Attacks on Cryptographic Hashes in Internet Protocols

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This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited.

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Copyright © The Internet Society (2005).

Abstract

Recent announcements of better-than-expected collision attacks in popular hash algorithms have caused some people to question whether common Internet protocols need to be changed, and if so, how. This document summarizes the use of hashes in many protocols, discusses how the collision attacks affect and do not affect the protocols, shows how to thwart known attacks on digital certificates, and discusses future directions for protocol designers.

1. Introduction

In summer 2004, a team of researchers showed concrete evidence that the MD5 hash algorithm was susceptible to collision attacks [MD5-attack]. In early 2005, the same team demonstrated a similar attack on a variant of the SHA-1 [RFC3174] hash algorithm, with a prediction that the normally used SHA-1 would also be susceptible with a large amount of work (but at a level below what should be required if SHA-1 worked properly) [SHA-1-attack]. Also in early 2005, researchers showed a specific construction of PKIX certificates [RFC3280] that use MD5 for signing [PKIX-MD5-construction], and another researcher showed a faster method for finding MD5 collisions (eight hours on a 1.6-GHz computer) [MD5-faster].

Because of these announcements, there has been a great deal of discussion by cryptography experts, protocol designers, and other concerned people about what, if anything, should be done based on the news. Unfortunately, some of these discussions have been based on erroneous interpretations of both the news and on how hash algorithms are used in common Internet protocols.

Hash algorithms are used by cryptographers in a variety of security protocols, for a variety of purposes, at all levels of the Internet protocol stack. They are used because they have two security properties: to be one way and collision free. (There is more about these properties in the next section; they're easier to explain in terms of breaking them.) The recent attacks have demonstrated that one of those security properties is not true. While it is certainly possible, and at a first glance even probable, that the broken security property will not affect the overall security of many specific Internet protocols, the conservative security approach is to change hash algorithms. The Internet protocol community needs to migrate in an orderly manner away from SHA-1 and MD5 -- especially MD5 -- and toward more secure hash algorithms.

This document summarizes what is currently known about hash algorithms and the Internet protocols that use them. It also gives advice on how to avoid the currently known problems with MD5 and SHA-1, and what to consider if predicted attacks become real.

A high-level summary of the current situation is:

• Both MD5 and SHA-1 have newly found attacks against them, the attacks against MD5 being much more severe than the attacks against SHA-1.

• The attacks against MD5 are practical on any modern computer.

• The attacks against SHA-1 are not feasible with today's computers, but will be if the attacks are improved or Moore's Law continues to make computing power cheaper.

• Many common Internet protocols use hashes in ways that are unaffected by these attacks.

• Most of the affected protocols use digital signatures.

• Better hash algorithms will reduce the susceptibility of these attacks to an acceptable level for all users.

2. Hash Algorithms and Attacks on Them

A "perfect" hash algorithm has a few basic properties. The algorithm converts a chunk of data (normally, a message) of any size into a fixed-size result. The length of the result is called the "hash length" and is often denoted as "L"; the result of applying the hash algorithm on a particular chunk of data is called the "hash value" for that data. Any two different messages of any size should have an exceedingly small probability of having the same hash value, regardless of how similar or different the messages are.

This description leads to two mathematical results. Finding a pair of messages M1 and M2 that have the same hash value takes 2^(L/2) attempts. For any reasonable hash length, this is an impossible problem to solve (collision free). Also, given a message M1, finding any other message M2 that has the same hash value as M1 takes 2^L attempts. This is an even harder problem to solve (one way).

Note that this is the description of a perfect hash algorithm; if the algorithm is less than perfect, an attacker can expend less than the full amount of effort to find two messages with the same hash value.

There are two categories of attacks.

Attacks against the "collision-free" property:

• A "collision attack" allows an attacker to find two messages M1 and M2 that have the same hash value in fewer than 2^(L/2) attempts.

Attacks against the "one-way" property:

• A "first-preimage attack" allows an attacker who knows a desired hash value to find a message that results in that value in fewer than 2^L attempts.

