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.
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.
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.
Abstract With the rapid development of quantum technology, modern cryptography is facing an increasing number of security threats. Given that the quantum circuit of symmetric‐key ciphers frequently serves as the core element of quantum attacks, it has attracted extensive attention. In this work, it is investigated that how the quantum circuit of SM4 and Camellia can be implemented with lower ‐depth. First, a general framework is proposed for designing Substitution‐box (S‐box) circuits with optimized ‐depth. Based on the framework, quantum circuits are respectively designed for SM4 S‐box and Camellia S‐box with ‐depth 4. Compared with existing quantum circuits requiring a ‐depth of 4, our circuits consume fewer qubits and quantum gates, as well as lower full depth. Besides, S‐box quantum circuits are introduced with ‐depth 3 for SM4 and Camellia for the first time. As an application, the designed S‐box circuits can reduce the ‐depth requiring for the subroutine and stand‐alone circuits of SM4 from 132 and 260 in the previous work to 99 and 195. Additionally, the ‐depth requiring for the subroutine and stand‐alone circuits of Camellia‐128/‐192/‐256 can be reduced from 92/126/126 and 108/150/150 in the previous work to 70/96/96 and 82/114/114, respectively.
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.
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 F24 F 2 4 enables two types of optimized F28 F 2 8 multiplication circuits to reduce DW-cost by at least 50%. For 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.
With the continuous development of quantum technology and the gradual advancement of quantum computers, the challenges faced by modern cryptography are becoming increasingly diverse. When analyzing the security strength of cryptographic algorithms against quantum attacks, the construction of quantum implementation circuits is a crucial aspect. Symmetric-key cryptography is an important component of modern cryptography. This study reviews the research results of optimizing the quantum implementation of symmetric-key cryptography under quantum computing models. Specifically, this work summarizes the construction of reversible circuits for linear layers, Substitution-boxes (S-boxes), and various addition operations, as well as the quantum implementation of symmetric-key ciphers such as AES, SM4, and Camellia.
SM3 is a hash algorithm independently developed by China. This work mainly studies the quantum circuit implementation of SM3 based on the Clifford+T gate set, and proposes two quantum implementation structures for optimizing the T-depth and width of the circuit, respectively. For the design of quantum circuits with lower T-depth, this paper implements multiple modulo adders applied in parallel, and designs an implementation of quantum circuits for nonlinear components with lower T-depth by utilizing the QAND gate and its conjugate transpose. Based on this, the paper proposes two quantum circuit implementations of the SM3 according to the out-of-place and in-place structures of the nonlinear component, with T-depths of 7040 and 7136, respectively. Compared with the existing circuit with the lowest T-depth, the proposed circuit reduces the T-depth by 72%. For the design of quantum circuits with lower width, this paper groups the constants and variables in the constant modulo addition step, leading to the implementation of the constant modulo operation based on 32 bits only consumes 11 ancilla qubits when the size of group is 4 or 8. Based on this, the paper proposes a quantum circuit implementation of the SM3 that consumes 779 qubits, including 11 ancilla qubits. Compared with the existing circuit with the least consumption of ancilla qubits, the proposed circuit reduces the consumption of ancilla qubits by 67%.