Privacy for Quantum Annealing. Attack on Spin Reversal Transformations in the case of cryptanalysis

This paper demonstrates that applying spin reversal transformations (SRT), commonly known as a sufficient method for privacy enhancement in problems solved using quantum annealing, does not guarantee privacy for all possible cases. We show how to recover the original problem from the Ising problem obtained using SRT when the resulting problem in Ising form represents the algebraic attack on the $E_0$ stream cipher. A small example illustrates how to retrieve the original problem from that transformed by SRT. Moreover, we show that our method is efficient also for full-scale problems.