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

Advances in Engineering Technology Research

Quantum Implementation of the SPARX Algorithm

Qi Zhao

Published May 15, 2026• 0 citations
Publisher

Abstract

The quantum implementation of SPARX, a lightweight ARX block cipher family, aims to address the security encryption requirements of the quantum internet. The SPARX algorithm utilizes three basic operations: modular addition, bit rotation, and XOR. Furthermore, modular addition is implemented using Toffoli gates, XOR using CNOT gates, and rotation operations are efficiently mapped to quantum register shifts. For three examples—SPARX-64/128, SPARX-128/128, and SPARX-128/256 ， quantum circuit architectures are designed, with a focus on optimizing the multi-round parallel execution ofthe ARX-Box and the quantum diffusion path of the linear layer, reducing qubit consumption and the number of gate operations The proposed implementation requires approximately 64 data bits + 128 key bits for the number of qubits , e.g. SPARX -64/128, and the circuit depth is controlled at the polynomial level, meeting the requirements of lightweight quantum devices. This research provides a feasible path for the quantum implementation of lightweight block ciphers, particularly suitable for encryption needs in resource-constrained quantum scenarios such as the quantum Internet of Things.

DOI
10.56028/aetr.16.1.1787.2026

Related papers

Grover on Korean Block Ciphers

Kyoungbae Jang, Seungju Choi, Hyeokdong Kwon +3 more

The Grover search algorithm reduces the security level of symmetric key cryptography with n-bit security level to O(2n/2). In order to evaluate the Grover search algorithm, the target block cipher should be efficiently implemented in quantum circuits. Recently, many research works evaluated required quantum resources of AES block ciphers by optimizing the expensive substitute layer. However, few works were devoted to the lightweight block ciphers, even though it is an active research area, nowadays. In this paper, we present optimized implementations of every Korean made lightweight block ciphers for quantum computers, which include HIGHT, CHAM, and LEA, and NSA made lightweight block ciphers, namely SPECK. Primitive operations for block ciphers, including addition, rotation, and exclusive-or, are finely optimized to achieve the optimal quantum circuit, in terms of qubits, Toffoli gate, CNOT gate, and X gate. To the best of our knowledge, this is the first implementation of ARX-based Korean lightweight block ciphers in quantum circuits.

Applied Sciences•Sep 14, 2020•34 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

Efficient quantum circuit implementation of the SM4 S-box

LIU JiaHong, Xiaoqing Tan, LI Ming +1 more

In recent years, the quantum circuit implementation in symmetric cryptography has attracted widespread attention. The SM4 block cipher algorithm is China's first commercial cipher standard and was accepted as an ISO/IEC international standard in 2021. S-box is the most complex component in the SM4 block cipher algorithm. This study investigates the quantum circuit implementation of the SM4 S-box. Based on the algebraic structure, using tower filed decomposition technology, the quantum circuit of the SM4 S-box is built. Based on the number of NCT gate sets, our quantum circuit requires 20 qubits, 52 Toffoli gates, 196 CNOT gates, and 13 X gates. The Toffoli depth of our circuit is 36. Compared with previous literature, the quantum circuit proposed herein requires fewer quantum resources.

Zhongguo kexue. Wulixue Lixue Tianwenxue•Dec 8, 2023•4 citations

Quantum Circuit Realization and Grover Cryptanalysis of the Hybrid ARX-SPN Cipher GFSPX

Ibrahim Ulgen, Hasan Ozgur Cildiroglu, Oğuz Yayla

The security of classical symmetric-key primitives is fundamentally challenged by the emergence of quantum computing, necessitating a rigorous evaluation of their post-quantum resilience. This paper presents a comprehensive quantum circuit realization and Grover cryptanalysis of GFSPX, a lightweight block cipher featuring a 64-bit data block and a 128-bit secret key. GFSPX utilizes a unique hybrid architecture that integrates a 4-branch generalized Feistel structure with both Addition-Rotation-XOR (ARX) and Substitution-Permutation Network (SPN) components. Our quantum implementation optimizes resource distribution by exploiting the inherent reversibility of the Feistel network and employing a compact ripple-carry adder for the ARX layers. The proposed architecture achieves a qubit-optimized footprint of 209 qubits with a baseline quantum cost of 32,498 and a circuit depth of 7,617. To evaluate the cipher's resistance against quantum adversaries, we construct a parallelized Grover oracle using three plaintext-ciphertext pairs to eliminate spurious matches. Our analysis reveals that the total quantum cost of a key-recovery attack on GFSPX is $1.12 \times 2^{159}$ quantum gates. Although this cost falls below the NIST Level 1 security threshold of $2^{170}$, the hybrid ARX-SPN design demonstrates a higher quantum attack resistance among other lightweight designs. These findings provide critical insights into the balance between classical efficiency and quantum resilience in next-generation cryptographic designs for resource-constrained environments.

