Improved Quantum Analysis of SPECK and LowMC

Jang, Kyungbae; Baksi, Anubhab; Kim, Hyunji; Seo, Hwajeong; Chattopadhyay, Anupam

doi:10.1007/978-3-031-22912-1_23

Cited by 13 publications

(24 citation statements)

References 28 publications

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“…The quantum circuit given by LIGHTER-R requires the optimal number of qubits. Recently, the tool has been widely applied in the quantum circuit implementation of other cryptography, such as Present and Gift [39], RECTANGLE and KNOT [40], DEFAULT [41] and so on.…”

Section: A Decomposition Of S-boxmentioning

confidence: 99%

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New record in the number of qubits for a quantum implementation of AES

Gao

Qin

et al. 2023

Front. Phys.

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Optimizing the quantum circuit for implementing Advanced Encryption Standard (AES) is crucial for estimating the necessary resources in attacking AES by the Grover algorithm. Previous studies have reduced the number of qubits required for the quantum circuits of AES-128/-192/-256 from 984/1112/1336 to 270/334/398, which is close to the optimal value of 256/320/384. It becomes a challenging task to further optimize them. AimTaking aim at this task, we find a method for how the quantum circuit of AES S-box can be designed with the help of the automation tool LIGHTER-R. Particularly, the multiplicative inversion in F28, which is the main part of the S-box, is converted into the multiplicative inversion (and multiplication) in F24, then the latter can be implemented by LIGHTER-R because its search space is small enough. By this method, we construct the quantum circuits of S-box for mapping |a⟩|0⟩ to |a⟩|S(a)⟩ and |a⟩|b⟩ to |a⟩|b ⊕ S(a)⟩ with 20 qubits instead of 22 in the previous studies. In addition, we introduce new techniques to reduce the number of qubits required by the S-box circuit for mapping |a⟩ to |S(a)⟩ from 22 in the previous studies to 16. Accordingly, we synthesize the quantum circuits of AES-128/-192/-256 with 264/328/392 qubits, which implies a new record.

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Section: A Decomposition Of S-boxmentioning

confidence: 99%

“…Huang et al [26] gave the circuit for |a〉|b〉 → |a〉|b ⊕ S(a)〉 with a T-depth of 3, and then further reduced the Tdepth required for the quantum circuit of AES-128 to 60. Jang et al [27] synthesized the quantum circuit of AES-128 with a T-depth of 30 by introducing an improved pipeline method for round function iteration.…”

Section: Introductionmentioning

confidence: 99%

New record in the number of qubits for a quantum implementation of AES

Gao

Qin

et al. 2023

Front. Phys.

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“…We added large adders circuits which are performing an addition over two registers of size 1024, 2048 and 4096 qubits, the implementation of these circuits is based on Reference [29]. We also added a circuit, given in Reference [30], that is an implementation of the block cipher DEFAULT. Finally, we added quantum circuits implementing the modular exponentiation part of Shor's algorithm for number factoring over 4, 8, 16 and 32 bits.…”

Section: Benchmarksmentioning

confidence: 99%

Optimal Hadamard gate count for Clifford$+T$ synthesis of Pauli rotations sequences

Vivien¹,

Martiel²,

Perdrix³

et al. 2023

Preprint

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The Clifford+T gate set is commonly used to perform universal quantum computation. In such setup the T gate is typically much more expensive to implement in a fault-tolerant way than Clifford gates. To improve the feasibility of fault-tolerant quantum computing it is then crucial to minimize the number of T gates. Many algorithms, yielding effective results, have been designed to address this problem. It has been demonstrated that performing a pre-processing step consisting of reducing the number of Hadamard gates in the circuit can help to exploit the full potential of these algorithms and thereby lead to a substantial T -count reduction. Moreover, minimizing the number of Hadamard gates also restrains the number of additional qubits and operations resulting from the gadgetization of Hadamard gates, a procedure used by some compilers to further reduce the number of T gates. In this work we tackle the Hadamard gate reduction problem, and propose an algorithm for synthesizing a sequence of Pauli rotations with a minimal number of Hadamard gates. Based on this result, we present an algorithm which optimally minimizes the number of Hadamard gates lying between the first and the last T gate of the circuit.

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“…In response, various symmetric key ciphers are being analysed under the Grover search algorithm [ 3 , 4 , 5 , 6 ]. It is worth noting that the quantum resources (elements that make up a quantum circuit such as quantum gates, qubits, and circuit depth) for applying the Grover’s search to AES [ 3 , 7 , 8 , 9 ] are being used as a standard for estimating post-quantum security strength by NIST [ 10 ].…”

Section: Introductionmentioning

confidence: 99%

Quantum Binary Field Multiplication with Optimized Toffoli Depth and Extension to Quantum Inversion

Jang

Kim

Lim

et al. 2023

Sensors

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The Shor’s algorithm can find solutions to the discrete logarithm problem on binary elliptic curves in polynomial time. A major challenge in implementing Shor’s algorithm is the overhead of representing and performing arithmetic on binary elliptic curves using quantum circuits. Multiplication of binary fields is one of the critical operations in the context of elliptic curve arithmetic, and it is especially costly in the quantum setting. Our goal in this paper is to optimize quantum multiplication in the binary field. In the past, efforts to optimize quantum multiplication have centred on reducing the Toffoli gate count or qubits required. However, despite the fact that circuit depth is an important metric for indicating the performance of a quantum circuit, previous studies have lacked sufficient consideration for reducing circuit depth. Our approach to optimizing quantum multiplication differs from previous work in that we aim at reducing the Toffoli depth and full depth. To optimize quantum multiplication, we adopt the Karatsuba multiplication method which is based on the divide-and-conquer approach. In summary, we present an optimized quantum multiplication that has a Toffoli depth of one. Additionally, the full depth of the quantum circuit is also reduced thanks to our Toffoli depth optimization strategy. To demonstrate the effectiveness of our proposed method, we evaluate its performance using various metrics such as the qubit count, quantum gates, and circuit depth, as well as the qubits-depth product. These metrics provide insight into the resource requirements and complexity of the method. Our work achieves the lowest Toffoli depth, full depth, and the best trade-off performance for quantum multiplication. Further, our multiplication is more effective when not used in stand-alone cases. We show this effectiveness by using our multiplication to the Itoh–Tsujii algorithm-based inversion of F(x8+x4+x3+x+1).

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Improved Quantum Analysis of SPECK and LowMC

Cited by 13 publications

References 28 publications

New record in the number of qubits for a quantum implementation of AES

New record in the number of qubits for a quantum implementation of AES

Optimal Hadamard gate count for Clifford$+T$ synthesis of Pauli rotations sequences

Quantum Binary Field Multiplication with Optimized Toffoli Depth and Extension to Quantum Inversion

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