tile.go

     1  // Copyright 2019 The Go Authors. All rights reserved.
     2  // Use of this source code is governed by a BSD-style
     3  // license that can be found in the LICENSE file.
     4  
     5  package tlog
     6  
     7  import (
     8  	"fmt"
     9  	"strconv"
    10  	"strings"
    11  )
    12  
    13  // A Tile is a description of a transparency log tile.
    14  // A tile of height H at level L offset N lists W consecutive hashes
    15  // at level H*L of the tree starting at offset N*(2**H).
    16  // A complete tile lists 2**H hashes; a partial tile lists fewer.
    17  // Note that a tile represents the entire subtree of height H
    18  // with those hashes as the leaves. The levels above H*L
    19  // can be reconstructed by hashing the leaves.
    20  //
    21  // Each Tile can be encoded as a “tile coordinate path”
    22  // of the form tile/H/L/NNN[.p/W].
    23  // The .p/W suffix is present only for partial tiles, meaning W < 2**H.
    24  // The NNN element is an encoding of N into 3-digit path elements.
    25  // All but the last path element begins with an "x".
    26  // For example,
    27  // Tile{H: 3, L: 4, N: 1234067, W: 1}'s path
    28  // is tile/3/4/x001/x234/067.p/1, and
    29  // Tile{H: 3, L: 4, N: 1234067, W: 8}'s path
    30  // is tile/3/4/x001/x234/067.
    31  // See the [Tile.Path] method and the [ParseTilePath] function.
    32  //
    33  // The special level L=-1 holds raw record data instead of hashes.
    34  // In this case, the level encodes into a tile path as the path element
    35  // "data" instead of "-1".
    36  //
    37  // See also https://golang.org/design/25530-sumdb#checksum-database
    38  // and https://research.swtch.com/tlog#tiling_a_log.
    39  type Tile struct {
    40  	H int   // height of tile (1 ≤ H ≤ 30)
    41  	L int   // level in tiling (-1 ≤ L ≤ 63)
    42  	N int64 // number within level (0 ≤ N, unbounded)
    43  	W int   // width of tile (1 ≤ W ≤ 2**H; 2**H is complete tile)
    44  }
    45  
    46  // TileForIndex returns the tile of fixed height h ≥ 1
    47  // and least width storing the given hash storage index.
    48  //
    49  // If h ≤ 0, [TileForIndex] panics.
    50  func TileForIndex(h int, index int64) Tile {
    51  	if h <= 0 {
    52  		panic(fmt.Sprintf("TileForIndex: invalid height %d", h))
    53  	}
    54  	t, _, _ := tileForIndex(h, index)
    55  	return t
    56  }
    57  
    58  // tileForIndex returns the tile of height h ≥ 1
    59  // storing the given hash index, which can be
    60  // reconstructed using tileHash(data[start:end]).
    61  func tileForIndex(h int, index int64) (t Tile, start, end int) {
    62  	level, n := SplitStoredHashIndex(index)
    63  	t.H = h
    64  	t.L = level / h
    65  	level -= t.L * h // now level within tile
    66  	t.N = n << uint(level) >> uint(t.H)
    67  	n -= t.N << uint(t.H) >> uint(level) // now n within tile at level
    68  	t.W = int((n + 1) << uint(level))
    69  	return t, int(n<<uint(level)) * HashSize, int((n+1)<<uint(level)) * HashSize
    70  }
    71  
    72  // HashFromTile returns the hash at the given storage index,
    73  // provided that t == TileForIndex(t.H, index) or a wider version,
    74  // and data is t's tile data (of length at least t.W*HashSize).
