# Improved Low-Depth SHA3 Quantum Circuit for Fault-Tolerant Quantum Computers
## 3 SHA3 Quantum Circuit
### Quantum Cost Analysis for SHA3  
Table 3 shows the proposed quantum resources for the Keccak-f function in SHA3, and Table 4 shows the quantum resources for our method, with the results of [PERSON] et al. [8] included for comparison. As shown in Table 3, in the proposed quantum circuit, \(\theta\) and \(\chi\) used the most quantum resources, and 1600 qubits in \(\theta\) and 640 qubits in \(\chi\) were used for each round. As shown in Table 4, the proposed quantum circuit increased the number of qubits to reduce the depth of the quantum circuit, resulting in a reduction in the depth of each function compared to previous implementations. In the theta (\(\theta\)) operation, we increased the CNOT gate by about 36.36% and reduced the depth by about 71.27% per round. To omit the \(\theta^{-1}\) process, 1600 additional qubits were used. The result of this quantum trade-off was a reduction of 1,360,000 CNOT gates + 25 depth for \(\theta^{-1}\) and an increase of 1600 qubits. In total, the full depth was reduced by about 73.67% in theta(\(\theta\)) and theta inverse \(\theta^{-1}\). In chi (\(\chi\)), 640 qubits were used additionally to reduce the CNOT gate by about 98.08%, the T depth by about 30.3%, and the full depth by about 90.08% per round (trade-off between qubits and gate + depth). In [8], the number of Toffoli gates used was not shown, but through the T depth, it can be inferred that Toffoli gates were used more than in our method. Our method used more 1 qClifford gates but reduced the number of CNOT and Toffoli gates, which are more expensive quantum gates than 1 qClifford gates, so we saw this as an appropriate quantum resource trade-off. For the operation of iota (\(\iota\)), the classic-to-quantum method reduced the quantum resources required for RC calculation and replaced the use of CNOT gates with X gates. As a result of these efforts, the proposed improved low-depth SHA3 quantum circuit for fault-tolerant quantum computers decreased the depth of all functions, reducing the overall quantum circuit depth by about 80.01%. We optimized the depth of each function in the SHA3 quantum circuit for low quantum computing error rates. Our approaches reduced the depth of the quantum circuits. In [32], the additional parts for Korean block ciphers LEA, HIGHT, and CHAM were implemented in parallel to reduce the overall depth compared to the first proposed quantum circuit [33]. The quantum resource estimation results of the preceding quantum circuit [32] presented in Table 5 were efficiently reduced in terms of depth through quantum resource trade-off, and the results are shown in Table 6. The method presented in [33] showed performance enhancements in terms of quantum circuit depth for LEA, HIGHT, and CHAM of 78%, 85%, and 70%, respectively. In [14], to reduce the depth of the Korean standard hash function LSH, a part that made parallel operation possible was identified in previous research [34] and designed to perform parallel operation inside the quantum circuit. As a result, compared to the initial research results presented in Table 7, the full depth of the quantum circuit was reduced by about 96%, and the results are shown in Table 8. The previous study reduced the internal calculation time and error by reducing the depth of the quantum circuit. The depth of the quantum circuit was reduced by about 70% to 96% compared to the initial work.