slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Arjen K. Lenstra 1,2 joint work with Benne de Weger 2 1 Lucent Technologies’ Bell Laboratories 2 Technische Universite PowerPoint Presentation
Download Presentation
Arjen K. Lenstra 1,2 joint work with Benne de Weger 2 1 Lucent Technologies’ Bell Laboratories 2 Technische Universite

Loading in 2 Seconds...

play fullscreen
1 / 26

Arjen K. Lenstra 1,2 joint work with Benne de Weger 2 1 Lucent Technologies’ Bell Laboratories 2 Technische Universite - PowerPoint PPT Presentation


  • 117 Views
  • Uploaded on

Progress in hashing cryptanalysis. Arjen K. Lenstra 1,2 joint work with Benne de Weger 2 1 Lucent Technologies’ Bell Laboratories 2 Technische Universiteit Eindhoven. Outline. Brief summary of cryptographic hash functions: purpose, design criteria, iterative design approach

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Arjen K. Lenstra 1,2 joint work with Benne de Weger 2 1 Lucent Technologies’ Bell Laboratories 2 Technische Universite' - Mercy


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2

Progress in hashing cryptanalysis

Arjen K. Lenstra1,2

joint work with

Benne de Weger2

1 Lucent Technologies’ Bell Laboratories

2 Technische Universiteit Eindhoven

slide3

Outline

  • Brief summary of cryptographic hash functions:
    • purpose, design criteria, iterative design approach
    • popular hash functions
  • Cryptanalysis until August 2004
    • Dobbertin, Dean et al.
  • Recent cryptanalytic developments
    • random collisions (Wang et al.)
    • cascading iterative hashes (Joux, etc.)
  • The possibility of undesirable constructions
  • Conclusion
    • what’s next?
    • how to respond?
slide4

Brief summary of cryptographic hash functions

  • purpose: fixed-size ‘fingerprint’ for message integrity applications
  • design criteria for L-bit hash function H:
    • H must be quickly computable
    • given L-bit y, finding x with H(x) = y should take effort  2L
        • (i.e., brute force): 1st pre-image resistant
    • given x, finding xx’ with H(x) = H(x’) should also take  2L
        • (i.e., same brute force): 2nd pre-image resistant
    • grey area
    • finding random x, x’ with xx’ and H(x) = H(x’)
        • should take effort  2L/2: random collision resistant
        • (can’t achieve better than this due to birthday paradox)
    • outputs indistinguishable from ‘random’: random oracle
slide5

Brief summary of cryptographic hash functions

  • purpose: fixed-size ‘fingerprint’ for message integrity applications
  • design criteria for L-bit hash function H:
    • H must be quickly computable
    • given L-bit y, finding x with H(x) = y should take effort  2L
        • (i.e., brute force): 1st pre-image resistant
    • given x, finding xx’ with H(x) = H(x’) should also take  2L
        • (i.e., same brute force): 2nd pre-image resistant
    • finding not-entirely-random collisions should be hard too
    • finding random x, x’ with xx’ and H(x) = H(x’)
        • should take effort  2L/2: random collision resistant
        • (can’t achieve better than this due to birthday paradox)
    • outputs indistinguishable from ‘random’: random oracle
slide6

Iterative design of cryptographic hash functions

  • Iterative L-bit hash function H:
  • Compression function f:
      • maps pair (512-bit block, L-bit string) to L-bit string
  • Fixed L-bit string h0: initialization vector (IV)
  • Input x written as concatenation of 512-bit blocks:
      • x1 || x2 || x3 || … || xm
  • where xm contains padding and x’s length (MD-strengthening)
  • For i = 1, 2, …, m in succession, compute hi = f(xi,hi1)
  • Resulting hash H(x) of x equals final L-bit string hm
  • Nice property: if f is collision resistant, then H is collision resistant
    • But (2004): falling apart as soon as collisions can be found
slide7