quant-pharXiv:2605.27443•Physica Scripta•May 26, 2026•0 citations

Quantum circuit implementation and security analysis of IVLBC

Lang Ding, Qing-bin Luo, Yi Lv +3 more

Abstract Grover’s algorithm reduces the security level of the target cipher from n-bit to n/2-bit. To implement Grover’s algorithm, a quantum circuit capable of performing the target cipher operations must be constructed. In this paper, we propose a quantum circuit implementation scheme for the involutive lightweight block cipher (IVLBC) block cipher. We utilized the DORCIS tool to implement the quantum circuit for the S-box and applied Gaussian elimination to construct the quantum circuit for matrix multiplication. Subsequently, we evaluated the overall quantum resource consumption required for the implementation. Based on this, we performed a quantum attack on IVLBC using Grover’s algorithm, calculating the attack cost using the NCT gate library, and further analyzed its security. Finally, we conducted a comparative analysis of the classical attack complexity and quantum attack complexity of IVLBC, highlighting the potential of using quantum complexity as a standard for future security assessments.

Classical and Quantum Gravity•Mar 28, 2025•1 citation

Quantum implementaion of SM4 block cipher with less qubits

Qing-bin Luo, Qiang Li, Xiaoyu Li +3 more

Abstract SM4 cryptographic algorithm is a block cipher algorithm issued by China's state cryptographic administration and has become an international standard. we implement the quantum circuits of SM4 Block cipher by optimizing the number of qubits and the value of depth-times-width. When the S-box is implemented, four kind of improved quantum circuits of S-box are presented for different phases in SM4 based on composite field arithmetic. When optimizing the number of qubits, we implement the quantum circuit of SM4 by connecting the quantum subcircuits in series. The implemented quantum circuit of SM4 only uses 260 qubits, which is the least number of qubits used not only in implementing the SM4 quantum circuit, but also in implementing the block cipher algorithms with 8-bit S-box, 128-bit plaintext and 128-bit secret key. When optimizing the value of depth-times-width, we achieve it through parallel implementation. The trade-off quantum circuit uses a total of 288 quantum bits and the Toffoli depth is 1716. The depth-times-width is 494208, which is less than the existing best value 825792.

