parses the base64-encoded string form of a hash.
+func ParseHash(s string) (Hash, error) {
+	data, err := base64.StdEncoding.DecodeString(s)
+	if err != nil || len(data) != HashSize {
+		return Hash{}, fmt.Errorf("malformed hash")
+	}
+	var h Hash
+	copy(h[:], data)
+	return h, nil
+}
+
+// maxpow2 returns k, the maximum power of 2 smaller than n,
+// as well as l = log₂ k (so k = 1<<l).
+func maxpow2(n int64) (k int64, l int) {
+	l = 0
+	for 1<<uint(l+1) < n {
+		l++
+	}
+	return 1 << uint(l), l
+}
+
+var zeroPrefix = []byte{0x00}
+
+// RecordHash returns the content hash for the given record data.
+func RecordHash(data []byte) Hash {
+	// SHA256(0x00 || data)
+	// https://tools.ietf.org/html/rfc6962#section-2.1
+	h := sha256.New()
+	h.Write(zeroPrefix)
+	h.Write(data)
+	var h1 Hash
+	h.Sum(h1[:0])
+	return h1
+}
+
+// NodeHash returns the hash for an interior tree node with the given left and right hashes.
+func NodeHash(left, right Hash) Hash {
+	// SHA256(0x01 || left || right)
+	// https://tools.ietf.org/html/rfc6962#section-2.1
+	// We use a stack buffer to assemble the hash input
+	// to avoid allocating a hash struct with sha256.New.
+	var buf [1 + HashSize + HashSize]byte
+	buf[0] = 0x01
+	copy(buf[1:], left[:])
+	copy(buf[1+HashSize:], right[:])
+	return sha256.Sum256(buf[:])
+}
+
+// For information about the stored hash index ordering,
+// see section 3.3 of Crosby and Wallach's paper
+// "Efficient Data Structures for Tamper-Evident Logging".
+// https://www.usenix.org/legacy/event/sec09/tech/full_papers/crosby.pdf
+
+// StoredHashIndex maps the tree coordinates (level, n)
+// to a dense linear ordering that can be used for hash storage.
+// Hash storage implementations that store hashes in sequential
+// storage can use this function to compute where to read or write
+// a given hash.
+func StoredHashIndex(level int, n int64) int64 {
+	// Level L's n'th hash is written right after level L+1's 2n+1'th hash.
+	// Work our way down to the level 0 ordering.
+	// We'll add back the orignal level count at the end.
+	for l := level; l > 0; l-- {
+		n = 2*n + 1
+	}
+
+	// Level 0's n'th hash is written at n+n/2+n/4+... (eventually n/2ⁱ hits zero).
+	i := int64(0)
+	for ; n > 0; n >>= 1 {
+		i += n
+	}
+
+	return i + int64(level)
+}
+
+// SplitStoredHashIndex is the inverse of StoredHashIndex.
+// That is, SplitStoredHashIndex(StoredHashIndex(level, n)) == level, n.
+func SplitStoredHashIndex(index int64) (level int, n int64) {
+	// Determine level 0 record before index.
+	// StoredHashIndex(0, n) < 2*n,
+	// so the n we want is in [index/2, index/2+log₂(index)].
+	n = index / 2
+	indexN := StoredHashIndex(0, n)
+	if indexN > index {
+		panic("bad math")
+	}
+	for {
+		// Each new record n adds 1 + trailingZeros(n) hashes.
+		x := indexN + 1 + int64(bits.TrailingZeros64(uint64(n+1)))
+		if x > index {
+			break
+		}
+		n++
+		indexN = x
+	}
+	// The hash we want was commited with record n,
+	// meaning it is one of (0, n), (1, n/2), (2, n/4), ...
+	level = int(index - indexN)
+	return level, n >> uint(level)
+}
+
+// StoredHashCount returns the number of stored hashes
+// that are expected for a tree with n records.
+func StoredHashCount(n int64) int64 {
+	if n == 0 {
+		return 0
+	}
+	// The tree will have the hashes up to the last leaf hash.
