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Searching for an Efficient System of Equations Defining the AES Sbox for the QUBO Problem

Burek Elżbieta, Mańk Krzysztof, Wroński Michał

Journal of Telecommunications and Information Technology

2023

nr 4

30--37

The time complexity of solving the QUBO problem depends mainly on the number of logical variables in the problem. This paper focuses mainly on finding a system of equations that uniquely defines the Sbox of the AES cipher and simultaneously allows us to obtain the smallest known optimization problem in the QUBO form for the algebraic attack on the AES cipher. A novel method of searching for an efficient system of equations using linear-feedback shift registers has been presented in order to perform that task efficiently. Transformation of the AES cipher to the QUBO problem, using the identified efficient system, is presented in this paper as well. This method allows us to reduce the target QUBO problem for AES- 128 by almost 500 logical variables, compared to our previous results, and allows us to perform the algebraic attack using quantum annealing four times faster.

Speeding Up Minimum Distance Randomness Tests

Mańk Krzysztof

Journal of Telecommunications and Information Technology

2022

nr 2

99--109

Randomness testing is one of the essential and easiest tools for the evaluation of the features and quality of cryptographic primitives. The faster we can test, the greater volumes of data can be checked and evaluated and, hence, more detailed analyses may be conducted. This paper presents a method that significantly reduces the number of distances calculated in the minimum distance, Bickel-Breiman, and m nearest points tests. By introducing a probabilistic approach with an arbitrarily low probability of failure, the number of calculated distances proportional to the number of required distances and independent of the number of points was achieved. In the well-known Diehard’s minimum distance and 3D spheres tests, the quantity of computations achieved is reduced by the factors of 394 and 771, respectively.