$$T{-}depth$$ Reduction Method for Efficient $$SHA{-}256$$ Quantum Circuit Construction

Lee, Jongheon; Lee, Sokjoon; Lee, You-Seok; Choi, Dooho

doi:10.1007/978-3-031-08896-4_20

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…This paper is an improved extension version of Ref. [13] with the following contents added. Section 2 introduces the pruning procedure [14].…”

Section: Introductionmentioning

confidence: 99%

T‐depth reduction method for efficient SHA‐256 quantum circuit construction

Lee

et al. 2022

IET Information Security

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To perform a quantum brute force attack on a cryptosystem 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, the authors propose a novel technique to reduce T‐depth (and T‐count) when some quantum circuits located in between two Toffoli‐gates are interchangeable with a controlled phase gate (CP gate), and the authors apply this technique to five types of quantum adders, reducing T‐depth by more than 33%. The authors also present new SHA‐256 quantum circuits which have a critical path with only three quantum adders while the critical paths of quantum circuits in the previous studies consist of seven or 10 quantum adders, and the authors also apply our technique to the proposed SHA‐256 quantum circuits. Four versions of SHA‐256 quantum circuit are presented. Among the previous results, T‐depth of the circuit with the smallest Width (the number of qubits) 801 was approximately 109,104. On the other hand, T‐depth of the proposed SHA‐256 quantum circuit with the Width 797 is 16,055, which is remarkably reduced by about 85%. Another proposed quantum circuit only requires 768 qubits, which is the smallest Width compared to the previous results to the best of our knowledge. Furthermore, one other version is the most time‐efficient circuit with an overall Toffoli‐depth (and T‐depth) that is less than 5000.

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“…This paper is an improved extension version of Ref. [13] with the following contents added. Section 2 introduces the pruning procedure [14].…”

Section: Introductionmentioning

confidence: 99%

T‐depth reduction method for efficient SHA‐256 quantum circuit construction

Lee

et al. 2022

IET Information Security

View full text Add to dashboard Cite

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MPMCT gate decomposition method reducing T-depth quickly in proportion to the number of work qubits

Lee,

Kang,

Lee

et al. 2023

Quantum Inf Process

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We propose a method for efficient mixed polarity multiple controlled Toffoli (MPMCT) gate decomposition from the perspective of a cost metric related to Toffoli gates, namely Toffoli-depth. When using the technique presented in a previous study, there is a range in which Toffoli-depth (consequently T-depth) of the implemented circuit increases proportionally as the number of provided (clean) work qubits increases. In other words, using the previous technique may result in more inefficient MPMCT gates even though the number of helpful work qubits has increased. In this work, a technique is devised to provide sufficient help from clean work qubits at the central part of the implemented circuit as many as possible, thereby addressing the issues with the previous technique. Meanwhile, one of the representative algorithms that use MPMCT gates is Grover’s algorithm. We show the implementation results for MPMCT gates according to the number of work qubits, using Grover’s algorithm as an example. It is experimentally demonstrated that T-depth decreases much more quickly when using our method than the previous method.

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Toffoli-depth reduction method preserving in-place quantum circuits and its application to SHA3-256

Lee,

Kang,

Lee

et al. 2024

Quantum Inf Process

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When implementing a quantum circuit for a desired reversible function, an attempt is made to design an accurate quantum circuit. Then, the quantum circuit is optimized based on a specific cost function, such as design cost, width (the number of qubits), depth, etc. In particular, if an in-place subcircuit itself can be optimized while maintaining its in-place property, it will be a very useful way to increase efficiency without changing the initial architecture of the entire quantum circuit. Furthermore, since its (clean) work qubits can easily be utilized in subsequent subroutines of the quantum circuit, it has an additional important advantage in terms of width. In this paper, for the first time to the best of our knowledge, we present a global Toffoli-depth reduction methodology for an in-place version reversible circuit in the case that the given input circuit is optimized with Toffoli-count. We mainly introduce a process to optimize the $$\chi $$ χ internal function block in SHA3-256 to explain our Toffoli-depth reduction approach preserving the in-place property, and hence, well-balanced five $$\chi $$ χ quantum circuits are induced in terms of its width and T-depth. And then, we apply these five $$\chi $$ χ circuits to design the entire SHA3-256 cryptosystem. One of the proposed SHA3-256 quantum circuits has a width of 1600 and a T-depth of 264, and this shows a result of 50% and 38.9% reduction compared to the previous circuit in terms of width and T-depth, respectively. Other versions of our SHA3-256 circuits just required 10–33 qubits per one T-depth compared to the previous results which require over 1800 qubits per T-depth, and so this means that our SHA3-256 circuits are well-balanced. Finally, we constructed Grover’s algorithm circuit using each version that realized SHA3-256. When output circuits for the presented method were used, quantum volume values of Grover’s algorithm circuits became 33 and 50$$\%$$ % of the value when the input circuit was used.

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$$T{-}depth$$ Reduction Method for Efficient $$SHA{-}256$$ Quantum Circuit Construction

Cited by 3 publications

References 20 publications

T‐depth reduction method for efficient SHA‐256 quantum circuit construction

T‐depth reduction method for efficient SHA‐256 quantum circuit construction

MPMCT gate decomposition method reducing T-depth quickly in proportion to the number of work qubits

Toffoli-depth reduction method preserving in-place quantum circuits and its application to SHA3-256

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