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# Collision attack

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 Title: Collision attack Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Collision attack

In cryptography, a collision attack on a cryptographic hash tries to find two inputs producing the same hash value, i.e. a hash collision. In contrast to a preimage attack the hash value is not specified.

There are roughly two types of collision attacks:

Collision attack
Find two different messages m1 and m2 such that hash(m1) = hash(m2).
Chosen-prefix collision attack
Given two different prefixes p1, p2 find two appendages m1 and m2 such that hash(p1 ∥ m1) = hash(p2 ∥ m2) (where is the concatenation operation).

## Contents

• Classical collision attack 1
• Chosen-prefix collision attack 2
• Attack scenarios 3
• Digital signatures 3.1
• References 5
• External links 6

## Classical collision attack

Mathematically stated, a collision attack finds two different messages m1 and m2, such that hash(m1) = hash(m2). In a classical collision attack, the attacker has no control over the content of either message, but they are arbitrarily chosen by the algorithm.

Much like symmetric-key ciphers are vulnerable to brute force attacks, every cryptographic hash function is inherently vulnerable to collisions using a birthday attack. Due to the birthday problem, these attacks are much faster than a brute force would be. A hash of n bits can be broken in 2n/2 time (evaluations of the hash function).

More efficient attacks are possible by employing cryptanalysis to specific hash functions. When a collision attack is discovered and is found to be faster than a birthday attack, a hash function is often denounced as "broken". The NIST hash function competition was largely induced by published collision attacks against two very commonly used hash functions, MD5[1] and SHA-1. The collision attacks against MD5 have improved so much that it takes just a few seconds on a regular computer.[2] Hash collisions created this way are usually constant length and largely unstructured, so cannot directly be applied to attack widespread document formats or protocols.

However, workarounds are possible by abusing dynamic constructs present in many formats. In this way, two documents would be created which are as similar as possible in order to have the same hash value. One document would be shown to an authority to be signed, and then the signature could be copied to the other file. Such a malicious document would contain two different messages in the same document, but conditionally display one or the other through subtle changes to the file:

• Some document formats like PostScript, or macros in Microsoft Word, have conditional constructs.[3][4] (if-then-else) that allow testing whether a location in the file has one value or another in order to control what is displayed.
• TIFF files can contain cropped images, with a different part of an image being displayed without affecting the hash value.[4]
• PDF files are vulnerable to collision attacks by using color value (such that text of one message is displayed with a white color that blends into the background, and text of the other message is displayed with a dark color) which can then be altered to change the signed document's content.[4]

## Chosen-prefix collision attack

An extension of the collision attack is the chosen-prefix collision attack, which is specific to Merkle–Damgård hash functions. In this case, the attacker can choose two arbitrarily different documents, and then append different calculated values that result in the whole documents having an equal hash value. This attack is much more powerful than a classical collision attack.

Mathematically stated, given two different prefixes p1, p2, the attack finds two appendages m1 and m2 such that hash(p1 ∥ m1) = hash(p2 ∥ m2) (where is the concatenation operation).

In 2007, a chosen-prefix collision attack was found against MD5, requiring roughly 250 evaluations of the MD5 function. The paper also demonstrates two X.509 certificates for different domain names, with colliding hash values. This means that a certificate authority could be asked to sign a certificate for one domain, and then that certificate could be used to impersonate another domain.[5]

A real-world collision attack was published in December 2008 when a group of security researchers published a forged

• "Meaningful Collisions", attack scenarios for exploiting cryptographic hash collisions
• Fast MD5 and MD4 Collision Generators - Bishop Fox (formerly Stach & Liu). Create MD4 and MD5 hash collisions using groundbreaking new code that improves upon the techniques originally developed by Xiaoyun Wang. Using a 1.6 GHz Pentium 4, MD5 collisions can be generated in an average of 45 minutes, and MD4 collisions can be generated in an average of 5 seconds. Originally released on 22Jun2006.