+	numHash := StoredHashIndex(0, n-1) + 1
+	// And it will have any hashes for subtrees completed by that leaf.
+	for i := uint64(n - 1); i&1 != 0; i >>= 1 {
+		numHash++
+	}
+	return numHash
+}
+
+// StoredHashes returns the hashes that must be stored when writing
+// record n with the given data. The hashes should be stored starting
+// at StoredHashIndex(0, n). The result will have at most 1 + log₂ n hashes,
+// but it will average just under two per call for a sequence of calls for n=1..k.
+//
+// StoredHashes may read up to log n earlier hashes from r
+// in order to compute hashes for completed subtrees.
+func StoredHashes(n int64, data []byte, r HashReader) ([]Hash, error) {
+	return StoredHashesForRecordHash(n, RecordHash(data), r)
+}
+
+// StoredHashesForRecordHash is like StoredHashes but takes
+// as its second argument RecordHash(data) instead of data itself.
+func StoredHashesForRecordHash(n int64, h Hash, r HashReader) ([]Hash, error) {
+	// Start with the record hash.
+	hashes := []Hash{h}
+
+	// Build list of indexes needed for hashes for completed subtrees.
+	// Each trailing 1 bit in the binary representation of n completes a subtree
+	// and consumes a hash from an adjacent subtree.
+	m := int(bits.TrailingZeros64(uint64(n + 1)))
+	indexes := make([]int64, m)
+	for i := 0; i < m; i++ {
+		// We arrange indexes in sorted order.
+		// Note that n>>i is always odd.
+		indexes[m-1-i] = StoredHashIndex(i, n>>uint(i)-1)
+	}
+
+	// Fetch hashes.
+	old, err := r.ReadHashes(indexes)
+	if err != nil {
+		return nil, err
+	}
+	if len(old) != len(indexes) {
+		return nil, fmt.Errorf("tlog: ReadHashes(%d indexes) = %d hashes", len(indexes), len(old))
+	}
+
+	// Build new hashes.
+	for i := 0; i < m; i++ {
+		h = NodeHash(old[m-1-i], h)
+		hashes = append(hashes, h)
+	}
+	return hashes, nil
+}
+
+// A HashReader can read hashes for nodes in the log's tree structure.
+type HashReader interface {
+	// ReadHashes returns the hashes with the given stored hash indexes
+	// (see StoredHashIndex and SplitStoredHashIndex).
+	// ReadHashes must return a slice of hashes the same length as indexes,
+	// or else it must return a non-nil error.
+	// ReadHashes may run faster if indexes is sorted in increasing order.
+	ReadHashes(indexes []int64) ([]Hash, error)
+}
+
+// A HashReaderFunc is a function implementing HashReader.
+type HashReaderFunc func([]int64) ([]Hash, error)
+
+func (f HashReaderFunc) ReadHashes(indexes []int64) ([]Hash, error) {
+	return f(indexes)
+}
+
+// TreeHash computes the hash for the root of the tree with n records,
+// using the HashReader to obtain previously stored hashes
+// (those returned by StoredHashes during the writes of those n records).
+// TreeHash makes a single call to ReadHash requesting at most 1 + log₂ n hashes.
+// The tree of size zero is defined to have an all-zero Hash.
+func TreeHash(n int64, r HashReader) (Hash, error) {
+	if n == 0 {
+		return Hash{}, nil
+	}
+	indexes := subTreeIndex(0, n, nil)
+	hashes, err := r.ReadHashes(indexes)
+	if err != nil {
+		return Hash{}, err
+	}
+	if len(hashes) != len(indexes) {
+		return Hash{}, fmt.Errorf("tlog: ReadHashes(%d indexes) = %d hashes", len(indexes), len(hashes))
+	}
+	hash, hashes := subTreeHash(0, n, hashes)
+	if len(hashes) != 0 {
+		panic("tlog: bad index math in TreeHash")
+	}
+	return hash, nil
+}
+
+// subTreeIndex returns the storage indexes needed to compute
+// the hash for the subtree containing records [lo, hi),
+// appending them to need and returning the result.
