computer science

Length extension attack

Length extension attack 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 Length extension attack rather than just read about it. In short: In cryptography and computer security, a length extension attack is a type of attack where an attacker can use Hash(message1) and the length of message1 to calculate Hash(message1 ‖ message2) for an attacker-controlled message2, without needing to know the content of message1. This is problematic when the hash is used as a message authentication code with construction Hash(secret ‖ message), and message and the leng…

Key takeaways

Length extension attack 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 Length extension attack to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Length extension attack from memory before moving on to harder problems.

Reference excerpt

In cryptography and computer security, a length extension attack is a type of attack where an attacker can use Hash(message1) and the length of message1 to calculate Hash(message1 ‖ message2) for an attacker-controlled message2, without needing to know the content of message1. This is problematic when the hash is used as a message authentication code with construction Hash(secret ‖ message), and message and the length of secret is known, because an attacker can include extra information at the end of the message and produce a valid hash without knowing the secret. Algorithms like MD5, SHA-1 and most of SHA-2 that are based on the Merkle–Damgård construction are susceptible to this kind of attack. Truncated versions of SHA-2, including SHA-384 and SHA-512/256 are not susceptible, nor is the SHA-3 algorithm. HMAC also uses a different construction and so is not vulnerable to length extension attacks. A secret suffix MAC, which is calculated as Hash(message ‖ secret), isn't vulnerable to a length extension attack, but is vulnerable to another attack based on a hash collision.

Explanation The vulnerable hashing functions work by taking the input message, and using it to transform an internal state. After all of the input has been processed, the hash digest is generated by outputting the internal state of the function. It is possible to reconstruct the internal state from the hash digest, which can then be used to process the new data. In this way, one may extend the message and compute the hash that is a valid signature for the new message.

Example A server for delivering waffles of a specified type to a specific user at a location could be implemented to handle requests of the given format:

Original Data: count=10&lat=37.351&user_id=1&long=-119.827&waffle=eggo Original Signature: 6d5f807e23db210bc254a28be2d6759a0f5f5d99

The server would perform the request given (to deliver ten waffles of type eggo to the given location for user "1") only if the signature is valid for the user. The signature used here is a MAC, signed with a key not known to the attacker. It is possible for an attacker to modify the request in this example by switching the requested waffle from "eggo" to "liege." This can be done by taking advantage of a flexibility in the message format if duplicate content in the query string gives preference to the latter value. This flexibility does not indicate an exploit in the message format, because the message format was never designed to be cryptographically secure in the first place, without the signature algorithm to help it.

Desired New Data: count=10&lat=37.351&user_id=1&long=-119.827&waffle=eggo&waffle=liege

In order to sign this new message, typically the attacker would need to know the key the message was signed with, and generate a new signature by generating a new MAC. However, with a length extension attack, it is possible to feed the hash (the signature given above) into the state of the hashing function, and continue where the original request had left off, so long as the length of the original request is known. In this request, the original key's length was 14 bytes, which could be determined by trying forged requests with various assumed lengths, and checking which length results in a request that the server accepts as valid. The message as fed into the hashing function is often padded, as many algorithms can only work on input messages whose lengths are a multiple of some given size. The content of this padding is always specified by the hash function used. The attacker must include all of these padding bits in their forged message before the internal states of their message and the original will line up. Thus, the attacker constructs a slightly different message using these padding rules:

New Data: count=10&lat=37.351&user_id=1&long=-119.827&waffle=eggo\x80\x00\x00 \x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00 \x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00 \x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00 \x00\x00\x00\x02\x28&waffle=liege

This message includes all of the padding that was appended to the original message inside of the hash function before their payload (in this case, a 0x80 followed by a number of 0x00s and a message length, 0x228 = 552 = (14+55)*8, which is the length of the key plus the original message, appended at the end). The attacker knows that the state behind the hashed key/message pair for the original message is identical to that of new message up to the final "&." The attacker also knows the hash digest at this point, which means they know the internal state of the hashing function at that point. It is then trivial to initialize a hashing algorithm at that point, input the last few characters, and generate a new digest which can sign his new message without the original key.

New Signature: 0e41270260895979317fff3898ab85668953aaa2

By combining the new signature and new data into a new request, the server will see the forged request as a valid request due to the signature being the same as it would have been generated if the password was known.

Notes

References

Worked examples

Example 1 — a first encounter with Length extension attack

Start with the simplest possible case. Write down what Length extension attack 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 Length extension attack 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 Length extension attack 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 Length extension attack

In research: Length extension attack 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 Length extension attack 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: Length extension attack is common in secondary-school and first-year university syllabi. It links to neighbouring topics Cryptographic attacks, so understanding it makes those chapters shorter.
In everyday life: Look for Length extension attack 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 Length extension attack in 20 minutes

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

Frequently asked questions

What is Length extension attack in simple terms?

Why does Length extension attack 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 Length extension attack?

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 Length extension attack.