I was looking a Wikipedia article on SHA-2, and the "Comparison of SHA functions" table seems to indicate that SHA-2 is less secure than SHA-1.

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Is this true, or is the table wrong / misleading?

What does $2^{28.5}$ mean for SHA-256 compared to $2^{60}$ for SHA-1 (table in SHA-1 article says $2^{53}$)? How does it relate to MD5 article, which says:

The security of the MD5 hash function is severely compromised. A collision attack exists that can find collisions within seconds on a computer with a 2.6 GHz Pentium 4 processor (complexity of $2^{24.1}$)

Assuming that no collisions have been found for the SHA-2 family, does that still mean it takes less work to find a collision than SHA-1? Or do these numbers ($2^{28.5}$, $2^{60}$, $2^{53}$, $2^{24.1}$) mean different things?

If the table is wrong, how should it be corrected?

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    $\begingroup$ The :24 is probably referring to a version reduced to 24 rounds. $\endgroup$ – CodesInChaos May 20 '13 at 23:01
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    $\begingroup$ I corrected the table to say "None (For a 24-round variant: $2^{28.5}$)". Thanks for finding this. $\endgroup$ – Paŭlo Ebermann May 21 '13 at 4:23
  • $\begingroup$ @PaŭloEbermann: Nit-pick, but if reduced round attacks are relevant, if found at least one against 2 round Keccak: naya.plasencia.free.fr/Maria/papers/Keccak_differential.pdf $\endgroup$ – Henrick Hellström May 21 '13 at 8:39
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    $\begingroup$ @HenrickHellström So you are saying we should simply write "None" here, or that we should add the attacks for Keccak too? I wanted to do a minimal change which still is correct. $\endgroup$ – Paŭlo Ebermann May 21 '13 at 9:12
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    $\begingroup$ @Paŭlo Ebermann: What about a separate column for the best reduced-round attacks? $\endgroup$ – fgrieu May 21 '13 at 11:13

No. The wikipedia article is in my honest opinion misrepresenting this article on a reduced round attack on the SHA-2 family of hashes.

Although these attacks improve upon the existing reduced round SHA-2 attacks, they do not threaten the security of the full SHA-2 family.

In other words, no collisions have been found in any of the SHA-2 hashes.

The numbers that the are shown in the table mean different things for SHA-1 and SHA-2. In the case of SHA-1, the theoretical attack finds a collision in the actual SHA-1 algorithm. In the case of SHA-2, the collision is found in a modified algorithm with only 24 of the normal 64/80 rounds. In practice, this means that the best collision attack against SHA-256 still has the theoretical upper bound of $2^{128}$ complexity, and the best collision attack against SHA-512 a $2^{256}$ complexity.


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