    75  func HashFromTile(t Tile, data []byte, index int64) (Hash, error) {
    76  	if t.H < 1 || t.H > 30 || t.L < 0 || t.L >= 64 || t.W < 1 || t.W > 1<<uint(t.H) {
    77  		return Hash{}, fmt.Errorf("invalid tile %v", t.Path())
    78  	}
    79  	if len(data) < t.W*HashSize {
    80  		return Hash{}, fmt.Errorf("data len %d too short for tile %v", len(data), t.Path())
    81  	}
    82  	t1, start, end := tileForIndex(t.H, index)
    83  	if t.L != t1.L || t.N != t1.N || t.W < t1.W {
    84  		return Hash{}, fmt.Errorf("index %v is in %v not %v", index, t1.Path(), t.Path())
    85  	}
    86  	return tileHash(data[start:end]), nil
    87  }
    88  
    89  // tileHash computes the subtree hash corresponding to the (2^K)-1 hashes in data.
    90  func tileHash(data []byte) Hash {
    91  	if len(data) == 0 {
    92  		panic("bad math in tileHash")
    93  	}
    94  	if len(data) == HashSize {
    95  		var h Hash
    96  		copy(h[:], data)
    97  		return h
    98  	}
    99  	n := len(data) / 2
   100  	return NodeHash(tileHash(data[:n]), tileHash(data[n:]))
   101  }
   102  
   103  // NewTiles returns the coordinates of the tiles of height h ≥ 1
   104  // that must be published when publishing from a tree of
   105  // size newTreeSize to replace a tree of size oldTreeSize.
   106  // (No tiles need to be published for a tree of size zero.)
   107  //
   108  // If h ≤ 0, NewTiles panics.
   109  func NewTiles(h int, oldTreeSize, newTreeSize int64) []Tile {
   110  	if h <= 0 {
   111  		panic(fmt.Sprintf("NewTiles: invalid height %d", h))
   112  	}
   113  	H := uint(h)
   114  	var tiles []Tile
   115  	for level := uint(0); newTreeSize>>(H*level) > 0; level++ {
   116  		oldN := oldTreeSize >> (H * level)
   117  		newN := newTreeSize >> (H * level)
   118  		if oldN == newN {
   119  			continue
   120  		}
   121  		for n := oldN >> H; n < newN>>H; n++ {
   122  			tiles = append(tiles, Tile{H: h, L: int(level), N: n, W: 1 << H})
   123  		}
   124  		n := newN >> H
   125  		if w := int(newN - n<<H); w > 0 {
   126  			tiles = append(tiles, Tile{H: h, L: int(level), N: n, W: w})
   127  		}
   128  	}
   129  	return tiles
   130  }
   131  
   132  // ReadTileData reads the hashes for tile t from r
   133  // and returns the corresponding tile data.
   134  func ReadTileData(t Tile, r HashReader) ([]byte, error) {
   135  	size := t.W
   136  	if size == 0 {
   137  		size = 1 << uint(t.H)
   138  	}
   139  	start := t.N << uint(t.H)
   140  	indexes := make([]int64, size)
   141  	for i := 0; i < size; i++ {
   142  		indexes[i] = StoredHashIndex(t.H*t.L, start+int64(i))
   143  	}
   144  
   145  	hashes, err := r.ReadHashes(indexes)
   146  	if err != nil {
   147  		return nil, err
   148  	}
   149  	if len(hashes) != len(indexes) {
   150  		return nil, fmt.Errorf("tlog: ReadHashes(%d indexes) = %d hashes", len(indexes), len(hashes))
   151  	}
   152  
   153  	tile := make([]byte, size*HashSize)
   154  	for i := 0; i < size; i++ {
   155  		copy(tile[i*HashSize:], hashes[i][:])
   156  	}
   157  	return tile, nil
   158  }
   159  
   160  // To limit the size of any particular directory listing,
   161  // we encode the (possibly very large) number N
   162  // by encoding three digits at a time.
   163  // For example, 123456789 encodes as x123/x456/789.
   164  // Each directory has at most 1000 each xNNN, NNN, and NNN.p children,
   165  // so there are at most 3000 entries in any one directory.