• A "second-preimage attack" allows an attacker who has a desired message M1 to find another message M2 that has the same hash value in fewer than 2^L attempts.

The two preimage attacks are very similar. In a first-preimage attack, you know a hash value but not the message that created it, and you want to discover any message with the known hash value; in the second-preimage attack, you have a message and you want to find a second message that has the same hash. Attacks that can find one type of preimage can often find the other as well.

When analyzing the use of hash algorithms in protocols, it is important to differentiate which of the two properties of hashes are important, particularly now that the collision-free property is becoming weaker for currently popular hash algorithms. It is certainly important to determine which parties select the material being hashed. Further, as shown by some of the early work, particularly [PKIX-MD5-construction], it is also important to consider which party can predict the material at the beginning of the hashed object.

2.1. Currently Known Attacks

All the currently known practical or almost-practical attacks on MD5 and SHA-1 are collision attacks. This is fortunate: significant first- and second-preimage attacks on a hash algorithm would be much more devastating in the real world than collision attacks, as described later in this document.

It is also important to note that the current collision attacks require at least one of the two messages to have a fair amount of structure in the bits of the message. This means that finding two messages that both have the same hash value *and* are useful in a real-world attack is more difficult than just finding two messages with the same hash value.

3. How Internet Protocols Use Hash Algorithms

Hash algorithms are used in many ways on the Internet. Most protocols that use hash algorithms do so in a way that makes them immune to harm from collision attacks. This is not by accident: good protocol designers develop their protocols to withstand as many future changes in the underlying cryptography as possible, including attacks on the cryptographic algorithms themselves.

Uses for hash algorithms include:

• Non-repudiable digital signatures on messages. Non-repudiation is a security service that provides protection against false denial of involvement in a communication. S/MIME and OpenPGP allow mail senders to sign the contents of a message they create, and the recipient of that message can verify whether or not the signature is actually associated with the message. A message is used for non-repudiation if the message is signed and the recipient of the message can later use the signature to prove that the signer indeed created the message.

• Digital signatures in certificates from trusted third parties. Although this is similar to "digital signatures on messages", certificates themselves are used in many other protocols for authentication and key management.

• Challenge-response protocols. These protocols combine a public large random number with a value to help hide the value when being sent over unencrypted channels.

• Message authentication with shared secrets. These are similar to challenge-response protocols, except that instead of using public values, the message is combined with a shared secret before hashing.

• Key derivation functions. These functions make repeated use of hash algorithms to mix data into a random string for use in one or more keys for a cryptographic protocol.

• Mixing functions. These functions also make repeated use of hash algorithms to mix data into random strings, for uses other than cryptographic keys.

• Integrity protection. It is common to compare a hash value that is received out-of-band for a file with the hash value of the file after it is received over an unsecured protocol such as FTP.

Of the above methods, only the first two are affected by collision attacks, and even then, only in limited circumstances. So far, it is believed that, in general, challenge-response protocols are not susceptible, because the sender is authenticating a secret already stored by the recipient. In message authentication with shared secrets, the fact that the secret is known to both parties is also believed to prevent any sensible attack. All key derivation functions in IETF protocols take random input from both parties, so the attacker has no way of structuring the hashed message.

4. Hash Collision Attacks and Non-Repudiation of Digital Signatures

The basic idea behind the collision attack on a hash algorithm used in a digital-signature protocol is that the attacker creates two messages that have the same hash value, causes one of them to be signed, and then uses that signature over the other message for some nefarious purpose. The specifics of the attack depend on the protocol being used and what the victim does when presented with the signed message.

The canonical example is where you create two messages, one of which says "I will pay $10 for doing this job" and the other of which says "I will pay $10,000 for doing this job". You present the first message to the victim, get them to sign it, do the job, substitute the second message in the signed authorization, present the altered signed message (whose signature still verifies), and demand the higher amount of money. If the victim refuses, you take them to court and show the second signed message.

Most non-repudiation attacks rely on a human assessing the validity of the purportedly signed message. In the case of the hash-collision attack, the purportedly signed message's signature is valid, but so is the signature on the original message. The victim can produce the original message, show that he/she signed it, and show that the two hash values are identical. The chance of this happening by accident is one in 2^L, which is infinitesimally small for either MD5 or SHA-1.

