Network Working Group                                         P. Hoffman
Internet-Draft                                            VPN Consortium
Obsoletes: 4270 (if approved)                                B. Schneier
Intended status: Informational             Counterpane Internet Security
Expires: October 31, 2013                                 April 29, 2013

         Attacks on Cryptographic Hashes in Internet Protocols


   Announcements in the past decade 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.
   It also gives rationales for moving away from some hash algorithms
   altogether and for choosing when to start using newer, presumably
   better, hash algorithms in Internet protocols.

   This document obsoletes RFC 4270 and introduces significant new
   material that has been learned since the publication of that

Status of This Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on October 31, 2013.

Copyright Notice

   Copyright (c) 2013 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

Hoffman & Schneier      Expires October 31, 2013                [Page 1]

Internet-Draft             Attacks on Hashes                  April 2013

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   ( in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Hash Algorithms and Attacks on Them . . . . . . . . . . . . .   3
     2.1.  Currently Known Attacks . . . . . . . . . . . . . . . . .   5
   3.  How Internet Protocols Use Hash Algorithms  . . . . . . . . .   5
   4.  Hash Collision Attacks and Non-repudiation of Digital
       Signatures  . . . . . . . . . . . . . . . . . . . . . . . . .   6
   5.  Hash Collision Attacks and Digital Certificates from Trusted
       Third Parties . . . . . . . . . . . . . . . . . . . . . . . .   7
     5.1.  Reducing the Likelihood of Hash-based Attacks on PKIX
           Certificates  . . . . . . . . . . . . . . . . . . . . . .   9
   6.  Cost of Creating Collisions in SHA-1  . . . . . . . . . . . .   9
   7.  The SHA-3 Competition and the Future  . . . . . . . . . . . .  11
   8.  Future Attacks and Their Effects  . . . . . . . . . . . . . .  11
   9.  Security Considerations . . . . . . . . . . . . . . . . . . .  12
   10. Informative References  . . . . . . . . . . . . . . . . . . .  13
   Appendix A.  Acknowledgements . . . . . . . . . . . . . . . . . .  14
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  14

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]; that work has been
   improved on more recently [Stevens].  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 was 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.

Hoffman & Schneier      Expires October 31, 2013                [Page 2]

Internet-Draft             Attacks on Hashes                  April 2013

   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 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, namely the SHA-2

   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

   A high-level summary of the current situation is:

   o  Both MD5 and SHA-1 have 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 practical for some attackers now,
      and will be more practical for more attackers in the near future.

   o  Attackers are able to use collisions in PKIX certificates to
      generate certificates that can act as trusted entities to create
      other certificates.

   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

Hoffman & Schneier      Expires October 31, 2013                [Page 3]

Internet-Draft             Attacks on Hashes                  April 2013

   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)

   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

Hoffman & Schneier      Expires October 31, 2013                [Page 4]

Internet-Draft             Attacks on Hashes                  April 2013

   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.

   Since the time that the collision attacks were first discovered, some
   attackers have used them to bootstrap other more devastating types of
   attacks.  Probably the most significant is [Chosen-Prefix], which
   shows how to use collisions to forge new CA certificates that would
   be accepted by web browsers at the time.  The "Flame" worm attack
   discovered in 2012 relied on spoofed Microsoft code-signing
   certificates that were acquired using the collision reduction attack
   on MD5 [Flame-Microsoft].

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

Hoffman & Schneier      Expires October 31, 2013                [Page 5]

Internet-Draft             Attacks on Hashes                  April 2013

      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

   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

Hoffman & Schneier      Expires October 31, 2013                [Page 6]

Internet-Draft             Attacks on Hashes                  April 2013

   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 they 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

   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

5.  Hash Collision Attacks and Digital Certificates from Trusted Third

Hoffman & Schneier      Expires October 31, 2013                [Page 7]

Internet-Draft             Attacks on Hashes                  April 2013

   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.

   One 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-

   After the above attack was described, many CAs continued to use the
   MD5 hash function.  Because of this, a group of researchers went
   further and showed how to create a rogue CA that would be accepted by
   all the common web browsers at the time [Chosen-Prefix].  After that,
   the CAs mostly (but not completely) stopped using the MD5 hash
   function, and most browsers stopped accepting signatures that used
   MD5.  It should be noted that the same attack would work with SHA-1,
   but it would take much more effort to mount such an attack.  An
   estimate for the actual amount of effort is described later in this

   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

Hoffman & Schneier      Expires October 31, 2013                [Page 8]

Internet-Draft             Attacks on Hashes                  April 2013

   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 should sign using a hash algorithm
   for which collisions are believed to be essentially impossible, such
   as those from the SHA-2 family.  If they want to use weaker hashes
   such as SHA-1, they can also 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

   o  making part of the certificate serial number unpredictable to the

   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.  Cost of Creating Collisions in SHA-1

   At the time that this document has been prepared, a scheme for
   creating collisions in SHA-1 has been widely discussed, but no
   collision has been published.  However, it is widely assumed that
   such a collision is currently possible in non-public settings, and
   that a public demonstration of a SHA-1 collision should be expected
   within a few years.  The current estimate is that creating a
   collision will take approximately 2^60 operations [Stevens].

