> From: Edward Ned Harvey (lopser)
> Sent: Saturday, August 17, 2013 4:53 PM
> 
> There's a specific question I wanted to look up.  I seem to recall, if you 
> want a
> block cipher to withstand 2^128 operations, you actually need 256 bits in the
> key.  I'm looking for clarification, if I'm remembering correctly, or not.  
> Sanity
> check.

I found my book and looked it up.  The answer is:

"Most modern block ciphers have a 128-bit block size, but they operate on 
32-bit words.  They build the encryption function from many 32-bit operations.  
This has proved to be a very successful method, but it has one side effect.  It 
is rather hard to build an odd permutation from small operations; as a result, 
virtually all block ciphers only generate even permutations."

"This [] has no practical significance whatsoever."

So, the even/odd permutation thing is a completely unrelated red herring.  The 
important question is regarding key length:

"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 sometimes 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."

In other words, if you want 128 bits of security, use a 256 bit key.  
Uncrackable by an international superpower within a lifetime.

If you use a 128 bit key, you should assume it's crackable in 2^64 operations, 
which can be achieved by a schmo with a laptop.  Maybe not in reality, maybe 
not in every situation, but take it as a baseline assumption.
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