computer science

Hash chain

Hash chain is a computer science 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 chain rather than just read about it. In short: A hash chain is the successive application of a cryptographic hash function to a piece of data. In computer security, a hash chain is a method used to produce many one-time keys from a single key or password.

Key takeaways

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

Reference excerpt

A hash chain is the successive application of a cryptographic hash function to a piece of data. In computer security, a hash chain is a method used to produce many one-time keys from a single key or password. For non-repudiation, a hash function can be applied successively to additional pieces of data in order to record the chronology of data's existence.

Definition A hash chain is a successive application of a cryptographic hash function h {\displaystyle h} to a string x {\displaystyle x} . For example,

h ( h ( h ( h ( x ) ) ) ) {\displaystyle h(h(h(h(x))))}

gives a hash chain of length 4, often denoted h 4 ( x ) {\displaystyle h^{4}(x)}

Applications

Leslie Lamport suggested the use of hash chains as a password protection scheme in an insecure environment. A server which needs to provide authentication may store a hash chain rather than a plain text password and prevent theft of the password in transmission or theft from the server. For example, a server begins by storing h 1000 ( p a s s w o r d ) {\displaystyle h^{1000}(\mathrm {password} )} which is provided by the user. When the user wishes to authenticate, they supply h 999 ( p a s s w o r d ) {\displaystyle h^{999}(\mathrm {password} )} to the server. The server computes h ( h 999 ( p a s s w o r d ) ) = h 1000 ( p a s s w o r d ) {\displaystyle h(h^{999}(\mathrm {password} ))=h^{1000}(\mathrm {password} )} and verifies this matches the hash chain it has stored. It then stores h 999 ( p a s s w o r d ) {\displaystyle h^{999}(\mathrm {password} )} for the next time the user wishes to authenticate. An eavesdropper seeing h 999 ( p a s s w o r d ) {\displaystyle h^{999}(\mathrm {password} )} communicated to the server will be unable to re-transmit the same hash chain to the server for authentication since the server now expects h 998 ( p a s s w o r d ) {\displaystyle h^{998}(\mathrm {password} )} . Due to the one-way property of cryptographically secure hash functions, it is infeasible for the eavesdropper to reverse the hash function and obtain an earlier piece of the hash chain. In this example, the user could authenticate 1000 times before the hash chain were exhausted. Each time the hash value is different, and thus cannot be duplicated by an attacker.

Binary hash chains

Binary hash chains are commonly used in association with a hash tree. A binary hash chain takes two hash values as inputs, concatenates them and applies a hash function to the result, thereby producing a third hash value.

The above diagram shows a hash tree consisting of eight leaf nodes and the hash chain for the third leaf node. In addition to the hash values themselves the order of concatenation (right or left 1,0) or "order bits" are necessary to complete the hash chain.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Hash chain

Start with the simplest possible case. Write down what Hash chain claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In computer science, 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 chain 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 chain 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 chain

In research: Hash chain appears in computer science 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 chain 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 chain is common in secondary-school and first-year university syllabi. It links to neighbouring topics Cryptographic algorithms, so understanding it makes those chapters shorter.
In everyday life: Look for Hash chain 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 chain in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Hash chain 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 chain out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Hash chain in simple terms?

Why does Hash chain matter?

Because it connects several computer science 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 chain?

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 chain.