   166  const pathBase = 1000
   167  
   168  // Path returns a tile coordinate path describing t.
   169  func (t Tile) Path() string {
   170  	n := t.N
   171  	nStr := fmt.Sprintf("%03d", n%pathBase)
   172  	for n >= pathBase {
   173  		n /= pathBase
   174  		nStr = fmt.Sprintf("x%03d/%s", n%pathBase, nStr)
   175  	}
   176  	pStr := ""
   177  	if t.W != 1<<uint(t.H) {
   178  		pStr = fmt.Sprintf(".p/%d", t.W)
   179  	}
   180  	var L string
   181  	if t.L == -1 {
   182  		L = "data"
   183  	} else {
   184  		L = fmt.Sprintf("%d", t.L)
   185  	}
   186  	return fmt.Sprintf("tile/%d/%s/%s%s", t.H, L, nStr, pStr)
   187  }
   188  
   189  // ParseTilePath parses a tile coordinate path.
   190  func ParseTilePath(path string) (Tile, error) {
   191  	f := strings.Split(path, "/")
   192  	if len(f) < 4 || f[0] != "tile" {
   193  		return Tile{}, &badPathError{path}
   194  	}
   195  	h, err1 := strconv.Atoi(f[1])
   196  	isData := false
   197  	if f[2] == "data" {
   198  		isData = true
   199  		f[2] = "0"
   200  	}
   201  	l, err2 := strconv.Atoi(f[2])
   202  	if err1 != nil || err2 != nil || h < 1 || l < 0 || h > 30 {
   203  		return Tile{}, &badPathError{path}
   204  	}
   205  	w := 1 << uint(h)
   206  	if dotP := f[len(f)-2]; strings.HasSuffix(dotP, ".p") {
   207  		ww, err := strconv.Atoi(f[len(f)-1])
   208  		if err != nil || ww <= 0 || ww >= w {
   209  			return Tile{}, &badPathError{path}
   210  		}
   211  		w = ww
   212  		f[len(f)-2] = dotP[:len(dotP)-len(".p")]
   213  		f = f[:len(f)-1]
   214  	}
   215  	f = f[3:]
   216  	n := int64(0)
   217  	for _, s := range f {
   218  		nn, err := strconv.Atoi(strings.TrimPrefix(s, "x"))
   219  		if err != nil || nn < 0 || nn >= pathBase {
   220  			return Tile{}, &badPathError{path}
   221  		}
   222  		n = n*pathBase + int64(nn)
   223  	}
   224  	if isData {
   225  		l = -1
   226  	}
   227  	t := Tile{H: h, L: l, N: n, W: w}
   228  	if path != t.Path() {
   229  		return Tile{}, &badPathError{path}
   230  	}
   231  	return t, nil
   232  }
   233  
   234  type badPathError struct {
   235  	path string
   236  }
   237  
   238  func (e *badPathError) Error() string {
   239  	return fmt.Sprintf("malformed tile path %q", e.path)
   240  }
   241  
   242  // A TileReader reads tiles from a go.sum database log.
   243  type TileReader interface {
   244  	// Height returns the height of the available tiles.
   245  	Height() int
   246  
   247  	// ReadTiles returns the data for each requested tile.
   248  	// If ReadTiles returns err == nil, it must also return
   249  	// a data record for each tile (len(data) == len(tiles))
   250  	// and each data record must be the correct length
   251  	// (len(data[i]) == tiles[i].W*HashSize).
   252  	//
   253  	// An implementation of ReadTiles typically reads
   254  	// them from an on-disk cache or else from a remote
   255  	// tile server. Tile data downloaded from a server should
   256  	// be considered suspect and not saved into a persistent
   257  	// on-disk cache before returning from ReadTiles.
   258  	// When the client confirms the validity of the tile data,
   259  	// it will call SaveTiles to signal that they can be safely
   260  	// written to persistent storage.
