Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE International Conference on Quantum Computing and Engineering (QCE)

A Quantum Circuit to Execute a Key-Recovery Attack Against the DES and 3DES Block Ciphers

Simone Perriello, Alessandro Barenghi, Gerardo Pelosi

Published Sep 15, 2024• 1 citation
Publisher

Abstract

Quantum computing enabled cryptanalytic techniques are able to concretely reduce the security margin of existing cryptographic primitives. While this reduction is only polynomial for symmetric cryptosystems, it still provides a reduction in their security margin. In this work, we propose a detailed quantum circuit designed to cryptanalyze both the Data Encryption Standard (DES) cryptosystem, and its successor Triple-DES (3DES), currently standardized in ISO/IEC 18033–3, and still widely employed in satellite data and bank card encryption. To do so, we introduce the first quantum circuit implementation of the 8 substitution tables (a.k.a. S-boxes), applying a bitslicing strategy, which is currently the most efficient classical combinatorial circuit design in terms of number of two inputs Boolean gates. Secondly, we present the complete quantum circuits required to attack both DES and 3DES leveraging Grover's algorithm. We provide finite regime, closed form equations, delineating the circuits complexities in terms of the number of qubits, gates, depth and number of qubits multiplied by depth. The complexity analysis is based on two distinct gate sets: a NOT-CNOT-Toffoli (NCT) extended with the Hadamard gate; and the fault-tolerant Clifford+T. Finally, akin to the classical attack to the 3DES, we introduce a meet-in-the-middle strategy relying on an exponential amount of Quantum Random Access Memory. Our findings show that the 3DES with keying option 2, the most widely employed variant of 3DES, can be attacked with a circuit depth of approximately$2^{67}$and less than a thousand qubits. This is close to the$2^{64}$value suggested by NIST for the depth achievable sequentially by a single quantum computer in a decade. Our technique can be further sped up parallelizing the approach onto multiple devices, pointing to the practicality of cryptanalyzing 3DES in such a scenario.

DOI
10.1109/qce60285.2024.00011

Related papers

Constructing quantum circuits for Grover key search in MK-3 featuring 16-bit S-boxes

Haoyu Liao, Qing-bin Luo, Yuanmeng Zheng +2 more

Abstract Quantum computing poses a significant threat to modern cryptosystems, prompting nations to initiate the development of next-generation cryptographic algorithms where quantum security assessment constitutes a critical task. In this work, we present the first complete quantum attack circuit construction and security evaluation of quantum resistance for the authenticated encryption algorithm MK-3, which features 16-bit S-boxes. Firstly, we achieve breakthroughs in finite field arithmetic. The arrangement method of Toffoli gates in the subfield $$F_{2^4}$$ F 2 4 enables two types of optimized $$F_{2^8}$$ F 2 8 multiplication circuits to reduce DW-cost by at least 50%. For $$F_{2^8}$$ F 2 8 inversion, by proposing a new intermediate state uncomputing technique, the DW-cost of the inversion circuit is reduced by at least 40% compared with existing solutions. This can also be used to optimize the quantum circuits of block ciphers such as AES and SM4. Secondly, we propose three types of quantum circuits for MK-3’s 16-bit S-box. The basic circuit reduces multiplicative bit operations to 115, representing at least 20% reduction. We propose a more compact S-box structure, reducing the number of circuit qubits for two types of S-boxes from 52 to 40. Finally, we implement full-algorithm quantum attacks and conduct security evaluations for MK-3. Complete quantum circuits supporting 128-bit and 256-bit keys are constructed, enabling Grover key search attacks. Security assessments confirm the 128-bit version meets NIST Security Category 1 (with reasonable inference of achieving Category 2), while the 256-bit version satisfies the highest Category 5 standards, demonstrating resistance against large-scale quantum computing attacks. This work achieves the first quantum circuit implementation for 16-bit S-boxes and provides critical evaluation benchmarks for post-quantum cryptography standardization.

Cybersecurity•Jun 17, 2026•0 citations

A Complete Quantum Circuit to Solve the Information Set Decoding Problem

Simone Perriello, Alessandro Barenghi, Gerardo Pelosi

Providing strong security margins against cryptanalytic attackers equipped with quantum computers is a major research direction fostered by the US National Institute of Standards and Technology (NIST) Post-quantum Cryptography Standardization process. Among the viable candidates, code-based asymmetric cryptosystems are one of the prominent approaches. In this work, we propose the first fully detailed quantum circuit to compute the solution to the Information Set Decoding problem, the main cryptanalytic tool against such cryptosystems. We evaluate the cryptanalytic effort with our circuit design on actual parameters from cryptosystems admitted to the final stage of the NIST standardization process and compare it with the previous conservative asymptotic estimates. We show that the actual computational effort of our solution is smaller than the one estimated via asymptotics by a factor of 24. We also perform a comparison of our results with the quantum-computational effort of breaking the AES cipher, following the guidelines of the US NIST in evaluating the security of the ciphers. To do this, we translate our design on gates of the Clifford+T gate set only, one of the most promising candidate for fault-tolerant quantum computation, and report that the parameter choices for Classic McEliece and BIKE, two candidates admitted to the final round of the NIST standardization process provide an adequate security margin with respect to our ISD solution technique.

