Merkle tree

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An example of a binary hash tree. Hashes 0-0 and 0-1 are the hash values of data blocks L1 and L2, respectively, and hash 0 is the hash of the concatenation of hashes 0-0 and 0-1. Hash Tree.svg
An example of a binary hash tree. Hashes 0-0 and 0-1 are the hash values of data blocks L1 and L2, respectively, and hash 0 is the hash of the concatenation of hashes 0-0 and 0-1.

In cryptography and computer science, a hash tree or Merkle tree is a tree in which every "leaf" node is labelled with the cryptographic hash of a data block, and every node that is not a leaf (called a branch, inner node, or inode) is labelled with the cryptographic hash of the labels of its child nodes. A hash tree allows efficient and secure verification of the contents of a large data structure. A hash tree is a generalization of a hash list and a hash chain.

Contents

Demonstrating that a leaf node is a part of a given binary hash tree requires computing a number of hashes proportional to the logarithm of the number of leaf nodes in the tree. [1] Conversely, in a hash list, the number is proportional to the number of leaf nodes itself. A Merkle tree is therefore an efficient example of a cryptographic commitment scheme, in which the root of the tree is seen as a commitment and leaf nodes may be revealed and proven to be part of the original commitment. [2]

The concept of a hash tree is named after Ralph Merkle, who patented it in 1979. [3] [4]

Uses

Hash trees can be used to verify any kind of data stored, handled and transferred in and between computers. They can help ensure 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.

Hash trees are used in:

Suggestions have been made to use hash trees in trusted computing systems. [11]

The initial Bitcoin implementation of Merkle trees by Satoshi Nakamoto applies the compression step of the hash function to an excessive degree, which is mitigated by using Fast Merkle Trees. [12]

Overview

A hash tree is a tree of hashes in which the leaves (i.e., leaf nodes, sometimes also called "leafs") are hashes of data blocks in, for instance, a file or set of files. Nodes farther up in the tree are the hashes of their respective children. For example, in the above picture hash 0 is the result of hashing the concatenation of hash 0-0 and 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-2 is used for the hashing. If the hash tree only needs to protect against unintentional damage, unsecured 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. [13]

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. For example, in the picture, the integrity of data block L2 can be verified immediately if the tree already contains hash 0-0 and hash 1 by hashing the data block and iteratively combining the result with hash 0-0 and then hash 1 and finally comparing the result with the top hash. Similarly, the integrity of data block L3 can be verified if the tree already has hash 1-1 and hash 0. 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 re-downloaded if they get damaged. If the hashed file is big, such a hash list or hash chain 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.[ citation needed ]

Second preimage attack

The Merkle hash root does not indicate the tree depth, enabling a second-preimage attack in which an attacker creates a document other than the original that has the same Merkle hash root. For the example above, an attacker can create a new document containing two data blocks, where the first is hash 0-0 + hash 0-1, and the second is hash 1-0 + hash 1-1. [14] [15]

One simple fix is defined in Certificate Transparency: when computing leaf node hashes, a 0x00 byte is prepended to the hash data, while 0x01 is prepended when computing internal node hashes. [13] Limiting the hash tree size is a prerequisite of some formal security proofs, and helps in making some proofs tighter. Some implementations limit the tree depth using hash tree depth prefixes before hashes, so any extracted hash chain is defined to be valid only if the prefix decreases at each step and is still positive when the leaf is reached.

Tiger tree hash

The Tiger tree hash is a 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 Tiger hash. [16]

Tiger tree hashes are used in Gnutella, [17] Gnutella2, and Direct Connect P2P file sharing protocols [18] and in file sharing applications such as Phex, [19] BearShare, LimeWire, Shareaza, DC++ [20] and gtk-gnutella. [21]

See also

Related Research Articles

Gnutella is a peer-to-peer network protocol. Founded in 2000, it was the first decentralized peer-to-peer network of its kind, leading to other, later networks adopting the model.

<span class="mw-page-title-main">Peer-to-peer</span> Type of decentralized and distributed network architecture

Peer-to-peer (P2P) computing or networking is a distributed application architecture that partitions tasks or workloads between peers. Peers are equally privileged, equipotent participants in the network, forming a peer-to-peer network of nodes. In addition, a personal area network (PAN) is also in nature a type of decentralized peer-to-peer network typically between two devices.

<span class="mw-page-title-main">Distributed hash table</span> Decentralized distributed system with lookup service

A distributed hash table (DHT) is a distributed system that provides a lookup service similar to a hash table. Key–value pairs are stored in a DHT, and any participating node can efficiently retrieve the value associated with a given key. The main advantage of a DHT is that nodes can be added or removed with minimum work around re-distributing keys. Keys are unique identifiers which map to particular values, which in turn can be anything from addresses, to documents, to arbitrary data. Responsibility for maintaining the mapping from keys to values is distributed among the nodes, in such a way that a change in the set of participants causes a minimal amount of disruption. This allows a DHT to scale to extremely large numbers of nodes and to handle continual node arrivals, departures, and failures.

gtk-gnutella

gtk-gnutella is a peer-to-peer file sharing application which runs on the gnutella network. gtk-gnutella uses the GTK+ toolkit for its graphical user interface. Released under the GNU General Public License, gtk-gnutella is free software.

