Quantum computing cryptography: Unveiling cryptographic Boolean functions with quantum annealing [article]

Feng Hu, Lucas Lamata, Mikel Sanz, Xi Chen, Xingyuan Chen, Chao Wang,, Enrique Solano
2018 arXiv   pre-print
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 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
more » ... s 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.
arXiv:1806.08706v2 fatcat:japqew5hyfgchjpfb56ujrqacm