   The following is an estimate, originated by Jesse Walker, of how much
   money and time it would take to create a SHA-1 hash collision in the
   future.  [Walker] It uses numbers based on hardware from the time
   this document is published, and has a lot of room for error.

   Using the eBACS benchmarks [eBACS], SHA-1 takes about 16 cycles per
   byte for 64-byte blocks on modern processors.  SHA-1 processes input
   data by blocks of 64 bytes, so the cost of one block of a SHA-1
   operation is 16 * 64, or 2^10 cycles.  If an attack of 2^60 SHA-1
   operations serves as the baseline, then finding a collision costs
   about 2^10 * 2^60, or 2^70, cycles.

Hoffman & Schneier      Expires October 31, 2013                [Page 9]

Internet-Draft             Attacks on Hashes                  April 2013

   A CPU core today provides about 2^31 cycles per second.  The state of
   the art is 2^3 cores per processor, for a total of 2^3 * 2^31, or
   2^34, cycles per second.  A server typically has 4 processors,
   increasing the total to 2^2 * 2^34, or 2^36, cycles per second.
   Because there are about 2^25 seconds per year, a server can deliver
   about 2^25 * 2^36, or 2^61, cycles per year, with the beginning of
   2013 as a base.  This is called a "server year" in this discussion.

   For this discussion, we assume that Moore's law as currently applied
   to server-level CPUs says that the speed will increase approximately
   40% per year, or double ever two years, and this will continue for
   the next decade.  (Note that the authors do not have a good reference
   for a respected estimate of applying Moore's law to current server-
   level CPUs, and would appreciate one!).

   This means that the processor power should double by 2015, double
   again by 2017, and then double again by 2019.  Thus, a commodity
   "server year" should be about

   2^1 * 2^61, or 2^62 cycles per year by 2015
   2^2 * 2^61, or 2^63 cycles per year by 2017
   2^4 * 2^61, or 2^65 cycles per year by 2019
   2^8 * 2^61, or 2^69 cycles per year by 2021

   With an attack that takes 2^69 iterations, the attack should cost

   2^70 / 2^62, or 2^8 server years by 2015
   2^70 / 2^63, or 2^7 server years by 2017
   2^70 / 2^65, or 2^5 server years by 2019
   2^70 / 2^69, or 2^1 server year by 2021

   Today, Amazon rents compute time on commodity servers for about
   US$0.04 per hour, or about US$350 per year.  Assume that compute
   rental fees remain fixed while server capacity keeps pace with
   Moore's law.  Then, because log2(350) is approximately 8.4, the cost
   of the attack will be approximately

   2^8 * 2^8.4, or about US$86K in 2015
   2^7 * 2^8.4, or about US$43K in 2017
   2^5 * 2^8.4, or about US$10K in 2019
   2^1 * 2^8.4, or about US$700 in 2021

Hoffman & Schneier      Expires October 31, 2013               [Page 10]

Internet-Draft             Attacks on Hashes                  April 2013

   A collision attack is therefore well within the range of what an
   organized crime syndicate can practically budget by 2015, and
   essentially any criminal by 2021.

   Since this argument only takes into account commodity server hardware
   and not instruction set improvements (for example, ARM 8 specifies a
   SHA-1 instruction), other commodity computing devices with even
   greater processing power (particularly GPUs) and custom hardware, the
   need to transition away from SHA-1 because of collision resistance
   functions could be more urgent than this back-of-the-envelope
   analysis suggests.

7.  The SHA-3 Competition and the Future

   After the events in 2005, NIST decided that it needed to have a
   backup hash function in case the SHA-2 family had problems similar to
   those found in MD5 and SHA-1.  NIST held a competition
   [SHA3-competition] to design a new family of hashes that was as
   strong as the SHA-2 family but was based on different underlying

   The competition was both a success and a disappointment.  It was a
   success in that there were many different strong candidates for the
   new family, and the competition caused a leap in understanding of the
   weaknesses in many proposals for hash functions.  It was a
   disappointment in that none of the finalists were actually faster or
   provably better than the SHA-2 family.

