AES 256 key and anti-key

Hi,

I have a simple question regarding AES with 256 bits key.

It is known that the input and output blocks for this algorithm is 128
bits.
Given a 256 bit key, K, a crypto-pair is defined as (a,b) where 'a' is
a 128 number and 'b' is a 128 bit number and b=AES(K,a).
There are (2**128)! / ((2**128-2)! * 2) posibble complete sets which
cover all the alpha-bet of 'a'. which is less than 2**256 (by more
than half). On the other hand, there are 2**256 different keys.

This means that there are on avarage 2 keys for every complete a set
of all crypto-pairs.your key K and the anti-key K' :)


-majorsoul
.

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