+// See https://tools.ietf.org/html/rfc6962#section-2.1
+func subTreeIndex(lo, hi int64, need []int64) []int64 {
+	// See subTreeHash below for commentary.
+	for lo < hi {
+		k, level := maxpow2(hi - lo + 1)
+		if lo&(k-1) != 0 {
+			panic("tlog: bad math in subTreeIndex")
+		}
+		need = append(need, StoredHashIndex(level, lo>>uint(level)))
+		lo += k
+	}
+	return need
+}
+
+// subTreeHash computes the hash for the subtree containing records [lo, hi),
+// assuming that hashes are the hashes corresponding to the indexes
+// returned by subTreeIndex(lo, hi).
+// It returns any leftover hashes.
+func subTreeHash(lo, hi int64, hashes []Hash) (Hash, []Hash) {
+	// Repeatedly partition the tree into a left side with 2^level nodes,
+	// for as large a level as possible, and a right side with the fringe.
+	// The left hash is stored directly and can be read from storage.
+	// The right side needs further computation.
+	numTree := 0
+	for lo < hi {
+		k, _ := maxpow2(hi - lo + 1)
+		if lo&(k-1) != 0 || lo >= hi {
+			panic("tlog: bad math in subTreeHash")
+		}
+		numTree++
+		lo += k
+	}
+
+	if len(hashes) < numTree {
+		panic("tlog: bad index math in subTreeHash")
+	}
+
+	// Reconstruct hash.
+	h := hashes[numTree-1]
+	for i := numTree - 2; i >= 0; i-- {
+		h = NodeHash(hashes[i], h)
+	}
+	return h, hashes[numTree:]
+}
+
+// A RecordProof is a verifiable proof that a particular log root contains a particular record.
+// RFC 6962 calls this a “Merkle audit path.”
+type RecordProof []Hash
+
+// ProveRecord returns the proof that the tree of size t contains the record with index n.
+func ProveRecord(t, n int64, r HashReader) (RecordProof, error) {
+	if t < 0 || n < 0 || n >= t {
+		return nil, fmt.Errorf("tlog: invalid inputs in ProveRecord")
+	}
+	indexes := leafProofIndex(0, t, n, nil)
+	if len(indexes) == 0 {
+		return RecordProof{}, nil
+	}
+	hashes, err := r.ReadHashes(indexes)
+	if err != nil {
+		return nil, err
+	}
+	if len(hashes) != len(indexes) {
+		return nil, fmt.Errorf("tlog: ReadHashes(%d indexes) = %d hashes", len(indexes), len(hashes))
+	}
+
+	p, hashes := leafProof(0, t, n, hashes)
+	if len(hashes) != 0 {
+		panic("tlog: bad index math in ProveRecord")
+	}
+	return p, nil
+}
+
+// leafProofIndex builds the list of indexes needed to construct the proof
+// that leaf n is contained in the subtree with leaves [lo, hi).
+// It appends those indexes to need and returns the result.
+// See https://tools.ietf.org/html/rfc6962#section-2.1.1
+func leafProofIndex(lo, hi, n int64, need []int64) []int64 {
+	// See leafProof below for commentary.
+	if !(lo <= n && n < hi) {
+		panic("tlog: bad math in leafProofIndex")
+	}
+	if lo+1 == hi {
+		return need
+	}
+	if k, _ := maxpow2(hi - lo); n < lo+k {
+		need = leafProofIndex(lo, lo+k, n, need)
+		need = subTreeIndex(lo+k, hi, need)
+	} else {
+		need = subTreeIndex(lo, lo+k, need)
+		need = leafProofIndex(lo+k, hi, n, need)
+	}
+	return need
+}
+
+// leafProof constructs the proof that leaf n is contained in the subtree with leaves [lo, hi).
+// It returns any leftover hashes as well.