   In late 2012, NIST announced that the winner of the competition was
   the Keccak hash function [KECCAK-winner].  NIST was pleased about the
   properties of KECCAK, noting that it was sufficiently different from
   SHA-2 to have made the competition worthwhile.  At the same time,
   NIST emphasized that "SHA-2 has held up well and NIST considers SHA-2
   to be secure and suitable for general use" and that KECCAK is "an
   essential insurance policy in case SHA-2 is ever broken".

8.  Future Attacks and Their Effects

Hoffman & Schneier      Expires October 31, 2013               [Page 11]

Internet-Draft             Attacks on Hashes                  April 2013

   The authors believe that everyone should start migrating to SHA-2
   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
   noted that at the time of this writing, there has still not been
   shown a successful collision in SHA-1 in public; there has also not
   been shown any problem with the descriptions of how such a collision
   could probably be found.

   It is preferable to migrate to the SHA-2 family of hashes 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
   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

   The authors acknowledge that deprecating a hash algorithm is
   difficult from an operational standpoint, but it needs to be done
   eventually, and this is a good time to again make a significant push
   to SHA-2.  When NIST finalizes the parameters and test vectors for
   SHA-3, implementors might want to start adding SHA-3 to their
   products.  However, the authors do not believe that any push to start
   using SHA-3 is warranted at any time soon.

   The authors also feel that work should continue to make all Internet
   protocols able to use different hash algorithms.  Fortunately, most
   protocols today already are capable of this; those that are not
   really should be fixed soon.

9.  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;

Hoffman & Schneier      Expires October 31, 2013               [Page 12]

Internet-Draft             Attacks on Hashes                  April 2013

   one that costs a few thousand dollars and takes a few weeks might be
   very practical.  Even a preimaging attack that costs millions of
   dollars and takes over a year would be practical in high-value
   environments such as issuance of certificates.

10.  Informative References

              , "Short Chosen-Prefix Collisions for MD5 and the Creation
              of a Rogue CA Certificate", 2009,

              , "TechNet Blogs: Flame malware collision attack
              explained", June 2012, <

              , "NIST Selects Winner of Secure Hash Algorithm (SHA-3)
              Competition", October 2012,

              X. Wang, , D. Feng, , X. Lai, , and H. Yu, "Collisions for
              Hash Functions MD4, MD5, HAVAL-128 and RIPEMD", August
              2004, <>.

              Vlastimil Klima, , "Finding MD5 Collisions - a Toy For a
              Notebook", March 2005,

              Arjen Lenstra, and Benne de Weger, "On the possibility of
              constructing meaningful hash collisions for public keys",
              February 2005, <

              John Kelsey, and Bruce Schneier, "Second Preimages on
              n-bit Hash Functions for Much Less than 2^n Work",
              November 2004, <>.

   [RFC3174]  Eastlake, D. and P. Jones, "US Secure Hash Algorithm 1
              (SHA1)", RFC 3174, September 2001.

Hoffman & Schneier      Expires October 31, 2013               [Page 13]

Internet-Draft             Attacks on Hashes                  April 2013

   [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.

   [RFC6234]  Eastlake, D. and T. Hansen, "US Secure Hash Algorithms
              (SHA and SHA-based HMAC and HKDF)", RFC 6234, May 2011.

              Xiaoyun Wang, , Yiqun Lisa Yin, , and Hongbo Yu,
              "Collision Search Attacks on SHA1", February 2005,

              , "Cryptographic Hash Algorithm Competition", October

   [Stevens]  , "Cryptanalysis of MD5 and SHA-1", 2010,

   [Walker]   , "When Will We See Collisions for SHA-1?", 2012, <http://

   [eBACS]    Dan Bernstein, , "eBACS: ECRYPT Benchmarking of
              Cryptographic Systems", 2012,

Appendix A.  Acknowledgements

   Acknowledgements from RFC 4270: 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, Arjen
   Lenstra, and Benne de Weger for material and significant comments on
   the first draft of this document.

   Jesse Walker contributed the analysis of the cost of creating SHA-1
   collisions.  [[ There will probably be more here.  ]]

Authors' Addresses

   Paul Hoffman
   VPN Consortium


Hoffman & Schneier      Expires October 31, 2013               [Page 14]

Internet-Draft             Attacks on Hashes                  April 2013

   Bruce Schneier
   Counterpane Internet Security


Hoffman & Schneier      Expires October 31, 2013               [Page 15]