Abstract Many quantum algorithms for attacking symmetric cryptography involve the rank problem of quantum linear equations. In this paper, two quantum algorithms are proposed to solve quantum linear systems of equations with coherent superposition, and their specific quantum circuits are constructed. In contrast to previous related studies, our quantum algorithms are universal, computing both the rank and general solution by one measurement. The difference between them is whether the data register containing the quantum coefficient matrix can be disentangled from the other registers while keeping the data qubits unchanged. On this basis, the two quantum algorithms are applied as subroutines to parallel Simon’s algorithm (with multiple periods), Grover Meets Simon algorithm, and Alg-PolyQ2 algorithm. Subsequently, a quantum classifier within Grover Meets Simon algorithm and a detailed test oracle within Alg-PolyQ2 algorithms are constructed, including their respective quantum circuits. To the best of our knowledge, no such specific analysis has been previously performed. The success probability of these algorithms is rigorously analyzed to ensure that the probability of success on the proposed quantum algorithms will not be lower than that of the original algorithms. Finally, we discuss the lower bound of the number of controlled-NOT gates for solving quantum linear systems of equations with coherent superposition. Our analysis indicates that the proposed algorithms are suitable for conducting attacks against lightweight symmetric ciphers within the effective working time of an ion-trap quantum computer.

Abstract The development of quantum computation enables exponential time complexity problems on classical computers to be solved in polynomial time on quantum computers. However, it also poses a threat to the security of classical cryptographic schemes based on integer factorization and discrete logarithms. In response to this challenge, quantum cryptographic schemes based on quantum computation and quantum communication environments have become a focal point of research. The quantum public-key cryptosystem based on the QSCDff problem stands as one of the influential schemes in the realm of quantum public-key cryptography, yet its feasibility remains unexplored in current literature. Our specific focus lies in the quantum circuit implementations and fault-tolerant construction, which serve as essential prerequisites for the physical feasibility of quantum cryptographic schemes. We provide quantum circuit implementations along with rigorous theoretical proofs for the computation of the permutation product operation and the permutation sign operation in quantum public-key cryptographic schemes. Based on the fault-tolerant quantum computation process of the aforementioned quantum circuit implementations, we propose two error-correction strategies and provide a theoretical feasibility analysis within a specified range in the ion-trap quantum computation environment, adhering to the theoretical limits of quantum computation. Rigorous proofs are presented to demonstrate the correctness and reliability of the proposed methods. Our contribution provides a theoretical foundation for the physical feasibility analysis of quantum cryptographic algorithms, offering insights into the challenges and prospects of implementing these algorithms in quantum computation environments.

There is no quantum election protocol that can fulfil the eight requirements of an electronic election protocol, i.e., completeness, robustness, privacy, legality, unreusability, fairness, verifiability, and receipt-freeness. To address this issue, we employ the general construction of quantum digital signature and quantum public key encryption, in conjunction with classic public key encryption, to develop and instantiate a general construction of quantum election protocol. The proposed protocol exhibits the following advantages: (i) no pre-shared key between any two participants is required, and no trusted third party or anonymous channels are required. The protocol is suitable for large-scale elections with numerous candidates and voters and accommodates the situation in which multiple voters vote simultaneously. (ii) It is the first protocol that dismantles the contradiction between verifiability and receipt-freeness in a quantum election protocol. It satisfies all eight requirements stated earlier under the physical assumptions that there exists a one-way untappable channel from the administrator to the voter and that there is no collusion between any of the three parties in the protocol. Compared with current election protocols with verifiability and receipt-freeness, this protocol relies upon fewer physical assumptions. (iii) This construction is flexible and can be instantiated into an election scheme having post-quantum security by applying cryptographic algorithms conveying post-quantum security. Moreover, utilizing quantum digital signature and public key encryption yields a good result: the transmitted ballots are in quantum states, so owing to the no-cloning theorem, ballot privacy is less likely to be compromised, even if private keys of the signature and public key encryption are leaked after the election. However, in existing election protocols employing classic digital signatures and public key encryption, ballot privacy can be easily violated if attackers obtain private keys. Thus, our construction enhances privacy.

In this paper, we study applications of Bernstein–Vazirani algorithm and present several new methods to attack block ciphers. Specifically, we first present a quantum algorithm for finding the linear structures of a function. Based on it, we propose new quantum distinguishers for the 3-round Feistel scheme and a new quantum algorithm to recover partial key of the Even–Mansour construction. Afterwards, by observing that the linear structures of a encryption function are actually high probability differentials of it, we apply our algorithm to differential analysis and impossible differential cryptanalysis respectively. We also propose a new kind of differential cryptanalysis, called quantum small probability differential cryptanalysis, based on the fact that the linear structures found by our algorithm are also the linear structure of each component function. To our knowledge, no similar method was proposed before. The efficiency and success probability of all attacks are analyzed rigorously. Since our algorithm treats the encryption function as a whole, it avoid the disadvantage of traditional differential cryptanalysis that it is difficult to extending the differential path.

The development of quantum computers has urged the cryptographic community to prepare cryptographic primitives for the eventual arrival of the post‐quantum world. To this end, the authors study the witness indistinguishability (WI) and witness hiding (WH) of proof systems against quantum adversaries. They give formal definitions of quantum WI (QWI) and quantum WH (QWH), present proof systems satisfying these definitions, and specify a condition under which QWI implies QWH. Regarding the non‐interactive proof systems, they prove that, even if a common reference string is used to generate polynomially many non‐interactive proofs, the QWI is still preserved, while quantum zero‐knowledge has no such beneficial property. To show the strength of QWI, they present two applications of them. First, they prove that the construction proposed by Feige et al . that transforms any non‐interactive bounded zero‐knowledge proof system to a general one is also feasible against quantum adversaries. Second, they construct a quantum‐secure signature scheme in the CRS model, which is existentially unforgeable against quantum adversaries and remains secure even if a common random string is used to sign polynomially many messages.