+// See https://tools.ietf.org/html/rfc6962#section-2.1.1
+func leafProof(lo, hi, n int64, hashes []Hash) (RecordProof, []Hash) {
+	// We must have lo <= n < hi or else the code here has a bug.
+	if !(lo <= n && n < hi) {
+		panic("tlog: bad math in leafProof")
+	}
+
+	if lo+1 == hi { // n == lo
+		// Reached the leaf node.
+		// The verifier knows what the leaf hash is, so we don't need to send it.
+		return RecordProof{}, hashes
+	}
+
+	// Walk down the tree toward n.
+	// Record the hash of the path not taken (needed for verifying the proof).
+	var p RecordProof
+	var th Hash
+	if k, _ := maxpow2(hi - lo); n < lo+k {
+		// n is on left side
+		p, hashes = leafProof(lo, lo+k, n, hashes)
+		th, hashes = subTreeHash(lo+k, hi, hashes)
+	} else {
+		// n is on right side
+		th, hashes = subTreeHash(lo, lo+k, hashes)
+		p, hashes = leafProof(lo+k, hi, n, hashes)
+	}
+	return append(p, th), hashes
+}
+
+var errProofFailed = errors.New("invalid transparency proof")
+
+// CheckRecord verifies that p is a valid proof that the tree of size t
+// with hash th has an n'th record with hash h.
+func CheckRecord(p RecordProof, t int64, th Hash, n int64, h Hash) error {
+	if t < 0 || n < 0 || n >= t {
+		return fmt.Errorf("tlog: invalid inputs in CheckRecord")
+	}
+	th2, err := runRecordProof(p, 0, t, n, h)
+	if err != nil {
+		return err
+	}
+	if th2 == th {
+		return nil
+	}
+	return errProofFailed
+}
+
+// runRecordProof runs the proof p that leaf n is contained in the subtree with leaves [lo, hi).
+// Running the proof means constructing and returning the implied hash of that
+// subtree.
+func runRecordProof(p RecordProof, lo, hi, n int64, leafHash Hash) (Hash, error) {
+	// We must have lo <= n < hi or else the code here has a bug.
+	if !(lo <= n && n < hi) {
+		panic("tlog: bad math in runRecordProof")
+	}
+
+	if lo+1 == hi { // m == lo
+		// Reached the leaf node.
+		// The proof must not have any unnecessary hashes.
+		if len(p) != 0 {
+			return Hash{}, errProofFailed
+		}
+		return leafHash, nil
+	}
+
+	if len(p) == 0 {
+		return Hash{}, errProofFailed
+	}
+
+	k, _ := maxpow2(hi - lo)
+	if n < lo+k {
+		th, err := runRecordProof(p[:len(p)-1], lo, lo+k, n, leafHash)
+		if err != nil {
+			return Hash{}, err
+		}
+		return NodeHash(th, p[len(p)-1]), nil
+	} else {
+		th, err := runRecordProof(p[:len(p)-1], lo+k, hi, n, leafHash)
+		if err != nil {
+			return Hash{}, err
+		}
+		return NodeHash(p[len(p)-1], th), nil
+	}
+}
+
+// A TreeProof is a verifiable proof that a particular log tree contains
+// as a prefix all records present in an earlier tree.
+// RFC 6962 calls this a “Merkle consistency proof.”
+type TreeProof []Hash
+
+// ProveTree returns the proof that the tree of size t contains
+// as a prefix all the records from the tree of smaller size n.
+func ProveTree(t, n int64, h HashReader) (TreeProof, error) {
+	if t < 1 || n < 1 || n > t {
+		return nil, fmt.Errorf("tlog: invalid inputs in ProveTree")
+	}
+	indexes := treeProofIndex(0, t, n, nil)
+	if len(indexes) == 0 {
+		return TreeProof{}, nil
+	}
+	hashes, err := h.ReadHashes(indexes)
+	if err != nil {
+		return nil, err
+	}
+	if len(hashes) != len(indexes) {
+		return nil, fmt.Errorf("tlog: ReadHashes(%d indexes) = %d hashes", len(indexes), len(hashes))
+	}
+
+	p, hashes := treeProof(0, t, n, hashes)
+	if len(hashes) != 0 {
+		panic("tlog: bad index math in ProveTree")
+	}
+	return p, nil
+}
+
+// treeProofIndex builds the list of indexes needed to construct
+// the sub-proof related to the subtree containing records [lo, hi).
