On 2013-08-17 at 20:52 +0000, Edward Ned Harvey (lopser) wrote:
> This is separate from and not to be confused with the birthday attack
> - wherein you only need 2^128 operations to produce an expected
> collision on a 256 bit hash function.

Skimmed past this before.

Quoting from the aforementioned section 3.5.7 (one paragraph should meet
"fair use" citation standards for copyright purposes):

  "A 128-bit key would be great, except for one problem: collision
  attacks.  Time and time again, we find systems that can be attacked --
  at least theoretically, if not practically -- by a birthday attack or
  a meet-in-the-middle attack.  We know these attacks exist.  Sometimes
  designers just ignore them, and sometime they think they are safe, but
  somebody finds a new, clever way of using them.  Most block cipher
  modes allow meet-in-the-middle attacks of some form.  We've had enough
  of this race, so here is our recommendation: For a security level of
  𝑛 bits, every cryptographic value should be at least 2𝑛 bits long."

So, not just for hash functions.

-Phil

PS: if '𝑛' is not rendering for you: 0x1D45B, "mathematical italic small n"
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