Tao Shang

With the rapid development of quantum computing technology, the classical cryptosystem will face a significant threat. It is an urgent security issue to study the security impact of quantum computing on classical cryptosystems and provide reliable cryptographic primitives for the post-quantum era. A powerful way to solve this problem is to quantize the classical cryptanalysis tools and use the improved versions for cryptanalysis. In this paper, we propose a quantum zero correlation analysis algorithm based on the Bernstein-Vazirani and Grover algorithms. It can find zero correlation linear hulls for Feistel and SPN ciphers. We prove the correctness of the algorithm and analyze its complexity. Compared with the classical algorithms, the proposed quantum algorithm has significant advantages when the number of encryption rounds of block ciphers is large. Moreover, compared with the existing quantum zero correlation linear analysis, the proposed algorithm is more efficient and does not depend on the algebraic characteristics of the target cipher, which makes the algorithm has more flexible application scenarios.

In distributed systems, Byzantine consensus serves as a practical approach to addressing the Byzantine general problem. Previous research has exploited quantum resources to develop quantum-detectable Byzantine consensus protocols, aiming to surpass the 1/3 fault-tolerance bound. However, these consensus protocols are designed under the assumption of secure channel. They ignored malicious participants' attacks on the communication process. In this paper, we introduce a new quantum protocol for quantum Byzantine consensus utilizing the full quantum one-way function, which is the foundation for generating verification state in list distribution phase and secure message in agreement phase. By relying on the quantum circuit of the full quantum one-way function, the honest participants are able to reach consensus, while the malicious participants are effectively detected. In order to enhance the scalability of the proposed quantum Byzantine consensus protocol, we categorize the participants into three-member groups when the number of participants is n > 3. Meanwhile, the election of commander is introduced in agreement phase. In the proposed multi-party quantum Byzantine consensus protocol, the full quantum one-way function verifies the honesty of the participants both in list distribution phase and agreement phase. Security analysis demonstrates that the proposed multiparty quantum Byzantine consensus protocol is secure against quantum attacks and the dishonest behaviors of participants.

Fully homomorphic encryption enables computation on encrypted data while maintaining secrecy. This leads to an important open question whether quantum computation can be delegated and verified in a non-interactive manner or not. In this paper, we affirmatively answer this question by constructing quantum fully homomorphic encryption (QFHE) schemes with quantum obfuscation. For different scenarios, we propose two QFHE schemes with multi-valued quantum point obfuscation. One is with single-qubit point obfuscation and the other is with multi-qubit point obfuscation. The correctness of two QFHE schemes is proved theoretically. The evaluator does not know the decryption key and does not require a regular interaction with a user. The output state has the property of complete mixture, which guarantees the security. Moreover, the security level of the QFHE schemes depends on quantum obfuscation and encryption operators.

One-way functions are fundamental tools for cryptography. Until now, quantum one-way functions have several input-output categories such as `classical-to-classical', `classical-to-quantum' and `quantum-to-classical', which are used for post-quantum cryptography or quantum cryptography. However, there are still no intrinsic `quantum-to-quantum' quantum one-way functions. In this paper, we propose the full quantum one-way function to design full quantum cryptographic schemes. By concatenating the `quantum-classical' one-way function and the rotation operation of a single qubit, the full quantum one-way function has the input and output of quantum states. We prove its one-way property from `easy computation' and `computationally difficult to invert'. Then we apply the full quantum one-way function to quantum identity authentication. Security analysis shows that the proposed quantum identity authentication scheme based on the full quantum one-way function is secure even under active attacks.

Quantum cryptography has developed some fundamental primitives on encryption of quantum data, such as quantum one-time pad and quantum IND (indistinguishability)-security. Compared with other terms in quantum cryptography, quantum obfuscation attracts less attention and is still in its infancy due to its difficulty in implementation and application. In this paper, we define a quantum point function and construct its obfuscation, then demonstrate the validity of applying quantum point obfuscation to quantum symmetric encryption scheme. We rigorously prove that IND-secure quantum symmetric encryption can be realized by quantum point obfuscators. Furthermore, with the properties of combinability or auxiliary inputs, a quantum point obfuscator can implement IND-CPA (indistinguishability under chosen plaintext attack)-secure quantum symmetric encryption or leakage-resilient quantum symmetric encryption, respectively. This work presents new usage of a quantum obfuscator and will complement the theory of quantum obfuscation.