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**2006/039**

**Title:**

Two-Round AES Differentials

**Authors:**
Joan Daemen, Vincent Rijmen

**Abstract:**

In this paper we study the probability of differentials and

characteristics over 2 rounds of the AES with the objective to

understand how the components of the AES round transformation

interact.

We extend and correct the analysis of the differential properties

of the multiplicative inverse in GF(2^n). We show that AES has characteristics with a

fixed-key probability that is many times larger than the EDP. For

instance, in the case of 2-round AES, we measured factors up to

2^{100}.

We study the number of characteristics with EDP >0 whose

probability adds up to the probability of a differential and

derive formulas that allow to produce a close estimate of this

number for any differential. We show how the properties discovered

in our study can be used to explain the values of the

differentials with the largest EDP values and to construct new

distinguishers using truncated differentials.

**ePrint:**
https://eprint.iacr.org/2006/039

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