June 11th, 2013, 10:52 AM

Differential cryptanalysis, SPN, sboxes selection help!!!
Hi guys, I'm contacting you because I'm trying to solve a differential cryptanalysis exercise, in which they give me the 16 values in hexa of the sbox. I'm required to construct the difference distribution table (which I've already achieved), and as a second question, they ask me to "find a good differential characteristic of 3 rounds".
I don't really know how to answer about a good differential characteristic. I guess that by observing the resulting difference distribution table, one must choose those combinations of input differences and output differences of HIGHEST probability.
To study this, I'm following this paper: http://www@engr@mun@ca/~howard/PAPERS/ldc_tutorial.pdf (change "@" for "."). From page 19, we have there Differential Cryptanalysis. The sboxes selected are these:
S12: ∆X = B > ∆Y = 2 with probability 8/16
S23: ∆X = 4 > ∆Y = 6 with probability 6/16
S32: ∆X = 2 > ∆Y = 5 with probability 6/16
S33: ∆X = 2 > ∆Y = 5 with probability 6/16
Questions:
01) Once you obtained the difference distribution table, how do you find a "good differential characteristic of 3 rounds"?
02) In the paper...it seems to have chosen arbitrary in page 23 the sboxes S12, S23, S32 and S33. Why are these the sboxes selected? What's the criterion for selection?
03) Related to the precedent question: the author arbitrary decided that, for instance, the sbox S12[/B] was going to be the one with the values ∆X = B > ∆Y = 2. Why didn't the author decided instead, for example, that the sbox S14[/B] would be the one with the values ∆X = B > ∆Y = 2.
As you can see, I don't get at all the criteria for selecting the sboxes y de decisions about assigning certain ∆X and ∆Y to the sboxes.
Could you experts be so kind to give me a hand in this? If it's better to discuss this with a particular example, I could post the difference distribution table to clarify my questions.
Thanks in advance!
G.