•Jun 29, 2023•2 citations
The quantum implementation of SPARX, a lightweight ARX block cipher family, aims to address the security encryption requirements of the quantum internet. The SPARX algorithm utilizes three basic operations: modular addition, bit rotation, and XOR. Furthermore, modular addition is implemented using Toffoli gates, XOR using CNOT gates, and rotation operations are efficiently mapped to quantum register shifts. For three examples—SPARX-64/128, SPARX-128/128, and SPARX-128/256 ， quantum circuit architectures are designed, with a focus on optimizing the multi-round parallel execution ofthe ARX-Box and the quantum diffusion path of the linear layer, reducing qubit consumption and the number of gate operations The proposed implementation requires approximately 64 data bits + 128 key bits for the number of qubits , e.g. SPARX -64/128, and the circuit depth is controlled at the polynomial level, meeting the requirements of lightweight quantum devices. This research provides a feasible path for the quantum implementation of lightweight block ciphers, particularly suitable for encryption needs in resource-constrained quantum scenarios such as the quantum Internet of Things.
The Grover search algorithm reduces the security level of symmetric key cryptography with n-bit security level to O(2n/2). In order to evaluate the Grover search algorithm, the target block cipher should be efficiently implemented in quantum circuits. Recently, many research works evaluated required quantum resources of AES block ciphers by optimizing the expensive substitute layer. However, few works were devoted to the lightweight block ciphers, even though it is an active research area, nowadays. In this paper, we present optimized implementations of every Korean made lightweight block ciphers for quantum computers, which include HIGHT, CHAM, and LEA, and NSA made lightweight block ciphers, namely SPECK. Primitive operations for block ciphers, including addition, rotation, and exclusive-or, are finely optimized to achieve the optimal quantum circuit, in terms of qubits, Toffoli gate, CNOT gate, and X gate. To the best of our knowledge, this is the first implementation of ARX-based Korean lightweight block ciphers in quantum circuits.
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.
In recent years, the quantum circuit implementation in symmetric cryptography has attracted widespread attention. The SM4 block cipher algorithm is China's first commercial cipher standard and was accepted as an ISO/IEC international standard in 2021. S-box is the most complex component in the SM4 block cipher algorithm. This study investigates the quantum circuit implementation of the SM4 S-box. Based on the algebraic structure, using tower filed decomposition technology, the quantum circuit of the SM4 S-box is built. Based on the number of NCT gate sets, our quantum circuit requires 20 qubits, 52 Toffoli gates, 196 CNOT gates, and 13 X gates. The Toffoli depth of our circuit is 36. Compared with previous literature, the quantum circuit proposed herein requires fewer quantum resources.
The security of classical symmetric-key primitives is fundamentally challenged by the emergence of quantum computing, necessitating a rigorous evaluation of their post-quantum resilience. This paper presents a comprehensive quantum circuit realization and Grover cryptanalysis of GFSPX, a lightweight block cipher featuring a 64-bit data block and a 128-bit secret key. GFSPX utilizes a unique hybrid architecture that integrates a 4-branch generalized Feistel structure with both Addition-Rotation-XOR (ARX) and Substitution-Permutation Network (SPN) components. Our quantum implementation optimizes resource distribution by exploiting the inherent reversibility of the Feistel network and employing a compact ripple-carry adder for the ARX layers. The proposed architecture achieves a qubit-optimized footprint of 209 qubits with a baseline quantum cost of 32,498 and a circuit depth of 7,617. To evaluate the cipher's resistance against quantum adversaries, we construct a parallelized Grover oracle using three plaintext-ciphertext pairs to eliminate spurious matches. Our analysis reveals that the total quantum cost of a key-recovery attack on GFSPX is 1.12×21591.12 \times 2^{159}1.12×2159 quantum gates. Although this cost falls below the NIST Level 1 security threshold of 21702^{170}2170, the hybrid ARX-SPN design demonstrates a higher quantum attack resistance among other lightweight designs. These findings provide critical insights into the balance between classical efficiency and quantum resilience in next-generation cryptographic designs for resource-constrained environments.
Abstract Grover’s algorithm reduces the security level of the target cipher from n-bit to n/2-bit. To implement Grover’s algorithm, a quantum circuit capable of performing the target cipher operations must be constructed. In this paper, we propose a quantum circuit implementation scheme for the involutive lightweight block cipher (IVLBC) block cipher. We utilized the DORCIS tool to implement the quantum circuit for the S-box and applied Gaussian elimination to construct the quantum circuit for matrix multiplication. Subsequently, we evaluated the overall quantum resource consumption required for the implementation. Based on this, we performed a quantum attack on IVLBC using Grover’s algorithm, calculating the attack cost using the NCT gate library, and further analyzed its security. Finally, we conducted a comparative analysis of the classical attack complexity and quantum attack complexity of IVLBC, highlighting the potential of using quantum complexity as a standard for future security assessments.
Abstract SM4 cryptographic algorithm is a block cipher algorithm issued by China's state cryptographic administration and has become an international standard. we implement the quantum circuits of SM4 Block cipher by optimizing the number of qubits and the value of depth-times-width. When the S-box is implemented, four kind of improved quantum circuits of S-box are presented for different phases in SM4 based on composite field arithmetic. When optimizing the number of qubits, we implement the quantum circuit of SM4 by connecting the quantum subcircuits in series. The implemented quantum circuit of SM4 only uses 260 qubits, which is the least number of qubits used not only in implementing the SM4 quantum circuit, but also in implementing the block cipher algorithms with 8-bit S-box, 128-bit plaintext and 128-bit secret key. When optimizing the value of depth-times-width, we achieve it through parallel implementation. The trade-off quantum circuit uses a total of 288 quantum bits and the Toffoli depth is 1716. The depth-times-width is 494208, which is less than the existing best value 825792.