+// See https://tools.ietf.org/html/rfc6962#section-2.1.2.
+func treeProofIndex(lo, hi, n int64, need []int64) []int64 {
+	// See treeProof below for commentary.
+	if !(lo < n && n <= hi) {
+		panic("tlog: bad math in treeProofIndex")
+	}
+
+	if n == hi {
+		if lo == 0 {
+			return need
+		}
+		return subTreeIndex(lo, hi, need)
+	}
+
+	if k, _ := maxpow2(hi - lo); n <= lo+k {
+		need = treeProofIndex(lo, lo+k, n, need)
+		need = subTreeIndex(lo+k, hi, need)
+	} else {
+		need = subTreeIndex(lo, lo+k, need)
+		need = treeProofIndex(lo+k, hi, n, need)
+	}
+	return need
+}
+
+// treeProof constructs the sub-proof related to the subtree containing records [lo, hi).
+// It returns any leftover hashes as well.
+// See https://tools.ietf.org/html/rfc6962#section-2.1.2.
+func treeProof(lo, hi, n int64, hashes []Hash) (TreeProof, []Hash) {
+	// We must have lo < n <= hi or else the code here has a bug.
+	if !(lo < n && n <= hi) {
+		panic("tlog: bad math in treeProof")
+	}
+
+	// Reached common ground.
+	if n == hi {
+		if lo == 0 {
+			// This subtree corresponds exactly to the old tree.
+			// The verifier knows that hash, so we don't need to send it.
+			return TreeProof{}, hashes
+		}
+		th, hashes := subTreeHash(lo, hi, hashes)
+		return TreeProof{th}, hashes
+	}
+
+	// Interior node for the proof.
+	// Decide whether to walk down the left or right side.
+	var p TreeProof
+	var th Hash
+	if k, _ := maxpow2(hi - lo); n <= lo+k {
+		// m is on left side
+		p, hashes = treeProof(lo, lo+k, n, hashes)
+		th, hashes = subTreeHash(lo+k, hi, hashes)
+	} else {
+		// m is on right side
+		th, hashes = subTreeHash(lo, lo+k, hashes)
+		p, hashes = treeProof(lo+k, hi, n, hashes)
+	}
+	return append(p, th), hashes
+}
+
+// CheckTree verifies that p is a valid proof that the tree of size t with hash th
+// contains as a prefix the tree of size n with hash h.
+func CheckTree(p TreeProof, t int64, th Hash, n int64, h Hash) error {
+	if t < 1 || n < 1 || n > t {
+		return fmt.Errorf("tlog: invalid inputs in CheckTree")
+	}
+	h2, th2, err := runTreeProof(p, 0, t, n, h)
+	if err != nil {
+		return err
+	}
+	if th2 == th && h2 == h {
+		return nil
+	}
+	return errProofFailed
+}
+
+// runTreeProof runs the sub-proof p related to the subtree containing records [lo, hi),
+// where old is the hash of the old tree with n records.
+// Running the proof means constructing and returning the implied hashes of that
+// subtree in both the old and new tree.
+func runTreeProof(p TreeProof, lo, hi, n int64, old Hash) (Hash, Hash, error) {
+	// We must have lo < n <= hi or else the code here has a bug.
+	if !(lo < n && n <= hi) {
+		panic("tlog: bad math in runTreeProof")
+	}
+
+	// Reached common ground.
+	if n == hi {
+		if lo == 0 {
+			if len(p) != 0 {
+				return Hash{}, Hash{}, errProofFailed
+			}
+			return old, old, nil
+		}
+		if len(p) != 1 {
+			return Hash{}, Hash{}, errProofFailed
+		}
+		return p[0], p[0], nil
+	}
+
+	if len(p) == 0 {
+		return Hash{}, Hash{}, errProofFailed
+	}
+
+	// Interior node for the proof.
