Information Security Stack Exchange is a question and answer site for information security professionals. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I was reading some e-books to understand the basics of block ciphers and how it works in AES. As i understood, Permutation plays a big part in AES and Block Ciphers,

Here is what i understood by permutation,

A permutation is an ordered arrangement of the elements of some set S
Let S = {a, b, c}
c, b, a is a permutation of S
b, c, a is a different permutation of S

Now, There was a power-point slide on Block ciphers i was reading and according to which,

enter image description here

Why did they call it a permutation, Could anyone please explain ?

share|improve this question
Think "shuffling" of the same deck of cards, and how many variations in their order there might be - that's permutations. I.e. multiple arrangements of the same set of elements. The right image is not a permutation, because its function of x f(x) adds and removes from to the topmost set. In our previous example of a deck of cards, you'd have to remove some, and replace them with cards from another deck to end up with the same number of cards that are not a permutation of a complete deck of cards. This is however not really a question on scope for Information Security. ;) – TildalWave Sep 24 '13 at 23:56
up vote 2 down vote accepted

In the example you have given S has a,b and c. It's permutation must have exactly the same number of elements of the same type. One a, one b and one c. In total it has to have 3 elements and order of elements can be different.

In the second example, x has these values:

  • a 00
  • a 01
  • a 10
  • a 11

It's permutation, f(x) can have these values with the same count. So the left f(x) is a permutation because it has a 00, a 01, a 10 and a 11. Right f(x) is NOT, because it has 2x 11, a 01, and a 10 which is different than the x values.

share|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.