T - depth Reduction Method for Efficient SH A-256 Quantum Circuit Construction

In order to perform a quantum brute force attack on a crypto-system based on Grover's algorithm, it is necessary to implement a quantum circuit of the cryptographic algorithm. Therefore an efficient quantum circuit design of a given cryptographic algorithm is essential, especially in terms of quantum security analysis, and it is well known that T-depth should be reduced for time complexity efficiency. In this paper, we propose a novel technique to reduce T depth (and T count) when some quantum circuits located in between two Toff oligates are interchangeable with a controlled phase gate (C ontrolled-P gate), and apply this technique to four types of quantum adders, resulting in a T-depth reduction of about 33%. We also present new SHA-256 quantum circuits which have a critical path with only 3 quantum adders while the critical paths of quantum circuits in the previous works consist of 7 or 9 quantum adders, and also apply our technique to the proposed S HA-256 quantum circuits and the included quantum adders. Among the previous results, the T-depth of the circuit with the smallest Width 801 was approximately 109,104. On the other hand, that of the proposed SHA-256 quantum circuit with the width 799 is 16,121, which is remarkably reduced by about 85%. Furthermore, the other proposed quantum circuit only requires 768 qubits which is the smallest Width compared to the previous results to the best of our knowledge.