IEEE International Conference on Quantum Computing and Engineering (QCE)•Oct 1, 2021•16 citations

Quantum Circuit Implementation and Resource Analysis for Triple Data Encryption Standard (DES) (Triple-DES)

Gyeongju Song, Seyoung Yoon, Hwajeong Seo

In this paper, various types of quantum circuits for DES components are proposed to analyze the trade-offs in quantum resources for both DES and TDES block ciphers. Specifically, multiple optimized structures within the DES framework are devised, and by integrating different elements from each type, 34 possible configurations for the DES block cipher are generated. The required quantum resources for these configurations are then estimated, identifying not only qubit-optimized and depth-optimized circuits but also those achieving a balanced trade-off between qubit and circuit depth. Building on these optimized DES designs, TDES circuits are constructed, and the corresponding cost of a Grover-based attack on the TDES is estimated.

Mathematics•Apr 2, 2025•1 citation

Quantum cryptanalysis of SPN ciphers with known plaintext

Uroosa Kiran, Aneela Safdar, Saif Ullah Khalid +2 more

Key recovery attack on SPN ciphers such as AES is NP hard in complexity. Previous studies have estimated the quantum resources required for implementing Grover’s key search for AES, but these are largely theoretical in nature. The key challenges to implement Grover’s algorithm on current quantum hardware include the number of available qubits, noise, and decoherence. However, the rapid advancement of hardware has brought us closer to practical realization for the cryptanalysis of light-weight SPN ciphers. This study presents an efficient quantum circuit implementation of Mini-AES, a 16-bit variant of AES, employing standard CNOT and Toffoli gates. To the best of our knowledge, our work provides the first complete quantum implementations of all core Mini-AES components for the quantum oracle. The effects of noise are emulated for each module of the quantum oracle and quantified. Furthermore, Grover’s algorithm is applied to Mini-AES to perform successful key recovery through a known-plaintext attack, demonstrating significant amplitude amplification while using near-optimal Grover’s iterations, thereby reducing the total quantum volume. The optimal Grover’s iterations have been obtained empirically as well as validated with finite-shot analysis. Notably, the application of Grover’s algorithm reveals key clustering behavior in Mini-AES, which has been corroborated through classical simulation.

npj Quantum Information•Apr 1, 2026•0 citations

Quantum Implementation of S‐Boxes Based on Polynomial Evaluation

Doyoung Chung, Seungkwang Lee

ABSTRACT Quantum computing environments make block ciphers susceptible to exhaustive key search attacks utilizing Grover's algorithm. However, such quantum‐based attacks remain impractical unless the targeted cipher is directly implemented on a quantum platform. Moreover, their efficiency significantly depends on the quantum circuit design and optimization of the block cipher in question. The cost of a quantum circuit implementation is typically measured by two main metrics: the number of qubits and the circuit depth ( T ‐depth). For most block ciphers, the S‐box is the principal factor contributing to increased T ‐depth and additional qubit requirements. This paper presents a method for generating quantum circuits directly from lookup tables of S‐boxes applicable to arbitrary block ciphers. We illustrate our approach using quantum circuit implementations of the PRESENT and DES ciphers as practical examples. Our proposed method is expected to efficiently implement arbitrary S‐boxes by employing polynomial evaluation, thus balancing time–space complexity.

