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Versions: 00 01 02 03 04 RFC 4270

Network Working Group                                         P. Hoffman
Internet-Draft                                            VPN Consortium
Expires: December 7, 2005                                    B. Schneier
                                           Counterpane Internet Security
                                                            June 5, 2005


         Attacks on Cryptographic Hashes in Internet Protocols
                   draft-hoffman-hash-attacks-04.txt

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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.



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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 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:

   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.




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   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
   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.



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   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.

   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:






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   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.

   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.






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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 they 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.




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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



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   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.

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



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   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 thousands of
   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>.



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   [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]  R. Housley, R., W. Polk, W., W. Ford, W., and D. 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.


Authors' Addresses

   Paul Hoffman
   VPN Consortium

   Email: paul.hoffman@vpnc.org


   Bruce Schneier
   Counterpane Internet Security

   Email: schneier@counterpane.com

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 draft, and Arjen Lenstra and Benne de Weger for significant
   comments on the first draft of this document.








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