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Improving the upper bound on the maximum differential and the maximum linear hull probability for SPN structures and AES. (English) Zbl 1254.94040

Johansson, Thomas (ed.), Fast software encryption. 10th international workshop, FSE 2003, Lund, Sweden, February 24–26, 2003. Revised papers. Berlin: Springer (ISBN 3-540-20449-0/pbk). Lect. Notes Comput. Sci. 2887, 247-260 (2003).
Summary: We present a new method for upper bounding the maximum differential probability and the maximum linear hull probability for 2 rounds of SPN structures. Our upper bound can be computed for any value of the branch number of the linear transformation and by incorporating the distribution of differential probability values and linear probability values for S-box. On application to AES, we obtain that the maximum differential probability and the maximum linear hull probability for 4 rounds of AES are bounded by \(1.144 \times 2^{-111}\) and \(1.075 \times 2^{-106}\), respectively.
For the entire collection see [Zbl 1029.00054].

MSC:

94A60 Cryptography
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