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

Mateusz Leśniak, Michał Wroński

TL;DR

This work investigates privacy for quantum annealing by challenging Spin Reversal Transformations (SRT), a proposed privacy method for Ising/QUBO problems in cloud quantum computing. It shows that when the outsourced optimization encodes a cryptanalytic attack, specifically an algebraic attack on the $E_0$ cipher, the original problem can be recovered from the transformed Ising instance, effectively breaking confidentiality. The authors formulate a parameterized attack pipeline, leveraging an oracle to build a parameterized Ising model, and demonstrate the attack on both a scaled-down and full $E_0$ instance, including resource estimates (e.g., $N=2728$ variables and $20598$ non-zero coefficients in the final QUBO). The results underscore a practical vulnerability of SRT-based privacy and motivate the development of more robust privacy-preserving mechanisms for quantum cloud computing, potentially favoring local computation or alternative cryptographic protections. The work provides concrete steps, from algebraic-to-QUBO translation to keystream recovery, highlighting the interplay between cryptanalysis and quantum optimization privacy.

Abstract

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.

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

TL;DR

This work investigates privacy for quantum annealing by challenging Spin Reversal Transformations (SRT), a proposed privacy method for Ising/QUBO problems in cloud quantum computing. It shows that when the outsourced optimization encodes a cryptanalytic attack, specifically an algebraic attack on the cipher, the original problem can be recovered from the transformed Ising instance, effectively breaking confidentiality. The authors formulate a parameterized attack pipeline, leveraging an oracle to build a parameterized Ising model, and demonstrate the attack on both a scaled-down and full instance, including resource estimates (e.g., variables and non-zero coefficients in the final QUBO). The results underscore a practical vulnerability of SRT-based privacy and motivate the development of more robust privacy-preserving mechanisms for quantum cloud computing, potentially favoring local computation or alternative cryptographic protections. The work provides concrete steps, from algebraic-to-QUBO translation to keystream recovery, highlighting the interplay between cryptanalysis and quantum optimization privacy.

Abstract

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 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.
Paper Structure (16 sections, 21 equations, 2 figures, 1 table)

This paper contains 16 sections, 21 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Background
  3. Quantum cloud services and privacy
  4. A description of the models used
  5. Spin Reversal Transformation in detail
  6. Description of the algorithm
  7. Details of the proposed attack
  8. The problem for the $E_0$ cipher
  9. From algebraic attack to quantum optimization
  10. How to identify the problem and parameterize it?
  11. Executing the attack, the most straightforward phase
  12. A practical example of the proposed attack
  13. Example parameterization
  14. An illustrative attack on a scaled-down instance
  15. Attack on the full version of the $E_0$ cipher
  16. ...and 1 more sections

Figures (2)

  • Figure 1: Data flow considered.
  • Figure 2: Key recovered as a result of the experiment.