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. This is in contrast to a preimage attack where a specific target hash value is specified.

There are roughly two types of collision attacks:

Collision attack
Find two different messages m1 and m2 such that hash(m1) = hash(m2).

More generally:

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

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, as of 2007, 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 (specially its signature) could be used to create a new rogue certificate to impersonate another domain.[5]

A real-world collision attack was published in December 2008 when a group of security researchers published a forged X.509 signing certificate that could be used to impersonate a certificate authority, taking advantage of a prefix collision attack against the MD5 hash function. This meant that an attacker could impersonate any SSL-secured website as a man-in-the-middle, thereby subverting the certificate validation built in every web browser to protect electronic commerce. The rogue certificate may not be revokable by real authorities, and could also have an arbitrary forged expiry time. Even though MD5 was known to be very weak in 2004,[1] certificate authorities were still willing to sign MD5-verified certificates in December 2008,[6] and at least one Microsoft code-signing certificate was still using MD5 in May 2012.

The Flame malware successfully used a new variation of a chosen-prefix collision attack to spoof code signing of its components by a Microsoft root certificate that still used the compromised MD5 algorithm.[7][8]

In 2019, researchers found a chosen-prefix collision attack against SHA-1 with computing complexity between 266.9 and 269.4 and cost less than 100,000 US dollars. [9][10] In 2020, researchers reduced the complexity of chosen-prefix collision attack against SHA-1 to 263.4. [11]

Attack scenarios

Many applications of cryptographic hash functions do not rely on collision resistance, thus collision attacks do not affect their security. For example, HMACs are not vulnerable.[12] For the attack to be useful, the attacker must be in control of the input to the hash function.

Digital signatures

Because digital signature algorithms cannot sign a large amount of data efficiently, most implementations use a hash function to reduce ("compress") the amount of data that needs to be signed down to a constant size. Digital signature schemes are often vulnerable to hash collisions, unless using techniques like randomized hashing.[13]

The usual attack scenario goes like this:

  1. Mallory creates two different documents A and B that have an identical hash value, i.e., a collision. Mallory seeks to deceive Bob into accepting document B, ostensibly from Alice.
  2. Mallory sends document A to Alice, who agrees to what the document says, signs its hash, and sends the signature to Mallory.
  3. Mallory attaches the signature from document A to document B.
  4. Mallory then sends the signature and document B to Bob, claiming that Alice signed B. Because the digital signature matches document B's hash, Bob's software is unable to detect the substitution.

In 2008, researchers used a chosen-prefix collision attack against MD5 using this scenario, to produce a rogue certificate authority certificate. They created two versions of a TLS public key certificate, one of which appeared legitimate and was submitted for signing by the RapidSSL certificate authority. The second version, which had the same MD5 hash, contained flags which signal web browsers to accept it as a legitimate authority for issuing arbitrary other certificates.[14]

Usage in DoS attacks

In 2003, a denial of service (DoS) attack was described that used hash collisions to exploit the worst-case runtime of hash table lookups.[15] This issue affected most major programming languages, as they used weaker hash functions.

gollark: How does one apply changes to a merged PR?
gollark: Fiix it yourself.
gollark: #include <stdio.h>printf("abcd\n");return 42;
gollark: !exe why
gollark: !interpret why

References
  1. Xiaoyun Wang, Dengguo Feng, Xuejia Lai, Hongbo Yu: Collisions for Hash Functions MD4, MD5, HAVAL-128 and RIPEMD, Cryptology ePrint Archive Report 2004/199, 16 Aug 2004, revised 17 Aug 2004. Retrieved July 27, 2008.
  2. M.M.J. Stevens (June 2007). "On Collisions for MD5" (PDF). [...] we are able to find collisions for MD5 in about 224.1 compressions for recommended IHVs which takes approx. 6 seconds on a 2.6GHz Pentium 4. Cite journal requires |journal= (help)
  3. Magnus Daum; Stefan Lucks. "Hash Collisions (The Poisoned Message Attack)". Eurocrypt 2005 rump session. Archived from the original on 2010-03-27.
  4. Max Gebhardt; Georg Illies; Werner Schindler. "A Note on the Practical Value of Single Hash Collisions for Special File Formats" (PDF). Cite journal requires |journal= (help)
  5. Marc Stevens; Arjen Lenstra; Benne de Weger (2007-11-30). "Chosen-prefix Collisions for MD5 and Colliding X.509 Certificates for Different Identities". Cite journal requires |journal= (help)
  6. Alexander Sotirov; et al. (2008-12-30). "Creating a rogue CA certificate". Archived from the original on 2012-04-18. Retrieved 2009-10-07.
  7. "Microsoft releases Security Advisory 2718704". Microsoft. 3 June 2012. Archived from the original on 7 June 2012. Retrieved 4 June 2012.
  8. Marc Stevens (7 June 2012). "CWI Cryptanalist Discovers New Cryptographic Attack Variant in Flame Spy Malware". Centrum Wiskunde & Informatica. Retrieved 9 June 2012.
  9. Catalin Cimpanu (2019-05-13). "SHA-1 collision attacks are now actually practical and a looming danger". ZDNet.
  10. Ga¨etan Leurent1 and Thomas Peyrin (2019-05-06). "From Collisions to Chosen-Prefix Collisions Application to Full SHA-1" (PDF).
  11. Gaëtan Leurent and Thomas Peyrin (2020-01-05). "SHA-1 is a Shambles - First Chosen-Prefix Collision on SHA-1 and Application to the PGP Web of Trust" (PDF).
  12. "Hash Collision Q&A". Cryptography Research Inc. 2005-02-15. Archived from the original on 2008-07-17. Because of the way hash functions are used in the HMAC construction, the techniques used in these recent attacks do not apply
  13. Shai Halevi and Hugo Krawczyk, Randomized Hashing and Digital Signatures
  14. Alexander Sotirov; Marc Stevens; Jacob Appelbaum; Arjen Lenstra; David Molnar; Dag Arne Osvik; Benne de Weger (30 December 2008). MD5 considered harmful today. Chaos Communication Congress 2008.
  15. "Hash DoS Attack". Crossmatch, part of HID Global. Retrieved 2019-08-17.
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