Quantum Circuit Implementations of AES with Fewer Qubits

Zou, Jian; Wei, Zihao; Sun, Siwei; Liu, Ximeng; Wu, Wenling

doi:10.1007/978-3-030-64834-3_24

Cited by 65 publications

(35 citation statements)

References 22 publications

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“…Among various Sboxes, one that has attracted the most attention from the research community is undoubtedly AES S-box. See, previous works [10,13,15,33] and related references therein. Table 1 in Jaques et al's work [13] neatly summarizes a few notable circuit designs from the literature, and we add one more entry to it as in Table 2 with the same Q# options being used as the first entry.…”

Section: Benchmark and Applicationmentioning

confidence: 99%

“…Early studies on quantum algorithms have been carried out in a rather abstract fashion, for example by adopting a unitary oracle specifying only its inputs and outputs, but recent progress in quantum computing and related fields seek lower-level descriptions involving the logic synthesis. For example in quantum cryptanalysis, a number of research groups are trying to measure the complexity of quantum algorithms in terms of elementary quantum gates [13,15,33].…”

Section: Introductionmentioning

confidence: 99%

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An Algorithm for Reversible Logic Circuit Synthesis Based on Tensor Decomposition

Lee¹,

Jung²,

Han³

et al. 2021

Preprint

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An algorithm for reversible logic synthesis is proposed. The task is, for given n-bit substitution map P n : {0, 1} n → {0, 1} n , to find a sequence of reversible logic gates that implements the map. The gate library adopted in this work consists of multiple-controlled Toffoli gates denoted by C m X, where m is the number of control bits that ranges from 0 to n − 1. Controlled gates with large m (> 2) are then further decomposed into C 0 X, C 1 X, and C 2 X gates. A primary concern in designing the algorithm is to reduce the use of C 2 X gate (also known as Toffoli gate) which is known to be universal [29].The main idea is to view an n-bit substitution map as a rank-2n tensor and to transform it such that the resulting map can be written as a tensor product of a rank-(2n − 2) tensor and the 2 × 2 identity matrix. Let P n be a set of all n-bit substitution maps. What we try to find is a size reduction map A red : P n → {P n : P n = P n−1 ⊗ I 2 }. One can see that the output P n−1 ⊗ I 2 acts nontrivially on n − 1 bits only, meaning that the map to be synthesized becomes P n−1 . The size reduction process is iteratively applied until it reaches tensor product of only 2 × 2 matrices.Time complexity of the algorithm is exponential in n as most previously known algorithms for reversible logic synthesis also are, but it terminates within reasonable time for not too large n which may find practical uses. As stated earlier, our primary concern is the number of Toffoli gates in the output circuit or quality for short, not the time complexity of the algorithm. Benchmark results show that the quality of circuits obtained in this work outperforms that of the previously reported ones for almost all hard benchmark functions suggested in [24,17]. A working code written in Python is publicly available from GitHub [1]. The algorithm is also applied to find reversible circuits for cryptographic substitution boxes which are being used in a certain type of encryption algorithms.

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Section: Benchmark and Applicationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Algorithm for Reversible Logic Circuit Synthesis Based on Tensor Decomposition

Lee¹,

Jung²,

Han³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Wang, Wei and Long in 2021 further reduced the implementation to 656 qubits, 1976 X gates, 101174 CNOT gates, but 18040 Toffoli gates (higher compared to the design of Langenberg et al) [15]. Zou et al in 2020 proposed their implementation of AES quantum circuit design with some optimization considerations on AES S-Box and key scheduling. The proposed implementation requires 512 qubits for AES-128 [16].…”

Section: Introductionmentioning

confidence: 99%

“…Zou et al in 2020 proposed their implementation of AES quantum circuit design with some optimization considerations on AES S-Box and key scheduling. The proposed implementation requires 512 qubits for AES-128 [16]. Some other lightweight symmetric encryption algorithms have been designed for quantum circuits such as PRESENT and GIFT by Jang et al in 2021 [17] and RECTANGLE and KNOT by Baksi et al in 2021 [18].…”

Section: Introductionmentioning

confidence: 99%

Quantum encryption with quantum permutation pad in IBMQ systems

Kuang

Perepechaenko

2022

EPJ Quantum Technol.

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Quantum permutation pad or QPP is a quantum-safe symmetric cryptographic algorithm proposed by Kuang and Bettenburg in 2020. The theoretical foundation of QPP leverages the linear algebraic representations of quantum gates which makes QPP realizable in both, quantum and classical systems. By applying the QPP with 64 of 8-bit permutation gates, holding respective entropy of over 100,000 bits, we accomplished quantum random number distributions digitally over today’s classical internet. The QPP has also been used to create pseudo quantum random numbers and served as a foundation for quantum-safe lightweight block and streaming ciphers. This paper continues to explore numerous applications of QPP, namely, we present an implementation of QPP as a quantum encryption circuit on today’s still noisy quantum computers. With the publicly available 5-qubit IBMQ devices, we demonstrate quantum secure encryption (256 bits of entropy) using 2-qubit QPP with 56 permutation gates, and 3-qubit QPP with 17 permutation gates respectively. Initial qubits of the encryption circuit correspond to the plaintext and after applying quantum encryption operations, cipher qubits are measured with probabilistic distributions, and the results with the highest probability are recorded as cipher bits. The cipher bits are then decrypted with an inverse QPP circuit. The output state plaintext qubits are measured and the most frequent count measurement results are recorded as plaintext bits. This quantum encryption and decryption process clearly demonstrates that QPP quantum implementations works exactly as symmetric encryption and decryption schemes should. The plaintext and ciphertext bits can also be encrypted and decrypted respectively by any classical computing device with the corresponding QPP algorithm as in quantum computers. This work reveals that it is possible to build quantum-secure communications between quantum-to-quantum and quantum-to-classical computers over today’s internet and the future quantum internet.

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“…Among them, in terms of quantum circuit implementation and optimization of cryptographic algorithms, B-Langenberg et al proposed the quantum circuit implementation and optimization of AES cryptographic algorithm [7], and many scholars have made further optimizations on it [8].…”

Section: Introductionmentioning

confidence: 99%

Circuit implementation of the globally optimized HHL algorithm and experiments on qiskit

Zhang

Liang

Zeng

et al. 2022

Preprint

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In 2019, Yonghae Lee et al. combined the circuit implementation of the HHL quantum algorithm with a classical computer, and designed a hybrid HHL quantum circuit optimization algorithm to reduce experimental errors caused by decoherence and so on. However, the optimization is achieved only in the auxiliary quantum coding phase, and no quantum resource reduction is done on the quantum phase estimation and inverse quantum phase estimation stages. At the same time, the circuit optimization illustration on the 2th-order linear equation system just has the result and no specific process. In this paper, based on the idea of the hybrid HHL algorithm and the general quantum circuit implementation framework of HHL, a global optimization HHL algorithm is proposed. The feasibility of the global optimization HHL algorithm is verified by IBM's qiskit. The detail circuit optimization illustrations on the 4th-order linear equations show that the global optimization HHL algorithm can effectively reduce quantum resources without losing the fidelity of the results. Thus the global optimization HHL algorithm can further avoid some result errors than the existing implementation methods.

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Quantum Circuit Implementations of AES with Fewer Qubits

Cited by 65 publications

References 22 publications

An Algorithm for Reversible Logic Circuit Synthesis Based on Tensor Decomposition

An Algorithm for Reversible Logic Circuit Synthesis Based on Tensor Decomposition

Quantum encryption with quantum permutation pad in IBMQ systems

Circuit implementation of the globally optimized HHL algorithm and experiments on qiskit

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