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Hacking Cryptographic Protocols with Advanced Variational Quantum Attacks

Borja Aizpurua, Pablo Bermejo, Josu Etxezarreta Martinez, Roman Orus

TL;DR

This paper advances cryptanalytic capability on Noisy Intermediate-Scale Quantum (NISQ) devices by developing an improved Variational Quantum Attack Algorithm (VQAA) that uses fewer qubits and shallower circuits through non-orthogonal encoding and classical pre/post-processing. It demonstrates that, for symmetric ciphers such as S-DES, S-AES, and Blowfish, the attack achieves substantial reductions in iterations and runtime compared with brute-force, with 100% success in the tested cases, and shows scalability to broader cryptographic tasks including asymmetric protocols and hash functions. The key innovations include measuring the key register prior to encryption, representing multiple classical bits per qubit, a Hamming-distance cost, and a VQC ansatz with multiple layers plus coordinate transformations to mitigate barren plateaus. Collectively, these results indicate a meaningful step toward assessing the vulnerability of classical cryptographic protocols to quantum-powered attacks on NISQ hardware, while highlighting the ongoing need for quantum-safe standards as hardware scales. The work provides a foundation for future research in quantum cybersecurity, including the potential application to larger key sizes and real-device experiments.

Abstract

Here we introduce an improved approach to Variational Quantum Attack Algorithms (VQAA) on crytographic protocols. Our methods provide robust quantum attacks to well-known cryptographic algorithms, more efficiently and with remarkably fewer qubits than previous approaches. We implement simulations of our attacks for symmetric-key protocols such as S-DES, S-AES and Blowfish. For instance, we show how our attack allows a classical simulation of a small 8-qubit quantum computer to find the secret key of one 32-bit Blowfish instance with 24 times fewer number of iterations than a brute-force attack. Our work also shows improvements in attack success rates for lightweight ciphers such as S-DES and S-AES. Further applications beyond symmetric-key cryptography are also discussed, including asymmetric-key protocols and hash functions. In addition, we also comment on potential future improvements of our methods. Our results bring one step closer assessing the vulnerability of large-size classical cryptographic protocols with Noisy Intermediate-Scale Quantum (NISQ) devices, and set the stage for future research in quantum cybersecurity.

Hacking Cryptographic Protocols with Advanced Variational Quantum Attacks

TL;DR

This paper advances cryptanalytic capability on Noisy Intermediate-Scale Quantum (NISQ) devices by developing an improved Variational Quantum Attack Algorithm (VQAA) that uses fewer qubits and shallower circuits through non-orthogonal encoding and classical pre/post-processing. It demonstrates that, for symmetric ciphers such as S-DES, S-AES, and Blowfish, the attack achieves substantial reductions in iterations and runtime compared with brute-force, with 100% success in the tested cases, and shows scalability to broader cryptographic tasks including asymmetric protocols and hash functions. The key innovations include measuring the key register prior to encryption, representing multiple classical bits per qubit, a Hamming-distance cost, and a VQC ansatz with multiple layers plus coordinate transformations to mitigate barren plateaus. Collectively, these results indicate a meaningful step toward assessing the vulnerability of classical cryptographic protocols to quantum-powered attacks on NISQ hardware, while highlighting the ongoing need for quantum-safe standards as hardware scales. The work provides a foundation for future research in quantum cybersecurity, including the potential application to larger key sizes and real-device experiments.

Abstract

Here we introduce an improved approach to Variational Quantum Attack Algorithms (VQAA) on crytographic protocols. Our methods provide robust quantum attacks to well-known cryptographic algorithms, more efficiently and with remarkably fewer qubits than previous approaches. We implement simulations of our attacks for symmetric-key protocols such as S-DES, S-AES and Blowfish. For instance, we show how our attack allows a classical simulation of a small 8-qubit quantum computer to find the secret key of one 32-bit Blowfish instance with 24 times fewer number of iterations than a brute-force attack. Our work also shows improvements in attack success rates for lightweight ciphers such as S-DES and S-AES. Further applications beyond symmetric-key cryptography are also discussed, including asymmetric-key protocols and hash functions. In addition, we also comment on potential future improvements of our methods. Our results bring one step closer assessing the vulnerability of large-size classical cryptographic protocols with Noisy Intermediate-Scale Quantum (NISQ) devices, and set the stage for future research in quantum cybersecurity.
Paper Structure (18 sections, 20 equations, 8 figures, 1 table)

This paper contains 18 sections, 20 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methodology
  3. Variational Quantum Attack Algorithm (VQAA) with Fewer Qubits
  4. Original VQAA
  5. Improved VQAA
  6. Non-Orthogonal Encoding
  7. Cost Function: Hamming Distance
  8. Variational Quantum Circuit Ansatz
  9. Coordinate Transformations for Classical Optimizations
  10. Results for Symmetric-Key Ciphers
  11. Simplified-Data Encryption Standard (S-DES)
  12. Simplified Advanced Encryption Standard (S-AES)
  13. Blowfish
  14. Beyond Symmetric-Key Protocols
  15. Asymmetric-Key Cryptographic Protocols
  16. ...and 3 more sections

Figures (8)

  • Figure 1: [Color online] Quantum circuits for (a) the original, and (b) improved VQAA algorithms, as described in the main text. Single lines correspond to qubits, and double lines correspond to classical bits. The part that runs on a quantum computer is the one inside the shaded red boxes. The improved circuit in (b) uses fewer qubits, fewer quantum gates, a big part of it is entirely classical, and produces exactly the same outcome as the original circuit in (a), which is way more expensive in terms of resources.
  • Figure 2: [Color online] The four configurations of two classical bits are mapped to four maximally close to orthogonal
  • Figure 3: [Color online] Variational Quantum Circuit (VQC) ansatz with a single layer, designed for the Simplified-DES encryption scheme. This circuit uses 5 qubits to encode a 10-bit key, demonstrating the encoding efficiency through non-orthogonal state representation. The configuration includes single-qubit unitary gates $U(\theta, \varphi, \lambda)$ for arbitrary rotations, complemented by a strategic arrangement of CNOT gates to enhance entanglement and optimize key space exploration.
  • Figure 4: [Color online] Comparison of the average number of iterations required to find the correct key in S-DES, using different methods: classical brute force, Original VQAA, and three different Enhanced VQAA methods (without and with coordinate transformations). The $x$-axis represents the cumulative index of simulation runs, each with different plaintexts and keys. The $y$-axis is the average number of iterations (measurements or key trials) that took to recover the correct key.
  • Figure 5: [Color online] Comparison of the average number of iterations required to find the key using the Enhanced VQAA and classical Brute-force Attack against S-AES. The $x$-axis represents the cumulative index of simulation runs, each with different plaintexts and keys. The $y$-axis is the average number of iterations (measurements or key trials) it takes to recover the key.
  • ...and 3 more figures