Popular cryptographic hash functions

  • Most eggs in the Message Digest basket:
  • MD4, L = 128
  • tweaked version: MD5, L = 128
  • length extension: SHA-0, L = 160
  • surprise tweak: SHA-1, L = 160
  • more tweaks, more length extensions:
      • SHA-224/256/384/512, L = 224/256/384/512
  • all in the same family, all iterative
slide8

Hashing cryptanalysis until August 2004

  • MD4 considered broken: Den Boer, Bosselaers, and Dobbertin,
    • 1996, ‘meaningful’ collisions
  • MD5 considered weak: Dobbertin,
    • 1996, collisions in the MD5 compression function
  • Iterated hash functions for which compression function
    • fixed points can be found (i.e., all hashes in the SHA family):
    • Drew Dean et al. (1999) found 2nd preimage weakness
      • (hidden in Dean’s thesis, never published)
  • MD5 and up:
    • security of practical applications not seriously questioned
  • Strong belief in effectiveness of tweaks
slide9

Recent cryptanalytic developments in hashing

  • August 2004:
    • X. Wang et al.: actual random collisions in MD4 (‘no time’),
      • MD5 in time  239, etc., for any IV
    • A. Joux: cascading of iterated L-bit and perfect M-bit hash
      • does not result in L+M-bit hash – as commonly believed

Last result particularly worrisome because of its simplicity

slide10

Intermezzo: Joux’s result

  • cascading of iterated L-bit and perfect M-bit hash does not result
    • in L+M-bit hash: collisions much faster than in time 2(L+M)/2

find y11, y12 with f(y11,h0) = f(y12,h0) = h1 in time  2L/2

find y21, y22 with f(y21,h1) = f(y22,h1) = h2 in time  2L/2

find yk1, yk2 with f(yk1,hk1) = f(yk2,hk1) = hk in time  2L/2

  • Then: y1u||y2v||…||ykw for all u, v, …, w {1,2} all collide
    •  2K- fold collision in time K2L/2
  • With K = M/2:
    • for any M-bit hash function there will be a pair among the
    • 2M/2-fold collision that collides for that M-bit hash as well

 simultaneous collision for L-bit hash and M-bit hash in time

(M/2)2L/2 + 2M/2, for iterated L-bit hash and any M-bit hash

slide11

Recent cryptanalytic developments in hashing

  • August 2004:
    • X. Wang et al.: actual random collisions in MD4 (‘no time’),
      • MD5 in time  239, etc., for any IV
    • A. Joux: cascading of iterated L-bit and perfect M-bit hash
      • does not result in L+M-bit hash – as commonly believed
    • A. Joux: actual random collision for SHA-0 in time  251
    • E. Biham: cryptanalysis of SHA-1 variants
  • October 2004, Kelsey/Schneier (based on Joux):
    • 2nd preimage weakness in any iterated hash (improving Dean)
  • February 7, 2005, NIST announcement:
    • recent developments have no effect on SHA-1
    • phase out SHA-1 by 2010, purely based on ‘Moore’s law’
slide12

Recent cryptanalytic developments in hashing

  • August 2004:
    • X. Wang et al.: actual random collisions in MD4 (‘no time’),
      • MD5 in time  239, etc., for any IV
    • A. Joux: cascading of iterated L-bit and perfect M-bit hash
      • does not result in L+M-bit hash – as commonly believed
    • A. Joux: actual random collision for SHA-0 in time  251
    • E. Biham: cryptanalysis of SHA-1 variants
  • October 2004, Kelsey/Schneier (based on Joux):
    • 2nd preimage weakness in any iterated hash (improving Dean)
  • February 14, 2005, X. Wang et al. (based on Wang/Joux/Biham):
    • actual random collision for SHA-0 in time  239
    • random collision possibility for SHA-1 in time  269 (or 266)

(269 < 280 – no reaction or retraction from NIST yet)

slide13

Long term prospects of

out, no news

out, no news

(never in)

out, an unpleasant surprise

??

