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

TL;DR

This paper demonstrates encoding the complex problem of designing cryptographically strong Boolean functions into a quantum annealer, showing potential for quantum speedup and paving the way toward quantum supremacy in cryptography.

Contribution

It introduces a novel method to encode cryptographic Boolean function design problems into Ising Hamiltonians for quantum annealing, enabling exploration of super-exponential search spaces.

Findings

D-Wave quantum annealer successfully designed bent functions for small n

Local search and chain repair improved quantum annealer performance

Benchmark results indicate potential for quantum speedup in cryptographic function design

Abstract

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.