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// 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".
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 height h ≥ 1
// and least width storing the given hash storage index.
func TileForIndex(h int, index int64) Tile {
if h < 1 {
panic("TileForIndex: invalid height")
}
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.)
func NewTiles(h int, oldTreeSize, newTreeSize int64) []Tile {
if h < 1 {
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).
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
}
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