Electronics Letters•Jan 1, 2025•2 citations

Resource-Constrained Quantum Implementation and Analysis of Mini-AES Cipher

Syed Shahmir, Ghulam Murtaza, Elmahdi Bentafat +4 more

Quantum search algorithms, such as Grover's algorithm, will soon pose a threat to current encryption standards as quantum computing advances toward practical implementation. These algorithms rely on quantum circuits that map cryptographic algorithms into appropriate Hilbert spaces, thus linking algorithmic inputs and outputs through quantum superposition. However, implementing and testing such circuits on existing quantum simulators, such as Qiskit, encounters significant memory and computational bottlenecks that limit research progress. To address these simulation constraints, we present a resource-optimized quantum circuit implementation of a complete two-round Mini-AES encryption algorithm. Our approach systematically converts the cipher's algebraic structure using algebraic normal form (ANF) equations, mapping XOR operations to CNOT gates and AND operations to Toffoli gates. To reduce memory overhead, we implement an ancilla-reuse strategy utilizing mid-circuit measurements and resets. Additionally, we introduce an automated procedure that generates Qiskitcompatible quantum circuits for arbitrary S-boxes and cryptographic primitives, streamlining the development of quantum cryptanalysis implementations. Our implementation achieves full encryption and decryption in a quantum circuit with modest gate requirements that can be achieved by the current or near-future state of the art quantum computers. In addition, we provide system utilization metrics to validate our resource-constrained implementation. This compact and pedagogically accessible implementation establishes a practical foundation for quantum cryptanalysis research and post-quantum cryptographic analysis.

