  As the building block in symmetric cryptography, designing Boolean functions
satisfying multiple properties is an important problem in sequence ciphers,
block ciphers, and hash functions. However, the search of $n$-variable Boolean
functions fulfilling global cryptographic constraints is computationally hard
due to the super-exponential size $\mathcal{O}(2^{2^n})$ of the space. Here, we
introduce a codification of the cryptographically relevant constraints in the
ground state of an Ising Hamiltonian, allowing us to naturally encode it in a
quantum annealer, which seems to provide a quantum speedup. Additionally, we
benchmark small $n$ cases in a D-Wave machine, showing its capacity of devising
bent functions, the most relevant set of cryptographic Boolean functions. We
have complemented it with local search and chain repair to improve the D-Wave
quantum annealer performance related to the low connectivity. This work shows
how to codify super-exponential cryptographic problems into quantum annealers
and paves the way for reaching quantum supremacy with an adequately designed
chip.
