Grunnleggende konsepter
This paper introduces efficient MILP-based models for representing linear and non-linear layers of block ciphers, enabling the automatic discovery of differential and impossible differential propagations.
Sammendrag
The paper presents the following key insights and contributions:
Modeling Linear and Non-linear Layers:
Greedy Random-Tiebreaker Algorithm: A novel algorithm that randomly selects inequalities from the outcomes of the greedy algorithm, improving the minimum number of inequalities for modeling 4-bit SBoxes compared to existing results.
Subset Addition Approach: A new algorithm that generates new inequalities by adding k-subsets of existing inequalities, leading to a more optimal subset of inequalities for modeling 4-bit, 5-bit, and 6-bit SBoxes.
New XOR Model: An efficient model for representing the linear layer using XOR operations, outperforming existing models in terms of computational efficiency.
Automatic Differential and Impossible Differential Searching Tool:
The authors developed an MILP-based tool that, given the round function specification of an SPN block cipher, generates a MILP model to discover differential characteristics that minimize the number of active SBoxes, as well as impossible differential characteristics.
The tool was successfully applied to five lightweight block ciphers: Lilliput, GIFT64, SKINNY64, Klein, and MIBS.
The paper demonstrates significant improvements in the minimum number of inequalities required to model SBoxes compared to existing techniques, as well as the efficiency of the automatic tool for finding differential and impossible differential propagations in block ciphers.