Network Working Group P. Hoffman

Network Working Group P. Hoffman
Request for Comments: 4270 VPN Consortium
Category: Informational B. Schneier
Counterpane Internet Security
November 2005

Attacks on Cryptographic Hashes in Internet Protocols

Status of This Memo

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

Copyright Notice

Copyright (C) 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

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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:

o 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.

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

o 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.

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

o Most of the affected protocols use digital signatures.

o 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

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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:

o 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:

o 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.

o 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,

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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:

o 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.

o 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.

o 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.

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o 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.

o 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.

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

o 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.

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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.

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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:

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

o adding a randomly chosen component to the identity

o 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.

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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.

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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.

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[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.

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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: [email protected]

Bruce Schneier
Counterpane Internet Security

EMail: [email protected]

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