In other words, to thwart a hash collision attack in a non- repudiation protocol where a human is using a signed message as authorization, the signer needs to keep a copy of the original message he/she signed. Messages that have other messages with the same hash must be created by the same person, and do not happen by accident under any known probable circumstances. The fact that the two messages have the same hash value should cause enough doubt in the mind of the person judging the validity of the signature to cause the legal attack to fail (and possibly bring intentional fraud charges against the attacker).

Thwarting hash collision attacks in automated non-repudiation protocols is potentially more difficult, because there may be no humans paying enough attention to be able to argue about what should have happened. For example, in electronic data interchange (EDI) applications, actions are usually taken automatically after authentication of a signed message. Determining the practical effects of hash collisions would require a detailed evaluation of the protocol.

5. Hash Collision Attacks and Digital Certificates from Trusted Third

Parties

Digital certificates are a special case of digital signatures. In general, there is no non-repudiation attack on trusted third parties due to the fact that certificates have specific formatting. Digital certificates are often used in Internet protocols for key management and for authenticating a party with whom you are communicating, possibly before granting access to network services or trusting the party with private data such as credit card information.

It is therefore important that the granting party can trust that the certificate correctly identifies the person or system identified by the certificate. If the attacker can get a certificate for two different identities using just one public key, the victim can be fooled into believing that one person is someone else.

The collision attack on PKIX certificates described in early 2005 relied on the ability of the attacker to create two different public keys that would cause the body of the certificate to have the same hash value. For this attack to work, the attacker needs to be able to predict the contents and structure of the certificate before it is issued, including the identity that will be used, the serial number that will be included in the certificate, and the start and stop dates of the validity period for the certificate.

The effective result of this attack is that one person using a single identity can get a digital certificate over one public key, but be able to pretend that it is over a different public key (but with the same identity, valid dates, and so on). Because the identity in the two certificates is the same, there are probably no real-world examples where such an attack would get the attacker any advantage. At best, someone could claim that the trusted third party made a mistake by issuing a certificate with the same identity and serial number based on two different public keys. This is indeed far-fetched.

It is very important to note that collision attacks only affect the parts of certificates that have no human-readable information in them, such as the public keys. An attack that involves getting a certificate with one human-readable identity and making that certificate useful for a second human-readable identity would require more effort than a simple collision attack.

5.1. Reducing the Likelihood of Hash-Based Attacks on PKIX Certificates

If a trusted third party who issues PKIX certificates wants to avoid the attack described above, they can prevent the attack by making other signed parts of the certificate random enough to eliminate any advantage gained by the attack. Ideas that have been suggested include:

• making part of the certificate serial number unpredictable to the attacker

• adding a randomly chosen component to the identity

• making the validity dates unpredictable to the attacker by skewing each one forwards or backwards

Any of these mechanisms would increase the amount of work the attacker needs to do to trick the issuer of the certificate into generating a certificate that is susceptible to the attack.

6. Future Attacks and Their Effects

There is a disagreement in the security community about what to do now. Even the two authors of this document disagree on what to do now.

   One of us (Bruce) believes that everyone should start migrating to
   SHA-256 [SHA-256] now, due to the weaknesses that have already been
   demonstrated in both MD5 and SHA-1.  There is an old saying inside
   the US National Security Agency (NSA): "Attacks always get better;
   they never get worse."  The current collision attacks against MD5 are
   easily done on a single computer; the collision attacks against SHA-1
   are at the far edge of feasibility today, but will only improve with
   time.  It is preferable to migrate to the new hash standard before
   there is a panic, instead of after.  Just as we all migrated from
   SHA-0 to SHA-1 based on some unknown vulnerability discovered inside
   the NSA, we need to migrate from SHA-1 to SHA-256 based on these most
   recent attacks.  SHA-256 has a 256-bit hash length.  This length will
   give us a much larger security margin in the event of newly
   discovered attacks.  Meanwhile, further research inside the
   cryptographic community over the next several years should point to
   further improvements in hash algorithm design, and potentially an
   even more secure hash algorithm.