   261  	// See also https://research.swtch.com/tlog#authenticating_tiles.
   262  	ReadTiles(tiles []Tile) (data [][]byte, err error)
   263  
   264  	// SaveTiles informs the TileReader that the tile data
   265  	// returned by ReadTiles has been confirmed as valid
   266  	// and can be saved in persistent storage (on disk).
   267  	SaveTiles(tiles []Tile, data [][]byte)
   268  }
   269  
   270  // TileHashReader returns a HashReader that satisfies requests
   271  // by loading tiles of the given tree.
   272  //
   273  // The returned [HashReader] checks that loaded tiles are
   274  // valid for the given tree. Therefore, any hashes returned
   275  // by the HashReader are already proven to be in the tree.
   276  func TileHashReader(tree Tree, tr TileReader) HashReader {
   277  	return &tileHashReader{tree: tree, tr: tr}
   278  }
   279  
   280  type tileHashReader struct {
   281  	tree Tree
   282  	tr   TileReader
   283  }
   284  
   285  // tileParent returns t's k'th tile parent in the tiles for a tree of size n.
   286  // If there is no such parent, tileParent returns Tile{}.
   287  func tileParent(t Tile, k int, n int64) Tile {
   288  	t.L += k
   289  	t.N >>= uint(k * t.H)
   290  	t.W = 1 << uint(t.H)
   291  	if max := n >> uint(t.L*t.H); t.N<<uint(t.H)+int64(t.W) >= max {
   292  		if t.N<<uint(t.H) >= max {
   293  			return Tile{}
   294  		}
   295  		t.W = int(max - t.N<<uint(t.H))
   296  	}
   297  	return t
   298  }
   299  
   300  func (r *tileHashReader) ReadHashes(indexes []int64) ([]Hash, error) {
   301  	h := r.tr.Height()
   302  
   303  	tileOrder := make(map[Tile]int) // tileOrder[tileKey(tiles[i])] = i
   304  	var tiles []Tile
   305  
   306  	// Plan to fetch tiles necessary to recompute tree hash.
   307  	// If it matches, those tiles are authenticated.
   308  	stx := subTreeIndex(0, r.tree.N, nil)
   309  	stxTileOrder := make([]int, len(stx))
   310  	for i, x := range stx {
   311  		tile, _, _ := tileForIndex(h, x)
   312  		tile = tileParent(tile, 0, r.tree.N)
   313  		if j, ok := tileOrder[tile]; ok {
   314  			stxTileOrder[i] = j
   315  			continue
   316  		}
   317  		stxTileOrder[i] = len(tiles)
   318  		tileOrder[tile] = len(tiles)
   319  		tiles = append(tiles, tile)
   320  	}
   321  
   322  	// Plan to fetch tiles containing the indexes,
   323  	// along with any parent tiles needed
   324  	// for authentication. For most calls,
   325  	// the parents are being fetched anyway.
   326  	indexTileOrder := make([]int, len(indexes))
   327  	for i, x := range indexes {
   328  		if x >= StoredHashIndex(0, r.tree.N) {
   329  			return nil, fmt.Errorf("indexes not in tree")
   330  		}
   331  
   332  		tile, _, _ := tileForIndex(h, x)
   333  
   334  		// Walk up parent tiles until we find one we've requested.
   335  		// That one will be authenticated.
   336  		k := 0
   337  		for ; ; k++ {
   338  			p := tileParent(tile, k, r.tree.N)
   339  			if j, ok := tileOrder[p]; ok {
   340  				if k == 0 {
   341  					indexTileOrder[i] = j
   342  				}
   343  				break
   344  			}
   345  		}
   346  
   347  		// Walk back down recording child tiles after parents.
   348  		// This loop ends by revisiting the tile for this index
   349  		// (tileParent(tile, 0, r.tree.N)) unless k == 0, in which
   350  		// case the previous loop did it.