+	k, _ := maxpow2(hi - lo)
+	if n <= lo+k {
+		oh, th, err := runTreeProof(p[:len(p)-1], lo, lo+k, n, old)
+		if err != nil {
+			return Hash{}, Hash{}, err
+		}
+		return oh, NodeHash(th, p[len(p)-1]), nil
+	} else {
+		oh, th, err := runTreeProof(p[:len(p)-1], lo+k, hi, n, old)
+		if err != nil {
+			return Hash{}, Hash{}, err
+		}
+		return NodeHash(p[len(p)-1], oh), NodeHash(p[len(p)-1], th), nil
+	}
+}
diff --git a/sumdb/tlog/tlog_test.go b/sumdb/tlog/tlog_test.go
new file mode 100644
index 0000000..584e728
--- /dev/null
+++ b/sumdb/tlog/tlog_test.go
@@ -0,0 +1,269 @@
+// Copyright 2019 The Go Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style
+// license that can be found in the LICENSE file.
+
+package tlog
+
+import (
+	"bytes"
+	"fmt"
+	"testing"
+)
+
+type testHashStorage []Hash
+
+func (t testHashStorage) ReadHash(level int, n int64) (Hash, error) {
+	return t[StoredHashIndex(level, n)], nil
+}
+
+func (t testHashStorage) ReadHashes(index []int64) ([]Hash, error) {
+	// It's not required by HashReader that indexes be in increasing order,
+	// but check that the functions we are testing only ever ask for
+	// indexes in increasing order.
+	for i := 1; i < len(index); i++ {
+		if index[i-1] >= index[i] {
+			panic("indexes out of order")
+		}
+	}
+
+	out := make([]Hash, len(index))
+	for i, x := range index {
+		out[i] = t[x]
+	}
+	return out, nil
+}
+
+type testTilesStorage struct {
+	unsaved int
+	m       map[Tile][]byte
+}
+
+func (t testTilesStorage) Height() int {
+	return 2
+}
+
+func (t *testTilesStorage) SaveTiles(tiles []Tile, data [][]byte) {
+	t.unsaved -= len(tiles)
+}
+
+func (t *testTilesStorage) ReadTiles(tiles []Tile) ([][]byte, error) {
+	out := make([][]byte, len(tiles))
+	for i, tile := range tiles {
+		out[i] = t.m[tile]
+	}
+	t.unsaved += len(tiles)
+	return out, nil
+}
+
+func TestTree(t *testing.T) {
+	var trees []Hash
+	var leafhashes []Hash
+	var storage testHashStorage
+	tiles := make(map[Tile][]byte)
+	const testH = 2
+	for i := int64(0); i < 100; i++ {
+		data := []byte(fmt.Sprintf("leaf %d", i))
+		hashes, err := StoredHashes(i, data, storage)
+		if err != nil {
+			t.Fatal(err)
+		}
+		leafhashes = append(leafhashes, RecordHash(data))
+		oldStorage := len(storage)
+		storage = append(storage, hashes...)
+		if count := StoredHashCount(i + 1); count != int64(len(storage)) {
+			t.Errorf("StoredHashCount(%d) = %d, have %d StoredHashes", i+1, count, len(storage))
+		}
+		th, err := TreeHash(i+1, storage)
+		if err != nil {
+			t.Fatal(err)
+		}
+
+		for _, tile := range NewTiles(testH, i, i+1) {
+			data, err := ReadTileData(tile, storage)
+			if err != nil {
+				t.Fatal(err)
+			}
+			old := Tile{H: tile.H, L: tile.L, N: tile.N, W: tile.W - 1}
+			oldData := tiles[old]
+			if len(oldData) != len(data)-HashSize || !bytes.Equal(oldData, data[:len(oldData)]) {
+				t.Fatalf("tile %v not extending earlier tile %v", tile.Path(), old.Path())
+			}
+			tiles[tile] = data
+		}
+		for _, tile := range NewTiles(testH, 0, i+1) {
+			data, err := ReadTileData(tile, storage)
+			if err != nil {
+				t.Fatal(err)
+			}
+			if !bytes.Equal(tiles[tile], data) {
+				t.Fatalf("mismatch at %+v", tile)
+			}
+		}
+		for _, tile := range NewTiles(testH, i/2, i+1) {
+			data, err := ReadTileData(tile, storage)
+			if err != nil {
+				t.Fatal(err)
+			}
+			if !bytes.Equal(tiles[tile], data) {
+				t.Fatalf("mismatch at %+v", tile)
+			}
+		}
+
+		// Check that all the new hashes are readable from their tiles.
