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Chinese Physics B

A novel quantum asymmetric key encryption scheme based on exact quantum search algorithm

Shi-Jin Zhong, Jin-Huan Li, Ying-Nan Zhao, Dai Guang-Zhen, Dao-Hua Wu

Published May 11, 2026• 0 citations
Publisher

Abstract

Abstract The quantum asymmetric key encryption (QAKE) is a prominent research frontier in quantum information. In this paper, we propose a quantum asymmetric key encryption scheme based on the exact quantum search algorithm (QAKE-EQSA). Leveraging EQSA’s deterministic amplitude amplification and a unique three-oracle structure, comprising an auxiliary oracle, its inverse, and a message-dependent oracle, the proposed QAKE-EQSA scheme guarantees a 100% decryption success rate. Within the scheme, the public key is generated by applying the auxiliary oracle to a specific quantum superposition state and subsequently shared via a public key center; the private key is constructed using a phase-matching diffusion operator; and the message is encoded into a unique target state within the search space, ensuring that only the legitimate receiver can recover it exactly. Furthermore, we demonstrate a 4-qubit instantiation of the QAKE-EQSA scheme on the MindQuantum platform and conduct a comprehensive analysis encompassing its security, qubit efficiency, and practical performance. Our analysis demonstrates that, in comparison to several existing QPKE schemes, the proposed QAKE-EQSA scheme achieves exact decryption, optimal qubit efficiency, and enhanced resistance against quantum attacks.