arXiv:2503.06566•International Conference on Quantum Communications, Networking, and Computing (QCNC)•Apr 6, 2026•0 citations
Quantum computing enabled cryptanalytic techniques are able to concretely reduce the security margin of existing cryptographic primitives. While this reduction is only polynomial for symmetric cryptosystems, it still provides a reduction in their security margin. In this work, we propose a detailed quantum circuit designed to cryptanalyze both the Data Encryption Standard (DES) cryptosystem, and its successor Triple-DES (3DES), currently standardized in ISO/IEC 18033–3, and still widely employed in satellite data and bank card encryption. To do so, we introduce the first quantum circuit implementation of the 8 substitution tables (a.k.a. S-boxes), applying a bitslicing strategy, which is currently the most efficient classical combinatorial circuit design in terms of number of two inputs Boolean gates. Secondly, we present the complete quantum circuits required to attack both DES and 3DES leveraging Grover's algorithm. We provide finite regime, closed form equations, delineating the circuits complexities in terms of the number of qubits, gates, depth and number of qubits multiplied by depth. The complexity analysis is based on two distinct gate sets: a NOT-CNOT-Toffoli (NCT) extended with the Hadamard gate; and the fault-tolerant Clifford+T. Finally, akin to the classical attack to the 3DES, we introduce a meet-in-the-middle strategy relying on an exponential amount of Quantum Random Access Memory. Our findings show that the 3DES with keying option 2, the most widely employed variant of 3DES, can be attacked with a circuit depth of approximately2672^{67}267and less than a thousand qubits. This is close to the2642^{64}264value suggested by NIST for the depth achievable sequentially by a single quantum computer in a decade. Our technique can be further sped up parallelizing the approach onto multiple devices, pointing to the practicality of cryptanalyzing 3DES in such a scenario.
Abstract Quantum computing poses a significant threat to modern cryptosystems, prompting nations to initiate the development of next-generation cryptographic algorithms where quantum security assessment constitutes a critical task. In this work, we present the first complete quantum attack circuit construction and security evaluation of quantum resistance for the authenticated encryption algorithm MK-3, which features 16-bit S-boxes. Firstly, we achieve breakthroughs in finite field arithmetic. The arrangement method of Toffoli gates in the subfield F24F_{2^4}F24​ F 2 4 enables two types of optimized F28F_{2^8}F28​ F 2 8 multiplication circuits to reduce DW-cost by at least 50%. For F28F_{2^8}F28​ F 2 8 inversion, by proposing a new intermediate state uncomputing technique, the DW-cost of the inversion circuit is reduced by at least 40% compared with existing solutions. This can also be used to optimize the quantum circuits of block ciphers such as AES and SM4. Secondly, we propose three types of quantum circuits for MK-3’s 16-bit S-box. The basic circuit reduces multiplicative bit operations to 115, representing at least 20% reduction. We propose a more compact S-box structure, reducing the number of circuit qubits for two types of S-boxes from 52 to 40. Finally, we implement full-algorithm quantum attacks and conduct security evaluations for MK-3. Complete quantum circuits supporting 128-bit and 256-bit keys are constructed, enabling Grover key search attacks. Security assessments confirm the 128-bit version meets NIST Security Category 1 (with reasonable inference of achieving Category 2), while the 256-bit version satisfies the highest Category 5 standards, demonstrating resistance against large-scale quantum computing attacks. This work achieves the first quantum circuit implementation for 16-bit S-boxes and provides critical evaluation benchmarks for post-quantum cryptography standardization.
Providing strong security margins against cryptanalytic attackers equipped with quantum computers is a major research direction fostered by the US National Institute of Standards and Technology (NIST) Post-quantum Cryptography Standardization process. Among the viable candidates, code-based asymmetric cryptosystems are one of the prominent approaches. In this work, we propose the first fully detailed quantum circuit to compute the solution to the Information Set Decoding problem, the main cryptanalytic tool against such cryptosystems. We evaluate the cryptanalytic effort with our circuit design on actual parameters from cryptosystems admitted to the final stage of the NIST standardization process and compare it with the previous conservative asymptotic estimates. We show that the actual computational effort of our solution is smaller than the one estimated via asymptotics by a factor of 24. We also perform a comparison of our results with the quantum-computational effort of breaking the AES cipher, following the guidelines of the US NIST in evaluating the security of the ciphers. To do this, we translate our design on gates of the Clifford+T gate set only, one of the most promising candidate for fault-tolerant quantum computation, and report that the parameter choices for Classic McEliece and BIKE, two candidates admitted to the final round of the NIST standardization process provide an adequate security margin with respect to our ISD solution technique.
In this paper, various types of quantum circuits for DES components are proposed to analyze the trade-offs in quantum resources for both DES and TDES block ciphers. Specifically, multiple optimized structures within the DES framework are devised, and by integrating different elements from each type, 34 possible configurations for the DES block cipher are generated. The required quantum resources for these configurations are then estimated, identifying not only qubit-optimized and depth-optimized circuits but also those achieving a balanced trade-off between qubit and circuit depth. Building on these optimized DES designs, TDES circuits are constructed, and the corresponding cost of a Grover-based attack on the TDES is estimated.
Key recovery attack on SPN ciphers such as AES is NP hard in complexity. Previous studies have estimated the quantum resources required for implementing Grover’s key search for AES, but these are largely theoretical in nature. The key challenges to implement Grover’s algorithm on current quantum hardware include the number of available qubits, noise, and decoherence. However, the rapid advancement of hardware has brought us closer to practical realization for the cryptanalysis of light-weight SPN ciphers. This study presents an efficient quantum circuit implementation of Mini-AES, a 16-bit variant of AES, employing standard CNOT and Toffoli gates. To the best of our knowledge, our work provides the first complete quantum implementations of all core Mini-AES components for the quantum oracle. The effects of noise are emulated for each module of the quantum oracle and quantified. Furthermore, Grover’s algorithm is applied to Mini-AES to perform successful key recovery through a known-plaintext attack, demonstrating significant amplitude amplification while using near-optimal Grover’s iterations, thereby reducing the total quantum volume. The optimal Grover’s iterations have been obtained empirically as well as validated with finite-shot analysis. Notably, the application of Grover’s algorithm reveals key clustering behavior in Mini-AES, which has been corroborated through classical simulation.
ABSTRACT Quantum computing environments make block ciphers susceptible to exhaustive key search attacks utilizing Grover's algorithm. However, such quantum‐based attacks remain impractical unless the targeted cipher is directly implemented on a quantum platform. Moreover, their efficiency significantly depends on the quantum circuit design and optimization of the block cipher in question. The cost of a quantum circuit implementation is typically measured by two main metrics: the number of qubits and the circuit depth ( T ‐depth). For most block ciphers, the S‐box is the principal factor contributing to increased T ‐depth and additional qubit requirements. This paper presents a method for generating quantum circuits directly from lookup tables of S‐boxes applicable to arbitrary block ciphers. We illustrate our approach using quantum circuit implementations of the PRESENT and DES ciphers as practical examples. Our proposed method is expected to efficiently implement arbitrary S‐boxes by employing polynomial evaluation, thus balancing time–space complexity.
Quantum search algorithms, such as Grover's algorithm, will soon pose a threat to current encryption standards as quantum computing advances toward practical implementation. These algorithms rely on quantum circuits that map cryptographic algorithms into appropriate Hilbert spaces, thus linking algorithmic inputs and outputs through quantum superposition. However, implementing and testing such circuits on existing quantum simulators, such as Qiskit, encounters significant memory and computational bottlenecks that limit research progress. To address these simulation constraints, we present a resource-optimized quantum circuit implementation of a complete two-round Mini-AES encryption algorithm. Our approach systematically converts the cipher's algebraic structure using algebraic normal form (ANF) equations, mapping XOR operations to CNOT gates and AND operations to Toffoli gates. To reduce memory overhead, we implement an ancilla-reuse strategy utilizing mid-circuit measurements and resets. Additionally, we introduce an automated procedure that generates Qiskitcompatible quantum circuits for arbitrary S-boxes and cryptographic primitives, streamlining the development of quantum cryptanalysis implementations. Our implementation achieves full encryption and decryption in a quantum circuit with modest gate requirements that can be achieved by the current or near-future state of the art quantum computers. In addition, we provide system utilization metrics to validate our resource-constrained implementation. This compact and pedagogically accessible implementation establishes a practical foundation for quantum cryptanalysis research and post-quantum cryptographic analysis.