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Parallel quantum addition for Korean block ciphers

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Abstract

Malicious users using quantum computers can employ quantum attacks on modern cryptography algorithms. Grover’s search algorithm, a well-known quantum algorithm, can reduce the search complexity of \(O(2^n)\) to \(\sqrt{2^n}\) for symmetric key cryptography with an n-bit key. To apply the Grover search algorithm, the target encryption process must be implemented in a quantum circuit. In this paper, we present optimized quantum circuits for Korean block ciphers based on ARX architectures. We adopt the optimal quantum adder and design it in parallel way. Compared to previous implementations, we provide performance improvements of 78%, 85%, and 70% in terms of circuit depth for LEA, HIGHT, and CHAM, respectively, while keeping the number of qubits and quantum gates minimum. The depth of a circuit is an important factor related to its execution time. Finally, we estimate the cost of the Grover key search for Korean block ciphers and evaluate the post-quantum security based on the criteria presented by NIST.

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Data Availability

Source codes of proposed implementations are available in https://github.com/starj1023/Korea-ARX-QC/.

Notes

  1. https://github.com/starj1023/Korea-ARX-QC/.

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Authors and Affiliations

  1. Division of IT Convergence Engineering, Hansung University, Seoul, South Korea

    Kyungbae Jang, Gyeongju Song, Hyunjun Kim, Hyeokdong Kwon, Hyunji Kim & Hwajeong Seo

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  1. Kyungbae Jang
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  2. Gyeongju Song
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Correspondence to Hwajeong Seo.

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This work was partly supported by Institute for Information & communications Technology Planning & Evaluation (IITP) grant funded by the Korea government (MSIT) (<Q|Crypton>, No.2019-0-00033, Study on Quantum Security Evaluation of Cryptography based on Computational Quantum Complexity, 50%), and this work was partly supported by Institute for Information & communications Technology Promotion (IITP) grant funded by the Korea government (MSIT) (No. 2018-0-00264, Research on Blockchain Security Technology for IoT Services, 25%), and this work of Kyungbae Jang was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (2022R1A6A3A13062701, 25%).

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Jang, K., Song, G., Kim, H. et al. Parallel quantum addition for Korean block ciphers. Quantum Inf Process 21, 373 (2022). https://doi.org/10.1007/s11128-022-03714-3

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