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

Abstract

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.

Quantum implementaion of SM4 block cipher with less qubits

“…However, the quantum circuit implemented by Luo et al did not restore the auxiliary qubit. The 5-qubit quantum circuits of multiplicative inversion in GF (2 4 ) implemented by Li et al [22] by using the tool LIGHTER-R [35] requires 8 Toffoli gates to restore the auxiliary bit to the state |0⟩, and 9 Toffoli gates to restore the auxiliary bit to an arbitrary quantum state. By using the tool DORCIS, the 5-qubit quantum circuit which we realized uses only 6 Toffoli gates when the auxiliary qubit is not restored.…”

“…Because the depth of a quantum circuit, especially the T depth, directly affects the running time of circuits in quantum computation [15], it is an important metric in the implementation of quantum circuits. More quantum circuits of AES were designed to reduce the number of qubits by improving the quantum circuits of S-box or round function [13,14,[16][17][18][19][20][21][22]. Because qubits are very important resource limited by current quantum computers [23].…”

“…So far Li et al proposed the method in Ref. [22] of using 264 qubits, which is the least number of qubits to implement the quantum circuit of AES-128, and the authors claimed that this is a new record.…”