+		for j := oldStorage; j < len(storage); j++ {
+			tile := TileForIndex(testH, int64(j))
+			data, ok := tiles[tile]
+			if !ok {
+				t.Log(NewTiles(testH, 0, i+1))
+				t.Fatalf("TileForIndex(%d, %d) = %v, not yet stored (i=%d, stored %d)", testH, j, tile.Path(), i, len(storage))
+				continue
+			}
+			h, err := HashFromTile(tile, data, int64(j))
+			if err != nil {
+				t.Fatal(err)
+			}
+			if h != storage[j] {
+				t.Errorf("HashFromTile(%v, %d) = %v, want %v", tile.Path(), int64(j), h, storage[j])
+			}
+		}
+
+		trees = append(trees, th)
+
+		// Check that leaf proofs work, for all trees and leaves so far.
+		for j := int64(0); j <= i; j++ {
+			p, err := ProveRecord(i+1, j, storage)
+			if err != nil {
+				t.Fatalf("ProveRecord(%d, %d): %v", i+1, j, err)
+			}
+			if err := CheckRecord(p, i+1, th, j, leafhashes[j]); err != nil {
+				t.Fatalf("CheckRecord(%d, %d): %v", i+1, j, err)
+			}
+			for k := range p {
+				p[k][0] ^= 1
+				if err := CheckRecord(p, i+1, th, j, leafhashes[j]); err == nil {
+					t.Fatalf("CheckRecord(%d, %d) succeeded with corrupt proof hash #%d!", i+1, j, k)
+				}
+				p[k][0] ^= 1
+			}
+		}
+
+		// Check that leaf proofs work using TileReader.
+		// To prove a leaf that way, all you have to do is read and verify its hash.
+		storage := &testTilesStorage{m: tiles}
+		thr := TileHashReader(Tree{i + 1, th}, storage)
+		for j := int64(0); j <= i; j++ {
+			h, err := thr.ReadHashes([]int64{StoredHashIndex(0, j)})
+			if err != nil {
+				t.Fatalf("TileHashReader(%d).ReadHashes(%d): %v", i+1, j, err)
+			}
+			if h[0] != leafhashes[j] {
+				t.Fatalf("TileHashReader(%d).ReadHashes(%d) returned wrong hash", i+1, j)
+			}
+
+			// Even though reading the hash suffices,
+			// check we can generate the proof too.
+			p, err := ProveRecord(i+1, j, thr)
+			if err != nil {
+				t.Fatalf("ProveRecord(%d, %d, TileHashReader(%d)): %v", i+1, j, i+1, err)
+			}
+			if err := CheckRecord(p, i+1, th, j, leafhashes[j]); err != nil {
+				t.Fatalf("CheckRecord(%d, %d, TileHashReader(%d)): %v", i+1, j, i+1, err)
+			}
+		}
+		if storage.unsaved != 0 {
+			t.Fatalf("TileHashReader(%d) did not save %d tiles", i+1, storage.unsaved)
+		}
+
+		// Check that ReadHashes will give an error if the index is not in the tree.