Popular cryptographic hash functions

  • Most eggs in the Message Digest basket:
  • MD4, L = 128
  • tweaked version: MD5, L = 128
  • length extension: SHA-0, L = 160
  • surprise tweak: SHA-1, L = 160
  • more tweaks, more length extensions:
      • SHA-224/256/384/512, L = 224/256/384/512
  • all in the same family, all iterative

Even given the ‘substantial changes’ compared to SHA-1,

  • to what extent can we still trust SHA-224/256/384/512?
slide14

How do the Wang et al. collision attacks work?

  • Interestingly:
    • people are still trying to figure it out
    • V. Klima succeeded: improved the MD5 attack to  233
  • Very roughly speaking:
    • differential paths of compression function f are analysed
    • find M0 and low Hamming weight 1,in and out such that
      • f(M0,h0) = f(M0+ 1,in,h0) + out = h1 + out
    • MD4 is so weak that out = 0 for low Hamming weight 1,in  0
    • find M1 and low Hamming weight 2,in such that
      • f(M1,h1) = f(M1+ 2,in,h1 + out)
    • as a result M0||M1 and M0+ 1,in||M1+ 2,in collide
    • for SHA-0, 1,in = 0 (and thus out = 0) to get ‘convenient’ h1,
    • (later version omits M0 altogether: single block SHA-0 collision)
slide15

The possibility of undesirable constructions

  • Often repeated argument:
    • random collisions are not good for anything
    • all collisions so far are ‘random’, so we’re fine
  • Despite this argument:
    • published random collisions used for actual attack examples
      • involving integrity checks for downloadable files
      • (Tripwire etc.)
    • random collisions combined with iterative structure
      • suffice for interesting X.509 constructions
    • so far no truly ‘disastrous’ applications (imo)
slide16

X.509 certificate

  • X.509 allows following format of data
    • that will be hashed and signed:
          • p1|| m || p2
    • where:
    • p1 contains header, distinguished names, and
        • header of public key part,
        • may assume that p1 consists of whole number of blocks
    • m is an RSA modulus
    • p2 contains public exponent and
        • all other data until signature part
  • For collision purposes, the obvious place

to ‘hide’ random data would be the RSA modulus

slide17

X.509 collision construction ingredients

  • if collisions can be found for any IV, then collisions can be
      • concocted such that they have same prescribed initial blocks
  • proper (and identical) data appended to random data pairs turns
      • random pair plus appendix into pair of valid RSA moduli
  • arbitrarily selected data can be appended to colliding
      • messages of same length, and they will still collide
  • Identical stuff of one’s choice can be prepended to new collision
  • Random collision can be promoted to meaningful data
  • Identical stuff of one’s choice can be appended to any collision

1 & 3: due to iterative nature of hashes

2: a new trick for RSA moduli construction

slide18

X.509 construction details

  • Construct colliding p1|| m || p2 and p1|| m’ || p2 as follows:
  • Prepend:
    • pick properly formatted p1 with names etc., whole # blocks
    • compute p1’s intermediate hash value h
    • ask X. Wang to find random collision m1, m2 with h as IV
    • p1||m1 and p1||m2 now collide as well
  • Promote:
    • find m3 s.t. m1||m3 = m and m2||m3 = m’ are RSA moduli
    • random m1, m2 extended to meaningful m1||m3 and m2||m3
  • Append:
    • p1||m1||m3 = p1|| m and p1||m2||m3 = p1|| m’ still collide
    • and so do p1|| m ||p2 and p1|| m’ ||p2 for any p2
slide19

Applications of X.509 colliding certificates?

