In cryptography and computer science Hash trees or Merkle trees are a type of data structure which contains a tree of summary information about a larger piece of data – for instance a file – used to verify its contents. Hash trees are an extension of hash lists, which in turn are an extension of hashing. Hash trees where the underlying hash function is Tiger are often called Tiger trees or Tiger tree hashes.

Contents 1 Uses 2 How hash trees work 3 Tiger tree hash 4 See also 5 References 6 External links

[edit] Uses

Hash trees can be used to protect any kind of data stored, handled and transferred in and between computers. Currently the main use of hash trees is to make sure that data blocks received from other peers in a peer-to-peer network are received undamaged and unaltered, and even to check that the other peers do not lie and send fake blocks. Suggestions have been made to use hash trees in trusted computing systems. Sun Microsystems has used Hash Trees in the ZFS filesystem^[1]. Hash Trees are used in Google Wave protocol and in tarsnap backup system.

Hash trees were invented in 1979 by Ralph Merkle ^[2]. The original purpose was to make it possible to efficiently handle many Lamport one-time signatures. Lamport signatures are believed to still be secure in the event that quantum computers become reality. Unfortunately each Lamport key can only be used to sign a single message. But combined with hash trees they can be used for many messages and then become a fairly efficient digital signature scheme.

[edit] How hash trees work

A hash tree is a tree of hashes in which the leaves are hashes of data blocks in, for instance, a file or set of files. Nodes further up in the tree are the hashes of their respective children. For example, in the picture hash 0 is the result of hashing hash 0-0 and then hash 0-1. That is, hash 0 = hash( hash 0-0 + hash 0-1 ) where + denotes concatenation.

Most hash tree implementations are binary (two child nodes under each node) but they can just as well use many more child nodes under each node.

Usually, a cryptographic hash function such as SHA-1, Whirlpool, or Tiger is used for the hashing. If the hash tree only needs to protect against unintentional damage, much less secure checksums such as CRCs can be used.

In the top of a hash tree there is a top hash (or root hash or master hash). Before downloading a file on a p2p network, in most cases the top hash is acquired from a trusted source, for instance a friend or a web site that is known to have good recommendations of files to download. When the top hash is available, the hash tree can be received from any non-trusted source, like any peer in the p2p network. Then, the received hash tree is checked against the trusted top hash, and if the hash tree is damaged or fake, another hash tree from another source will be tried until the program finds one that matches the top hash.

The main difference from a hash list is that one branch of the hash tree can be downloaded at a time and the integrity of each branch can be checked immediately, even though the whole tree is not available yet. This can be an advantage since it is efficient to split files up in very small data blocks so that only small blocks have to be redownloaded if they get damaged. If the hashed file is very big, such a hash tree or hash list becomes fairly big. But if it is a tree, one small branch can be downloaded quickly, the integrity of the branch can be checked, and then the downloading of data blocks can start.

There are several additional tricks, benefits and details regarding hash trees. See the references and external links below for more in-depth information.

[edit] Tiger tree hash

The Tiger tree hash is probably the most widely used form of hash tree. It uses a binary hash tree (two child nodes under each node), usually has a data block size of 1024-bytes and uses the cryptographically secure Tiger hash.

Tiger tree hashes are used in the Gnutella, Gnutella2, and Direct Connect P2P file sharing protocols and in file sharing applications such as Phex, BearShare, LimeWire, Shareaza, DC++ and Valknut.

[edit] See also

• Hash list
• Cryptographic hash function
• Binary tree which is a tree data structure.
• Ralph Merkle – The cryptographer who invented hash trees (Merkle trees).
• Lamport signature – Hash trees were originally invented to make it possible to handle Lamport signatures efficiently.
• Hash table - Not to be confused with...
• Hash trie

[edit] References

• Merkle tree patent 4,309,569 – Explains both the hash tree structure and the use of it to handle many one-time signatures.
• Tree Hash EXchange format (THEX) – A detailed description of Tiger trees.
• Efficient Use of Merkle Trees – RSA labs explanation of the original purpose of Merkle trees: To handle many Lamport one-time signatures.

1. ^ Jeff Bonwick's Blog ZFS End-to-End Data Integrity
2. ^ R. C. Merkle, A digital signature based on a conventional encryption function, Crypto '87

[edit] External links

• http://www.codeproject.com/cs/algorithms/thexcs.asp – Tiger Tree Hash (TTH) source code in C# – by Gil Schmidt
• http://sourceforge.net/projects/tigertree/ – Tiger Tree Hash (TTH) implementations in C and Java

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