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As the building block in symmetric cryptography, designing Boolean functionssatisfying multiple properties is an important problem in sequence ciphers,block ciphers, and hash functions. However, the search of $n$-variable Booleanfunctions fulfilling global cryptographic constraints is computationally harddue to the super-exponential size $\mathcal{O}(2^{2^n})$ of the space. Here, weintroduce a codification of the cryptographically relevant constraints in theground state of an Ising Hamiltonian, allowing us to naturally encode it in aquantum annealer, which seems to provide a quantum speedup. Additionally, webenchmark small $n$ cases in a D-Wave machine, showing its capacity of devisingbent functions, the most relevant set of cryptographic Boolean functions. Wehave complemented it with local search and chain repair to improve the D-Wavequantum annealer performance related to the low connectivity. This work showshow to codify super-exponential cryptographic problems into quantum annealersand paves the way for reaching quantum supremacy with an adequately designedchip.

Quantum computing cryptography: Finding cryptographic Boolean functions with quantum annealing by a 2000 qubit D-wave quantum computer