Quantum computers will have a significant impact on the security aspects of many conventional cryptographic algorithms as the quantum circuit implementation of the cryptographic algorithms can be attacked with the help of Grover’s key search algorithm. This work proposes quantum circuit design of RECTANGLE lightweight cipher for 80-bit and 128-bit key variants. All the individual modules of the cipher are designed with minimal quantum resources and finally they are integrated together to build the complete quantum circuit. The quantum circuit synthesis is performed with Toffoli family of quantum gates. The proposed design outperforms the existing design by achieving low-latency. The quantum resources are also estimated to mount the quantum attack by using Grover’s key search algorithm.
Quantum computers will have a significant impact on the security aspects of many conventional cryptographic algorithms as the quantum circuit implementation of the cryptographic algorithms can be attacked with the help of Grover’s key search algorithm. This work proposes quantum circuit design of RECTANGLE lightweight cipher for 80-bit and 128-bit key variants. All the individual modules of the cipher are designed with minimal quantum resources and finally they are integrated together to build the complete quantum circuit. The quantum circuit synthesis is performed with Toffoli family of quantum gates. The proposed design outperforms the existing design by achieving low-latency. The quantum resources are also estimated to mount the quantum attack by using Grover’s key search algorithm.
Grover search algorithm is the most representative quantum attack method that threatens the security of symmetric key cryptography. If the Grover search algorithm is applied to symmetric key cryptography, the security level of target symmetric key cryptography can be lowered from n-bit to n2-bit. When applying Grover’s search algorithm to the block cipher that is the target of potential quantum attacks, the target block cipher must be implemented as quantum circuits. Starting with the AES block cipher, a number of works have been conducted to optimize and implement target block ciphers into quantum circuits. Recently, many studies have been published to implement lightweight block ciphers as quantum circuits. In this paper, we present optimal quantum circuit designs of symmetric key cryptography, including PRESENT and GIFT block ciphers. The proposed method optimized PRESENT and GIFT block ciphers by minimizing qubits, quantum gates, and circuit depth. We compare proposed PRESENT and GIFT quantum circuits with other results of lightweight block cipher implementations in quantum circuits. Finally, quantum resources of PRESENT and GIFT block ciphers required for the oracle of the Grover search algorithm were estimated.
Quantum computing plays a vital role in the next generation computing platforms as researchers have achieved quantum supremacy by proving that quantum computers can outperform classical computers. These high performance computers will pose a serious threat to the security of the conventional cryptographic algorithms. The secret key of the conventional cryptographic algorithms when implemented by quantum circuits can easily be recovered with the help of Grover key search algorithm. The Grover’s algorithm requires low cost quantum implementation of cryptographic algorithms in order to mount the quantum key recovery attack successfully. Hence the low cost quantum implementation of conventional cryptographic algorithms to mount quantum key recovery attack using Grover search algorithm is an active area of research. This work proposes a novel quantum circuit implementation of two lightweight block ciphers namely PUFFIN and PRINT and for the first time in literature In-place method is used to optimize the quantum resources in these two ciphers which helps to build compact quantum circuits without extra ancilla inputs. The performance metrics considered in this work to quantify the quantum resources of the proposed circuits are number of quantum gates, quantum cost, latency and number of qubits. In addition, the quantum resources are also estimated to mount the quantum key recovery attacks on the proposed quantum circuit implementations of PUFFIN and PRINT using Grover-based key search algorithm.
The emergence of quantum computers is threatening the security of cryptography through various quantum algorithms. Among them, the Grover search algorithm is known to be efficient in accelerating brute force attacks on block cipher algorithms. To utilize the Grover’s algorithm for brute force attacks, block ciphers must be implemented in quantum circuits. In this paper, we present optimized quantum circuits of the SPN (Substitution Permutation Network) structured lightweight block cipher, namely the PIPO block cipher. In particular, the compact design of quantum circuits for the 8-bit Sbox is investigated. These optimization techniques are used to implement other cryptographic operations as quantum circuits. Finally, we evaluate quantum resources of Grover search algorithm for the PIPO block cipher in ProejctQ, a quantum simulator provided by IBM.
With the advancement of quantum computing, quantum circuit implementations of symmetric cryptographic algorithms are essential for evaluating their resistance to quantum attacks. As an ISO-standardized cipher, the efficient quantum circuit construction of Camellia is of great significance. Focusing on minimizing the DW-cost (qubits × Toffoli-depth) while balancing ancilla qubits and Toffoli-depth, this paper proposes an optimized quantum circuit design for Camellia. Specifically: (1) using a serial-multiplication and out-of-place inversion architecture under composite-field decomposition, combined with hierarchical screening for parallelizing bilinear multiplications, a compact in-place S-box quantum circuit is constructed with a DW-cost of 276, 28% lower than the state of the art; (2) a low-gate-count linear-layer circuit is obtained via heuristic search, and gate-sequence reordering then reduces the full depth from 9 to 7 without increasing the gate count; (3) Camellia-128/192/256 quantum circuits are constructed with DW-costs of 119,168, 257,664, and 257,664, achieving reductions of 48%, 52%, and 52% respectively over prior work. A pipelined Grover oracle is further designed and the total resources required for a full Grover search attacking Camellia are evaluated. For Camellia-128, the complete Grover search requires a T-depth of 2.10 × 2⁷⁶ and a total TDW-cost (qubits × T-depth) of 1.00 × 2⁸⁶, reducing T-depth by 75% and TDW-cost by 84% over prior work. The first full Grover search resource estimates for Camellia-192/256 are also presented, with T-depths of 7.20 × 2¹⁰⁸ and 8.11 × 2¹⁴⁰ and TDW-costs of 2.03 × 2¹²³ and 2.79 × 2¹⁵³, respectively. These results show that Grover's attack on Camellia requires fewer quantum resources than on AES at the 128-bit level, implying comparatively weaker post-quantum security at that key size, while the picture reverses at larger key sizes (Section 4).
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.
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.