mathematics

Hash list

Hash list is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Hash list rather than just read about it. In short: 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 (hash tables) and distributed databases (distributed hash tables).

Key takeaways

Hash list belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Hash list to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Hash list from memory before moving on to harder problems.

Reference excerpt

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 (hash tables) and distributed databases (distributed hash tables).

A hash list is an extension of the concept of hashing an item (for instance, a file). A hash list is a subtree of a Merkle tree.

Root hash Often, an additional hash of the hash list itself (a top hash, also called root hash or master hash) is used. 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 list can be received from any non-trusted source, like any peer in the p2p network. Then the received hash list is checked against the trusted top hash, and if the hash list is damaged or fake, another hash list from another source will be tried until the program finds one that matches the top hash. In some systems (for example, BitTorrent), instead of a top hash the whole hash list is available on a web site in a small file. Such a "torrent file" contains a description, file names, a hash list and some additional data.

Applications Hash lists can be used to protect any kind of data stored, handled and transferred in and between computers. An important use of hash lists is to make sure that data blocks received from other peers in a peer-to-peer network are received undamaged and unaltered, and to check that the other peers do not "lie" and send fake blocks. Usually a cryptographic hash function such as SHA-256 is used for the hashing. If the hash list only needs to protect against unintentional damage unsecured checksums such as CRCs can be used. Hash lists are better than a simple hash of the entire file since, in the case of a data block being damaged, this is noticed, and only the damaged block needs to be redownloaded. With only a hash of the file, many undamaged blocks would have to be redownloaded, and the file reconstructed and tested until the correct hash of the entire file is obtained. Hash lists also protect against nodes that try to sabotage by sending fake blocks, since in such a case the damaged block can be acquired from some other source. Hash lists are used to identify CSAM online.

Protocols using hash lists Rsync Zsync Bittorrent

See also Hash tree Hash table Hash chain Ed2k: URI scheme, which uses an MD4 top hash of an MD4 hash list to uniquely identify a file Cryptographic hash function List

References

Illustrations

Worked examples

Example 1 — a first encounter with Hash list

Start with the simplest possible case. Write down what Hash list claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Hash list before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Hash list ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Hash list

In research: Hash list appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Hash list in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Hash list is common in secondary-school and first-year university syllabi. It links to neighbouring topics Cryptographic hash functions, Error detection and correction, Hashing, so understanding it makes those chapters shorter.
In everyday life: Look for Hash list outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Hash list in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hash list means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Hash list out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hash list in simple terms?

Why does Hash list matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Hash list?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Hash list.