<span class="mw-page-title-main">GNUnet</span> Framework for decentralized, peer-to-peer networking which is part of the GNU Project

GNUnet is a software framework for decentralized, peer-to-peer networking and an official GNU package. The framework offers link encryption, peer discovery, resource allocation, communication over many transports and various basic peer-to-peer algorithms for routing, multicast and network size estimation.

<span class="mw-page-title-main">Gnutella2</span>

Gnutella2, often referred to as G2, is a peer-to-peer protocol developed mainly by Michael Stokes and released in 2002.

<span class="mw-page-title-main">Cryptographic hash function</span> Hash function that is suitable for use in cryptography

A cryptographic hash function (CHF) is a hash algorithm that has special properties desirable for a cryptographic application:

In cryptography, Tiger is a cryptographic hash function designed by Ross Anderson and Eli Biham in 1995 for efficiency on 64-bit platforms. The size of a Tiger hash value is 192 bits. Truncated versions can be used for compatibility with protocols assuming a particular hash size. Unlike the SHA-2 family, no distinguishing initialization values are defined; they are simply prefixes of the full Tiger/192 hash value.

Kademlia is a distributed hash table for decentralized peer-to-peer computer networks designed by Petar Maymounkov and David Mazières in 2002. It specifies the structure of the network and the exchange of information through node lookups. Kademlia nodes communicate among themselves using UDP. A virtual or overlay network is formed by the participant nodes. Each node is identified by a number or node ID. The node ID serves not only as identification, but the Kademlia algorithm uses the node ID to locate values.

<span class="mw-page-title-main">Magnet URI scheme</span> Scheme that defines the format of magnet links

Magnet is a URI scheme that defines the format of magnet links, a de facto standard for identifying files (URN) by their content, via cryptographic hash value rather than by their location.

GnucDNA was a software library for building peer-to-peer applications. It provides developers with a common layer to create their own Gnutella or Gnutella2 client or network. As a separate component, GnucDNA can be updated independently of the client, passing down improvements to the applications already using it.

<span class="mw-page-title-main">Hash list</span>

In computer science, a hash list is typically a list of hashes of the data blocks in a file or set of files. Lists of hashes are used for many different purposes, such as fast table lookup and distributed databases.

In cryptography, a Lamport signature or Lamport one-time signature scheme is a method for constructing a digital signature. Lamport signatures can be built from any cryptographically secure one-way function; usually a cryptographic hash function is used.

<span class="mw-page-title-main">Merkle–Damgård construction</span> Method of building collision-resistant cryptographic hash functions

In cryptography, the Merkle–Damgård construction or Merkle–Damgård hash function is a method of building collision-resistant cryptographic hash functions from collision-resistant one-way compression functions. This construction was used in the design of many popular hash algorithms such as MD5, SHA-1, and SHA-2.

In computing, eD2k links (ed2k://) are hyperlinks used to denote files stored on computers connected to the eDonkey filesharing P2P network.

Peer-to-peer file sharing (P2P) systems like Gnutella, KaZaA, and eDonkey/eMule, have become extremely popular in recent years, with the estimated user population in the millions. An academic research paper analyzed Gnutella and eMule protocols and found weaknesses in the protocol; many of the issues found in these networks are fundamental and probably common on other P2P networks. Users of file sharing networks, such as eMule and Gnutella, are subject to monitoring of their activity. Clients may be tracked by IP address, DNS name, software version they use, files they share, queries they initiate, and queries they answer to. Clients may also share their private files to the network without notice due to inappropriate settings.

<span class="mw-page-title-main">Phex</span> Peer to peer file sharing client

Phex is a peer-to-peer file sharing client for the gnutella network, released under the terms of the GNU General Public License, so Phex is free software. Phex is based on Java SE 5.0 or later.

In the BitTorrent file distribution system, a torrent file or meta-info file is a computer file that contains metadata about files and folders to be distributed, and usually also a list of the network locations of trackers, which are computers that help participants in the system find each other and form efficient distribution groups called swarms. Torrent files are normally named with the extension .torrent.

A hash calendar is a data structure that is used to measure the passage of time by adding hash values to an append-only database with one hash value per elapsed second. It can be thought of special kind of Merkle or hash tree, with the property that at any given moment, the tree contains a leaf node for each second since 1970‑01‑01 00:00:00 UTC.

Hash-based cryptography is the generic term for constructions of cryptographic primitives based on the security of hash functions. It is of interest as a type of post-quantum cryptography.