+		if _, err := thr.ReadHashes([]int64{(i + 1) * 2}); err == nil {
+			t.Fatalf("TileHashReader(%d).ReadHashes(%d) for index not in tree <nil>, want err", i, i+1)
+		}
+		if storage.unsaved != 0 {
+			t.Fatalf("TileHashReader(%d) did not save %d tiles", i+1, storage.unsaved)
+		}
+
+		// Check that tree proofs work, for all trees so far, using TileReader.
+		// To prove a tree that way, all you have to do is compute and verify its hash.
+		for j := int64(0); j <= i; j++ {
+			h, err := TreeHash(j+1, thr)
+			if err != nil {
+				t.Fatalf("TreeHash(%d, TileHashReader(%d)): %v", j, i+1, err)
+			}
+			if h != trees[j] {
+				t.Fatalf("TreeHash(%d, TileHashReader(%d)) = %x, want %x (%v)", j, i+1, h[:], trees[j][:], trees[j])
+			}
+
+			// Even though computing the subtree hash suffices,
+			// check that we can generate the proof too.
+			p, err := ProveTree(i+1, j+1, thr)
+			if err != nil {
+				t.Fatalf("ProveTree(%d, %d): %v", i+1, j+1, err)
+			}
+			if err := CheckTree(p, i+1, th, j+1, trees[j]); err != nil {
+				t.Fatalf("CheckTree(%d, %d): %v [%v]", i+1, j+1, err, p)
+			}
+			for k := range p {
+				p[k][0] ^= 1
+				if err := CheckTree(p, i+1, th, j+1, trees[j]); err == nil {
+					t.Fatalf("CheckTree(%d, %d) succeeded with corrupt proof hash #%d!", i+1, j+1, k)
+				}
+				p[k][0] ^= 1
+			}
+		}
+		if storage.unsaved != 0 {
+			t.Fatalf("TileHashReader(%d) did not save %d tiles", i+1, storage.unsaved)
+		}
+	}
+}
+
+func TestSplitStoredHashIndex(t *testing.T) {
+	for l := 0; l < 10; l++ {
+		for n := int64(0); n < 100; n++ {
+			x := StoredHashIndex(l, n)
+			l1, n1 := SplitStoredHashIndex(x)
+			if l1 != l || n1 != n {
+				t.Fatalf("StoredHashIndex(%d, %d) = %d, but SplitStoredHashIndex(%d) = %d, %d", l, n, x, x, l1, n1)
+			}
+		}
+	}
+}
+
+// TODO(rsc): Test invalid paths too, like "tile/3/5/123/456/078".
+var tilePaths = []struct {
+	path string
+	tile Tile
+}{
+	{"tile/4/0/001", Tile{4, 0, 1, 16}},
+	{"tile/4/0/001.p/5", Tile{4, 0, 1, 5}},
+	{"tile/3/5/x123/x456/078", Tile{3, 5, 123456078, 8}},
+	{"tile/3/5/x123/x456/078.p/2", Tile{3, 5, 123456078, 2}},
+	{"tile/1/0/x003/x057/500", Tile{1, 0, 3057500, 2}},
+	{"tile/3/5/123/456/078", Tile{}},
+	{"tile/3/-1/123/456/078", Tile{}},
+	{"tile/1/data/x003/x057/500", Tile{1, -1, 3057500, 2}},
+}
+
+func TestTilePath(t *testing.T) {
+	for _, tt := range tilePaths {
+		if tt.tile.H > 0 {
+			p := tt.tile.Path()
+			if p != tt.path {
+				t.Errorf("%+v.Path() = %q, want %q", tt.tile, p, tt.path)
+			}
+		}
+		tile, err := ParseTilePath(tt.path)
+		if err != nil {
+			if tt.tile.H == 0 {
+				// Expected error.
+				continue
+			}
+			t.Errorf("ParseTilePath(%q): %v", tt.path, err)
+		} else if tile != tt.tile {
+			if tt.tile.H == 0 {
+				t.Errorf("ParseTilePath(%q): expected error, got %+v", tt.path, tt.tile)
+				continue
+			}
+			t.Errorf("ParseTilePath(%q) = %+v, want %+v", tt.path, tile, tt.tile)
+		}
+	}
+}