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In this paper, we propose a new method for drawing a cryptographically strong substitution box using the Lorenz system and quantum genetic algorithm techniques. We used the chaotic function to generate an initial random sequence of bits and the quantum crossover to provide a new and improved substitution box with increased non-linearity. The aim of the proposed algorithm was to generate a strong and secure substitution box that can be utilized in symmetric cryptosystems. The use of chaotic Boolean functions, genetic algorithm techniques, and the quantum crossover helped achieve this goal, and statistical tests further confirmed the randomness and efficiency of the generated substitution box. The results of the statistical test suite showed that the substitution box produced by the proposed algorithm is a “pass” in terms of randomness and has strong cryptographic properties. The tests include a frequency (monobit) test, a frequency test within a block, a linear complexity test, an approximate entropy test, and a cumulative sums test among others. The p-values obtained in the tests indicate that the randomness of the generated substitution box meets the requirements of a cryptographically secure substitution box.