Quantum computers can model and solve several problems that have posed challenges for classical super computers, leveraging their natural quantum mechanical characteristics. A large-scale quantum computer is poised to significantly reduce security strength in cryptography. In this context, extensive research has been conducted on quantum cryptanalysis.In this paper, we present optimized quantum circuits for Korean block ciphers, HIGHT and LEA. Our quantum circuits for HIGHT and LEA demonstrate the lowest circuit depth compared to previous results. Specifically, we achieve depth reductions of 48% and 74% for HIGHT and LEA, respectively. We employ multiple novel techniques that effectively reduce the quantum circuit depth with a reasonable increase in qubit count. Based on our depth-optimized quantum circuits for HIGHT and LEA block ciphers, we estimate the lowest quantum attack complexity for Grover’s key search. Our quantum circuit can be utilized for other quantum algorithms, not only for Grover’s algorithm. Furthermore, the optimization methods gathered in this work can be adopted for generic quantum implementations in cryptography.
Quantum computers can model and solve several problems that have posed challenges for classical super computers, leveraging their natural quantum mechanical characteristics. A large-scale quantum computer is poised to significantly reduce security strength in cryptography. In this context, extensive research has been conducted on quantum cryptanalysis.In this paper, we present optimized quantum circuits for Korean block ciphers, HIGHT and LEA. Our quantum circuits for HIGHT and LEA demonstrate the lowest circuit depth compared to previous results. Specifically, we achieve depth reductions of 48% and 74% for HIGHT and LEA, respectively. We employ multiple novel techniques that effectively reduce the quantum circuit depth with a reasonable increase in qubit count. Based on our depth-optimized quantum circuits for HIGHT and LEA block ciphers, we estimate the lowest quantum attack complexity for Grover’s key search. Our quantum circuit can be utilized for other quantum algorithms, not only for Grover’s algorithm. Furthermore, the optimization methods gathered in this work can be adopted for generic quantum implementations in cryptography.
Security vulnerabilities in the symmetric-key primitives of a cipher can undermine the overall security claims of the cipher. With the rapid advancement of quantum computing in recent years, there is an increasing effort to evaluate the security of symmetric-key cryptography against potential quantum attacks. This paper focuses on analyzing the quantum attack resistance of AIM, a symmetric-key primitive used in the AIMer digital signature scheme. We present the first quantum circuit implementation of AIM and estimate its complexity (such as qubit count, gate count, and circuit depth) with respect to Grover’s search algorithm. For Grover’s key search, the most important optimization metric is depth, especially when considering parallel search. Our implementation gathers multiple methods for a low-depth quantum circuit of AIM in order to reduce the Toffoli depth and full depth (such as the Karatsuba multiplication and optimization of inner modules; Mer, LinearLayer).
Quantum computing advancements pose security challenges for cryptography. Specifically, Grover’s search algorithm affects the reduction in the search complexity of symmetric-key encryption and hash functions. Recent efforts have been made to estimate the complexity of Grover’s search and evaluate post-quantum security. In this paper, we propose a depth-optimized quantum circuit implementation for ASCON, including both symmetric-key encryption and hashing algorithms, as a part of the lightweight cryptography standardization by NIST (National Institute of Standards and Technology). As far as we know, this is the first implementation of a quantum circuit for the ASCON AEAD (Authenticated Encryption with Associated Data) scheme, which is a symmetric-key algorithm. Also, our quantum circuit implementation of the ASCON-HASH achieves a reduction of more than 88.9% in the Toffoli depth and more than 80.5% in the full depth compared to the previous work. As per our understanding, the most effective strategy against Grover’s search involves minimizing the depth of the quantum circuit for the target cipher. We showcase the optimal Grover’s search cost for ASCON and introduce a proposed quantum circuit optimized for depth. Furthermore, we utilize the estimated cost to evaluate post-quantum security strength of ASCON, employing the relevant evaluation criteria and the latest advancements in research.
A quantum computer capable of running the Grover search algorithm, which reduces the complexity of brute-force attacks by a square root, has the potential to undermine the security strength of symmetric-key cryptography and hash functions. Recently, studies on quantum approaches have proposed analyzing potential quantum attacks using the Grover search algorithm in conjunction with optimized quantum circuit implementations for symmetric-key cryptography and hash functions. Analyzing quantum attacks on a cipher (i.e., quantum cryptanalysis) and estimating the necessary quantum resources are related to evaluating post-quantum security for the target cryptography algorithms. In this paper, we revisit quantum implementations of CHAM block cipher, an ultra lightweight cipher, with a focus on optimizing the linear operations in its key schedule. We optimized the linear equations of CHAM as matrices by applying novel optimized decomposition techniques. Using the improved CHAM quantum circuits, we estimate the cost of Grover’s key search and evaluate the post-quantum security strength with further reduced costs.
Grover’s search algorithm accelerates the key search on the symmetric key cipher and the pre-image attack on the hash function. To conduct Grover’s search algorithm, the target cipher algorithm should be efficiently implemented in a quantum circuit. Currently, small quantum computers are difficult to operate with large quantum circuits due to limited performance. Therefore, if a large quantum computer that can operate Grover’s algorithm appears, it is expected that a cipher attack will be possible. In this paper, we propose a parallel structure quantum circuit for the Korean hash function standard (i.e., LSH). The proposed quantum circuit designed a parallel operation structure for the message expansion (i.e., MsgExp) function and the mix function, which are the internal structures of the LSH hash function. This approach shows an efficient result for quantum circuit implementation in terms of quantum resources by reducing the depth of the quantum circuit by about 96% through the trade-off of appropriate quantum resources compared to previous work. This result can be a reference for the implementation of a parallel quantum circuit in the future and is expected to advance the attack timing of the search algorithm for Grover’s LSH hash function.
Quantum computers have the capacity to solve certain complex problems more efficiently than classical computers. To fully leverage these quantum advantages, adapting classical arithmetic for quantum systems in a circuit level is essential. In this paper, we introduce a depth-optimized quantum circuit of Gauss–Jordan elimination for matrices in binary. This quantum circuit is a crucial module for accelerating Information Set Decoding (ISD) using Grover’s algorithm. ISD is a cryptographic technique used in analyzing code-based cryptographic algorithms. When combined with Grover’s search, it achieves a square root reduction in complexity. The proposed method emphasizes the potential for parallelization in the quantum circuit implementation of Gauss–Jordan elimination. We allocate additional ancilla qubits to enable parallel operations within the target matrix and further reuse these ancilla qubits to minimize overhead from our additional allocation. The proposed quantum circuit for Gauss–Jordan elimination achieves the lowest Toffoli depth compared to the-state-of-art previous works.
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).