DOI
10.1088/1674-1056/ae6b31

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Abstract The quantum asymmetric key encryption (QAKE) is a prominent research frontier in quantum information. In this paper, we propose a quantum asymmetric key encryption scheme based on the exact quantum search algorithm (QAKE-EQSA). Leveraging EQSA’s deterministic amplitude amplification and a unique three-oracle structure, comprising an auxiliary oracle, its inverse, and a message-dependent oracle, the proposed QAKE-EQSA scheme guarantees a 100% decryption success rate. Within the scheme, the public key is generated by applying the auxiliary oracle to a specific quantum superposition state and subsequently shared via a public key center; the private key is constructed using a phase-matching diffusion operator; and the message is encoded into a unique target state within the search space, ensuring that only the legitimate receiver can recover it exactly. Furthermore, we demonstrate a 4-qubit instantiation of the QAKE-EQSA scheme on the MindQuantum platform and conduct a comprehensive analysis encompassing its security, qubit efficiency, and practical performance. Our analysis demonstrates that, in comparison to several existing QPKE schemes, the proposed QAKE-EQSA scheme achieves exact decryption, optimal qubit efficiency, and enhanced resistance against quantum attacks.
Abstract Asymmetric encryption has some important applications in the field of communication. In classical computers, most public key encryption schemes are designed based on computational assumption. In other words, they can ensure computational security. When the computing power is large enough, it will pose a threat to these encryption schemes. We propose a quantum public key encryption scheme which based on properties of quantum physics. Our scheme realizes encryption and decryption with few resources and does not rely on any computational assumption. The key in our scheme consists of classical bits and qubits. Where the private key are classical bit and public key are qubits. The public key are generated through private key. We analyze the performance and security of the scheme. Our scheme ensures the information-theoretic secure and can be implemented easily.
Quantum cryptography and quantum search algorithm are considered as two important research topics in quantum information science. An asymmetrical quantum encryption protocol based on the properties of quantum one-way function and quantum search algorithm is proposed. Depending on the no-cloning theorem and trapdoor one-way functions of the public-key, the eavesdropper cannot extract any private-information from the public-keys and the ciphertext. Introducing key-generation randomized logarithm to improve security of our proposed protocol, i.e., one private-key corresponds to an exponential number of public-keys. Using unitary operations and the single photon measurement, secret messages can be directly sent from the sender to the receiver. The security of the proposed protocol is proved that it is information-theoretically secure. Furthermore, compared the symmetrical Quantum key distribution, the proposed protocol is not only efficient to reduce additional communication, but also easier to carry out in practice, because no entangled photons and complex operations are required.
Here, we propose a quantum asymmetric key cryptography scheme using Grover's quantum search algorithm. In the proposed scheme, Alice generates a pair of public and private keys, keeps the private keys safe, and only discloses public keys to the outside. Bob uses Alice's public key to send a secret message to Alice and Alice uses her private key to decrypt the secret message. Furthermore, we discuss the safety of quantum asymmetric key encryption techniques based on quantum mechanical properties.
In the quantum era, the advent of quantum computers poses significant threats to the security of current cryptosystems. Therefore, designing quantum-resistant cryptoschemes becomes important to guarantee information security. This work concentrates on the development of the post-quantum public key encryption (PKE) scheme. Non-commutative cryptography (NCC) has entered the field of post-quantum cryptography. We utilize the TSPEM problem with asymmetric structures (which serve as a potential candiate for resisting quantum attacks) to construct two PKE schemes which are demonstrated to be CPA security under the DTSPEM assumption. By representing the plaintext as a matrix, these schemes can effectively encrypt a significant amount of information in a single operation. Assuming an equal amount of messages for encryption, the proposed schemes acheive superior efficiency compared to existing PKE schemes. Structurally, our systems exhibit a level of synchronization and coexistence due to the distinct public keys $ (P) $ and ciphertexts $ (C_{1}) .Theefficiencyanalysisisconductedbycomparingknownschemesfromtheaspectofspecificcryptographicindicators.Generally,theproposedonesofferseveraladvantagesincludingprovablesecurity,highefficiency,potentialquantum−resistant,andrelativeeaseofimplementation;alongwithsynchronizationandcoexistence.OurinvestigationhasestablishedthefeasibilityofconstructingPKEschemesbasedontheTSPEMproblem,specificallyforasymmetriccommunicationscenarios.ThepreliminaryresultspavethewayforfurtherexplorationoftheTSPEMproblem. The efficiency analysis is conducted by comparing known schemes from the aspect of specific cryptographic indicators. Generally, the proposed ones offer several advantages including provable security, high efficiency, potential quantum-resistant, and relative ease of implementation; along with synchronization and coexistence. Our investigation has established the feasibility of constructing PKE schemes based on the TSPEM problem, specifically for asymmetric communication scenarios. The preliminary results pave the way for further exploration of the TSPEM problem.Theefficiencyanalysisisconductedbycomparingknownschemesfromtheaspectofspecificcryptographicindicators.Generally,theproposedonesofferseveraladvantagesincludingprovablesecurity,highefficiency,potentialquantum−resistant,andrelativeeaseofimplementation;alongwithsynchronizationandcoexistence.OurinvestigationhasestablishedthefeasibilityofconstructingPKEschemesbasedontheTSPEMproblem,specificallyforasymmetriccommunicationscenarios.ThepreliminaryresultspavethewayforfurtherexplorationoftheTSPEMproblem ' $s potential in developing other cryptosystems suitable for quantum computing environments.
The emergence of quantum computing poses significant threats to conventional public-key cryptography, driving the urgent need for quantum-resistant cryptographic solutions. While quantum key distribution addresses secure key exchange, its dependency on symmetric keys and point-to-point limitations present scalability constraints. Quantum Asymmetric Encryption (QAE) offers a promising alternative by leveraging quantum mechanical principles for security. This paper presents the first practical implementation of a QAE protocol on IBM Quantum devices, building upon the theoretical framework originally proposed by Yoon et al. We develop a generalized Grover Search Algorithm (GSA) framework that supports non-standard initial quantum states through novel diffusion operator designs, extending its applicability beyond idealized conditions. The complete QAE protocol, including key generation, encryption, and decryption stages, is translated into executable quantum circuits and evaluated on both IBM Quantum simulators and real quantum hardware. Experimental results demonstrate significant scalability challenges, with success probabilities deteriorating considerably for larger systems. The 2-qubit implementation achieves near-perfect accuracy (100% on the simulator, and 93.88% on the hardware), while performance degrades to 78.15% (simulator) and 45.84% (hardware) for 3 qubits, and declines critically to 48.08% (simulator) and 7.63% (hardware) for 4 qubits. This degradation is primarily attributed to noise and decoherence effects in current Noisy Intermediate-Scale Quantum (NISQ) devices, highlighting the limitations of single-iteration GSA approaches. Our findings underscore the critical need for enhanced hardware fidelity and algorithmic optimization to advance the practical viability of quantum cryptographic systems, providing valuable insights for bridging the gap between theoretical quantum cryptography and real-world implementations.
Public-key cryptosystems for quantum messages are considered from two aspects: public-key encryption and public-key authentication. Firstly, we propose a general construction of quantum public-key encryption scheme, and then construct an information-theoretic secure instance. Then, we propose a quantum public-key authentication scheme, which can protect the integrity of quantum messages. This scheme can both encrypt and authenticate quantum messages. It is information-theoretic secure with regard to encryption, and the success probability of tampering decreases exponentially with the security parameter with regard to authentication. Compared with classical public-key cryptosystems, one private-key in our schemes corresponds to an exponential number of public-keys, and every quantum public-key used by the sender is an unknown quantum state to the sender.