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Journal of Intelligent Decision Making and Information Science

Optimized Quantum Circuit Design and Grover Search Resource Estimation for the Camellia Block Cipher

Vandana B Patil

Published Sep 16, 2026• 0 citations
Publisher

Abstract

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).

DOI
10.17762/jidmis.v3.3394

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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).
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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).
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.
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