   351  		for k--; k >= 0; k-- {
   352  			p := tileParent(tile, k, r.tree.N)
   353  			if p.W != 1<<uint(p.H) {
   354  				// Only full tiles have parents.
   355  				// This tile has a parent, so it must be full.
   356  				return nil, fmt.Errorf("bad math in tileHashReader: %d %d %v", r.tree.N, x, p)
   357  			}
   358  			tileOrder[p] = len(tiles)
   359  			if k == 0 {
   360  				indexTileOrder[i] = len(tiles)
   361  			}
   362  			tiles = append(tiles, p)
   363  		}
   364  	}
   365  
   366  	// Fetch all the tile data.
   367  	data, err := r.tr.ReadTiles(tiles)
   368  	if err != nil {
   369  		return nil, err
   370  	}
   371  	if len(data) != len(tiles) {
   372  		return nil, fmt.Errorf("TileReader returned bad result slice (len=%d, want %d)", len(data), len(tiles))
   373  	}
   374  	for i, tile := range tiles {
   375  		if len(data[i]) != tile.W*HashSize {
   376  			return nil, fmt.Errorf("TileReader returned bad result slice (%v len=%d, want %d)", tile.Path(), len(data[i]), tile.W*HashSize)
   377  		}
   378  	}
   379  
   380  	// Authenticate the initial tiles against the tree hash.
   381  	// They are arranged so that parents are authenticated before children.
   382  	// First the tiles needed for the tree hash.
   383  	th, err := HashFromTile(tiles[stxTileOrder[len(stx)-1]], data[stxTileOrder[len(stx)-1]], stx[len(stx)-1])
   384  	if err != nil {
   385  		return nil, err
   386  	}
   387  	for i := len(stx) - 2; i >= 0; i-- {
   388  		h, err := HashFromTile(tiles[stxTileOrder[i]], data[stxTileOrder[i]], stx[i])
   389  		if err != nil {
   390  			return nil, err
   391  		}
   392  		th = NodeHash(h, th)
   393  	}
   394  	if th != r.tree.Hash {
   395  		// The tiles do not support the tree hash.
   396  		// We know at least one is wrong, but not which one.
   397  		return nil, fmt.Errorf("downloaded inconsistent tile")
   398  	}
   399  
   400  	// Authenticate full tiles against their parents.
   401  	for i := len(stx); i < len(tiles); i++ {
   402  		tile := tiles[i]
   403  		p := tileParent(tile, 1, r.tree.N)
   404  		j, ok := tileOrder[p]
   405  		if !ok {
   406  			return nil, fmt.Errorf("bad math in tileHashReader %d %v: lost parent of %v", r.tree.N, indexes, tile)
   407  		}
   408  		h, err := HashFromTile(p, data[j], StoredHashIndex(p.L*p.H, tile.N))
   409  		if err != nil {
   410  			return nil, fmt.Errorf("bad math in tileHashReader %d %v: lost hash of %v: %v", r.tree.N, indexes, tile, err)
   411  		}
   412  		if h != tileHash(data[i]) {
   413  			return nil, fmt.Errorf("downloaded inconsistent tile")
   414  		}
   415  	}
   416  
   417  	// Now we have all the tiles needed for the requested hashes,
   418  	// and we've authenticated the full tile set against the trusted tree hash.
   419  	r.tr.SaveTiles(tiles, data)
   420  
   421  	// Pull out the requested hashes.
   422  	hashes := make([]Hash, len(indexes))
   423  	for i, x := range indexes {
   424  		j := indexTileOrder[i]
   425  		h, err := HashFromTile(tiles[j], data[j], x)
   426  		if err != nil {
   427  			return nil, fmt.Errorf("bad math in tileHashReader %d %v: lost hash %v: %v", r.tree.N, indexes, x, err)
   428  		}
   429  		hashes[i] = h
   430  	}
   431  
   432  	return hashes, nil
   433  }
   434
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