The other of us (Paul) believes that this may not be wise for two reasons. First, the collision attacks on current protocols have not been shown to have any discernible real-world effects. Further, it is not yet clear which stronger hash algorithm will be a good choice for the long term. Moving from one algorithm to another leads to inevitable lack of interoperability and confusion for typical crypto users. (Of course, if any practical attacks are formulated before there is community consensus of the properties of the cipher-based hash algorithms, Paul would change his opinion to "move to SHA-256 now".)

Both authors agree that work should be done to make all Internet protocols able to use different hash algorithms with longer hash values. Fortunately, most protocols today already are capable of this; those that are not should be fixed soon.

The authors of this document feel similarly for new protocols being developed: Bruce thinks they should start using SHA-256 from the start, and Paul thinks that they should use SHA-1 as long as the new protocols are not susceptible to collision attacks. Any new protocol must have the ability to change all of its cryptographic algorithms, not just its hash algorithm.

7. Security Considerations

The entire document discusses security on the Internet.

The discussion in this document assumes that the only attacks on hash algorithms used in Internet protocols are collision attacks. Some significant preimaging attacks have already been discovered [Preimaging-attack], but they are not yet practical. If a practical preimaging attack is discovered, it would drastically affect many Internet protocols. In this case, "practical" means that it could be executed by an attacker in a meaningful amount of time for a meaningful amount of money. A preimaging attack that costs trillions of dollars and takes decades to preimage one desired hash value or one message is not practical; one that costs a few thousand dollars and takes a few weeks might be very practical.

8. Informative References

   [MD5-attack]            X. Wang, D. Feng, X. Lai, and H. Yu,
   
                           "Collisions for Hash Functions MD4, MD5,
                           HAVAL-128 and RIPEMD", August 2004,
                           <http://eprint.iacr.org/2004/199>.
   
   [MD5-faster]            Vlastimil Klima, "Finding MD5 Collisions - a
                           Toy For a Notebook", March 2005,
                           <http://cryptography.hyperlink.cz/
                           md5/MD5_collisions.pdf>.
   
   [PKIX-MD5-construction] Arjen Lenstra and Benne de Weger, "On the
                           possibility of constructing meaningful hash
                           collisions for public keys", February 2005,
                           <http://www.win.tue.nl/~bdeweger/
                           CollidingCertificates/ddl-final.pdf>.
   
   [Preimaging-attack]     John Kelsey and Bruce Schneier, "Second
                           Preimages on n-bit Hash Functions for Much
                           Less than 2^n Work", November 2004,
                           <http://eprint.iacr.org/2004/304>.
   
   [RFC3174]               Eastlake, D. and P. Jones, "US Secure Hash
                           Algorithm 1 (SHA1)", RFC 3174,
                           September 2001.
   
   [RFC3280]               Housley, R., Polk, W., Ford, W., and D. Solo,
                           "Internet X.509 Public Key Infrastructure
                           Certificate and Certificate Revocation List
                           (CRL) Profile", RFC 3280, April 2002.
   
   [SHA-1-attack]          Xiaoyun Wang, Yiqun Lisa Yin, and Hongbo Yu,
                           "Collision Search Attacks on SHA1",
                           February 2005,
                           <http://theory.csail.mit.edu/~yiqun/shanote.pdf>.
   
   [SHA-256]               NIST, "Federal Information Processing
                           Standards Publication (FIPS PUB) 180-2,
                           Secure Hash Standard", August 2002.

Appendix A. Acknowledgements

The authors would like to thank the IETF community, particularly those active on the SAAG mailing list, for their input. We would also like to thank Eric Rescorla for early material that went into the first version, and Arjen Lenstra and Benne de Weger for significant comments on the first version of this document.

Authors' Addresses

Paul Hoffman
VPN Consortium

   EMail: paul.hoffman@vpnc.org

Bruce Schneier
Counterpane Internet Security

EMail:

          schneier@counterpane.com

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