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arXiv:1505.02854

Symmetric Ternary Quantum Homomorphic Encryption Schemes Based on the Ternary Quantum One-Time Pad

Yuqi Wang, Kun She, Qing-bin Luo, Fan Yang, Chao Zhao

Published May 12, 2015• 1 citation
arXivHTMLPDF

Abstract

Aiming at a ternary quantum logic circuit, four symmetric ternary quantum homomorphic encryption schemes, based on ternary quantum one-time protocol, were presented. First, for a one-qutrit rotation gate, a homomorphic quantum encryption scheme was constructed. Second, in view of the synthesis of a 3x3 general unitary transformation, another one-qutrit quantum homomorphic encryption scheme was proposed. Third, according to the one-qutrit scheme, the two-qutrit quantum homomorphic encryption scheme about GCX(m') gate was constructed and was further generalized to the n-qutrit unitary matrix case. Finally, the security of these schemes was analyzed from two perspectives. It could be concluded that the attacker can correctly guess the encryption key with a maximum probability ${p_k} = {1 \mathord{\left/ {\vphantom {1 {3^{3n}}}} \right. \kern-\nulldelimiterspace} {3^{3n}}}$, thus it can better protect the privacy of users' data. Moreover these schemes can be well integrated into future quantum remote server architecture, and the computational security of the user's private quantum information can be well solved in a distributed computing environment.

DOI
10.48550/arxiv.1505.02854

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Aiming at a ternary quantum logic circuit, four symmetric ternary quantum homomorphic encryption schemes, based on ternary quantum one-time protocol, were presented. First, for a one-qutrit rotation gate, a homomorphic quantum encryption scheme was constructed. Second, in view of the synthesis of a 3x3 general unitary transformation, another one-qutrit quantum homomorphic encryption scheme was proposed. Third, according to the one-qutrit scheme, the two-qutrit quantum homomorphic encryption scheme about GCX(m') gate was constructed and was further generalized to the n-qutrit unitary matrix case. Finally, the security of these schemes was analyzed from two perspectives. It could be concluded that the attacker can correctly guess the encryption key with a maximum probability {p_k} = {1 \mathord{\left/ {\vphantom {1 {3^{3n}}}} \right. \kern-\nulldelimiterspace} {3^{3n}}}, thus it can better protect the privacy of users' data. Moreover these schemes can be well integrated into future quantum remote server architecture, and the computational security of the user's private quantum information can be well solved in a distributed computing environment.
Based on a ternary quantum logic circuit, four symmetric weak ternary quantum homomorphic encryption (QHE) schemes were proposed. First, for a one-qutrit rotation gate, a QHE scheme was constructed. Second, in view of the synthesis of a general [Formula: see text] unitary transformation, another one-qutrit QHE scheme was proposed. Third, according to the one-qutrit scheme, the two-qutrit QHE scheme about generalized controlled [Formula: see text] (GCX([Formula: see text])) gate was constructed and further generalized to the [Formula: see text]-qutrit unitary matrix case. Finally, the security of these schemes was analyzed in two respects. It can be concluded that the attacker can correctly guess the encryption key with a maximum probability [Formula: see text], thus it can better protect the privacy of users’ data. