Abstract
In this paper we introduce new algorithms that, based only on the independent round keys assumption, allow to practically compute the exact expected differential probability of (truncated) differentials and the expected linear potential of (multidimensional) linear hulls. That is, we can compute the exact sum of the probability or the potential of all characteristics that follow a given activity pattern. We apply our algorithms to various recent SPN ciphers and discuss the results.
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Notes
- 1.
It is also known as Markov cipher assumptions.
- 2.
In [LMM91], the authors used the term Markov cipher assumption.
- 3.
\(\mathrm {hw}(\delta _i)\) is the Hamming weight of \(\delta _i\) and it is equal to the number of active S-boxes in the i-th round.
- 4.
For \(x, y \in \mathbb {F}_2^m\), we use \(x \preceq y\) to denote that for all i with \(0\le i <m\), \(x[i] \le y[i]\).
- 5.
Due to the structure of the Midori cipher, it is enough to check for representative S-boxes of Affine equivalence classes together with a bijective \(4\times 4\) matrix in the output of S-box, i.e., \(302 \times 20160 \approx 2^{22.5}\) S-boxes.
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Acknowledgments
The authors gratefully thank Arnab Roy for his comments and suggestions in preparing the final draft of this paper. This work was partially supported by the DFG (LE 3372/5-1).
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Eichlseder, M., Leander, G., Rasoolzadeh, S. (2020). Computing Expected Differential Probability of (Truncated) Differentials and Expected Linear Potential of (Multidimensional) Linear Hulls in SPN Block Ciphers. In: Bhargavan, K., Oswald, E., Prabhakaran, M. (eds) Progress in Cryptology – INDOCRYPT 2020. INDOCRYPT 2020. Lecture Notes in Computer Science(), vol 12578. Springer, Cham. https://doi.org/10.1007/978-3-030-65277-7_16
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