International Association
for Cryptologic Research

This paper explores the optimization of quantum circuits for Argon2, a memory-hard function used for password hashing and other applications. With the rise of quantum computers, the security of classical cryptographic systems is at risk. It emphasizes the need to accurately measure the quantum security strength of cryptographic schemes using optimized quantum circuits. The proposed method focuses on two perspectives: qubit reduction (qubit optimization) and depth reduction (depth optimization). The qubit-optimized quantum circuit was designed to find a point where an appropriate inverse is possible and reuses the qubit through the inverse to minimize the number of qubits. The start point and end point of the inverse are set by finding a point where qubits can be reused with minimal computation. The depth-optimized quantum circuit reduces the depth by using the minimum number of qubits as necessary without performing an inverse operation. The trade-off between qubit and depth is confirmed by modifying the internal structure of the circuits and the quantum adders. Qubit optimization achieved up to a 12,229 qubit reduction, while depth optimization resulted in approximately 196,741 (approximately 69.02%) depth reduction. In conclusion, this research demonstrates the importance of implementing and analyzing quantum circuits from various optimization perspectives. The results contribute to the post-quantum strength analysis of Argon2 and provide valuable insights for future research on quantum circuit design, considering the appropriate trade-offs of quantum resources in response to advancements in quantum computing technology.