References

  1. ↑ Becker, Georg (2008-07-18). "Merkle Signature Schemes, Merkle Trees and Their Cryptanalysis" (PDF). Ruhr-Universität Bochum. p. 16. Archived from the original (PDF) on 2014-12-22. Retrieved 2013-11-20.
  2. ↑ "Handbook of Applied Cryptography". cacr.uwaterloo.ca. Section 13.4.1. Retrieved 2024-03-07.
  3. ↑ Merkle, R. C. (1988). "A Digital Signature Based on a Conventional Encryption Function". Advances in Cryptology – CRYPTO '87. Lecture Notes in Computer Science. Vol. 293. pp. 369–378. doi:10.1007/3-540-48184-2_32. ISBN   978-3-540-18796-7.
  4. ↑ USpatent 4309569,Ralph Merkle,"Method of providing digital signatures",published Jan 5, 1982, assigned to The Board of Trustees of the Leland Stanford Junior University
  5. ↑ Bonwick, Jeff (2005-12-08). "ZFS End-to-End Data Integrity". blogs.oracle.com. Archived from the original on April 3, 2012. Retrieved 2013-09-19.
  6. ↑ Likai Liu. "Bitrot Resistance on a Single Drive". likai.org.
  7. ↑ "General Verifiable Federation". Google Wave Protocol. Archived from the original on 2018-04-08. Retrieved 2017-03-09.
  8. ↑ Koblitz, Neal; Menezes, Alfred J. (January 2016). "Cryptocash, cryptocurrencies, and cryptocontracts". Designs, Codes and Cryptography. 78 (1): 87–102. CiteSeerX   10.1.1.701.8721 . doi:10.1007/s10623-015-0148-5. S2CID   16594958.
  9. ↑ Dolstra, E. The Purely Functional Software Deployment Model. PhD thesis, Faculty of Science, Utrecht, The Netherlands. January 2006. p.21 ISBN   90-393-4130-3.
  10. ↑ Adam Marcus. "The NoSQL Ecosystem". aosabook.org. When a replica is down for an extended period of time, or the machine storing hinted handoffs for an unavailable replica goes down as well, replicas must synchronize from one another. In this case, Cassandra and Riak implement a Dynamo-inspired process called anti-entropy. In anti-entropy, replicas exchange Merkle trees to identify parts of their replicated key ranges which are out of sync. A Merkle tree is a hierarchical hash verification: if the hash over the entire keyspace is not the same between two replicas, they will exchange hashes of smaller and smaller portions of the replicated keyspace until the out-of-sync keys are identified. This approach reduces unnecessary data transfer between replicas which contain mostly similar data.
  11. ↑ Kilian, J. (1995). "Improved efficient arguments (preliminary version)" (PDF). CRYPTO. doi: 10.1007/3-540-44750-4_25 .
  12. ↑ Mark Friedenbach: Fast Merkle Trees
  13. 1 2 Laurie, B.; Langley, A.; Kasper, E. (June 2013). "Certificate Transparency". IETF: RFC6962. doi:10.17487/rfc6962.
  14. ↑ Elena Andreeva; Charles Bouillaguet; Orr Dunkelman; John Kelsey (January 2009). "Herding, Second Preimage and Trojan Message Attacks beyond Merkle-Damgård". Selected Areas in Cryptography. Lecture Notes in Computer Science. Vol. 5867. SAC. pp. 393–414. doi:10.1007/978-3-642-05445-7_25. ISBN   978-3-642-05443-3.
  15. ↑ Elena Andreeva; Charles Bouillaguet; Pierre-Alain Fouque; Jonathan J. Hoch; John Kelsey; Adi Shamir; Sebastien Zimmer (2008). "Second Preimage Attacks on Dithered Hash Functions". In Smart, Nigel (ed.). Advances in Cryptology – EUROCRYPT 2008. Lecture Notes in Computer Science. Vol. 4965. Istanbul, Turkey. pp. 270–288. doi:10.1007/978-3-540-78967-3_16. ISBN   978-3-540-78966-6. S2CID   12844017.{{cite book}}: CS1 maint: location missing publisher (link)
  16. ↑ Chapweske, J.; Mohr, G. (March 4, 2003). "Tree Hash EXchange format (THEX)". Archived from the original on 2009-08-03.
  17. ↑ "tigertree.c File Reference". Gtk-Gnutella. Retrieved 23 September 2018.
  18. ↑ "Audit: P2P DirectConnect Application". Symantec. Archived from the original on January 29, 2015. Retrieved 23 September 2018.
  19. ↑ Arne Babenhauserheide (7 Jan 2007). "Phex 3.0.0 released". Phex. Retrieved 23 September 2018.
  20. ↑ "DC++'s feature list". dcplusplus.sourceforge.net.
  21. ↑ "Development". GTK-Gnutella. Retrieved 23 September 2018.

Further reading

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