  • Can get one certificate for the price of two
  • Sign using one certificate, later deny based on other certificate
    • Keys involved must have been generated simultaneously,
        • so detection of this fraud attempt is easy
  • No other attack scenarios that are facilitated by
      • these types of collisions
  • (see www.win.tue.nl/~bdeweger/CollidingCertificates)
slide20

Outsider’s X.509 collision assessment

  • CA can no longer establish
      • proof of possession of private key
  • Does not seem to lead to dangerous attack scenarios
      • (we refer to it as a ‘construction’, not an ‘attack’)
        • Insider’s point of view may be different
  • Greater danger if m and m’ could be made to contain
      • different ‘subject distinguished name’ information
      • This may be possible if ‘grey area’ is exploited
      • Stay tuned –seems more is possible than we thought
  • Problems can be avoided by making sure that:
    • no one can predict any prefix of the hashed & signed part
      • before hashing and signing take place
        • (this is not part of the X.509 specs)
slide21

RSA moduli construction

  • The problem:
    • for any m1 and m2 of same length N,
    • find m3 such that m1||m3 and m2||m3 are secure RSA moduli
  • The solution (for ‘any’ M > 0):
    • repeatedly pick two M/2-bit primes p and q
    • use Chinese remaindering to find M-bit m3 such that
      • p divides m1||m3 and q divides m2||m3
    • until (m1||m3)/p and (m2||m3)/q are both prime

N = 1024, M = 1024, 2048-bit moduli, 512-bit smallest factors:

secure

N = 512, M = 512, 1024-bit moduli, 256-bit smallest factors:

not secure

slide22

Other strange RSA moduli

  • Variants of our new RSA moduli construction allow:
  • ‘Twin RSA’: RSA moduli (n, n+2), with factors of same size
  • ‘predetermined Twin RSA’: RSA moduli (n, n+2) with
    • fixed leading half bits, and factors of different sizes
slide23

Predetermined Twin RSA, 2048-bit example

  • n= 80000000 00000000 00000000 00000000
  • 00000000 00000000 00000000 00000000
  • 00000000 00000000 00000000 00000000
      • 00000000 00000000 00000000 00000000
      • 00000000 00000000 00000000 00000000
      • 00000000 00000000 00000000 00000000
      • 00000000 00000000 00000000 00000000
      • 00000000 00000000 00000000 00000000
      • 396099A3 5F9D2B49 E7BB729E 9542A7B0
      • A1FAD34B EE884199 E29A5DB4 E49DE1C8
      • 279682F4 2A92FBFF 4F0F891F 65638997
      • B28D26DA 10B7529A 40CFA534 8BB95BE8
      • ADF4A21B 7DC562D4 93590D53 6B6124C5
      • 6DB5D693 1004A7B4 C031C401 A4B6E1E8
      • EA5C8362 E7B2DB3F BFDEF87D 75311FEA
      • 7D9BF1C3 9E3E64DF 9163E468 6D5D2711
  • and n+2 are secure RSA moduli, with independent factorizations
    •  two 2048-bit RSA moduli for just 1024 bits
slide24

Other strange RSA moduli

  • Variants of our new RSA moduli construction allow:
  • ‘Twin RSA’: RSA moduli (n, n+2), with factors of same size
  • ‘predetermined Twin RSA’: RSA moduli (n, n+2) with
    • fixed leading half bits, and factors of different sizes
  • These moduli look highly suspicious
  • Questions:
    • Can anyone break them?
    • Can anyone break n given factorization of n+2 (or vice versa)?
    • Good for what? (One to sign, other to encrypt? Backup key?)
slide25

Conclusion

  • What’s next?
  • Continued improvements of random collision attacks very likely
  • Exploitation of ‘grey area’ looks promising
  • More ‘interesting’ constructions may emerge
  • How to respond?
  • short term: case by case risk analysis, in most cases no need for
    • changes, migrate in high risk cases only (to what? SHA-256?)
  • long term:
    • hard to defend long term application of SHA family
    • also hard to defend application of SHA-1 until 2010
    • current iterated approach has undesirable properties
    • what about AES-like
      • competition for AHS, ‘Advanced Hash Standard’?