## Cryptology ePrint Archive: Report 2021/1507

Parallel Quantum Addition for Korean Block Cipher

Kyungbae Jang and Gyeongju Song and Hyunjun Kim and Hyeokdong Kwon and Hyunji Kim and Hwajeong Seo

Abstract: Adversaries using quantum computers can employ new attacks on cryptography that are not possible with classical computers. 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 using an $n$-bit key. To apply the Grover search algorithm, the target encryption process must be implemented as 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 in parallel way with only a few trade-offs between quantum resources. As a result, we provide a performance improvement of 78\% in LEA, 85\% in HIGHT, and 70\% in CHAM in terms of circuit depth, respectively. 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.

Category / Keywords: implementation / Parallel Quantum Addition and Korean Block Cipher and ARX Architecture and Grover Algorithm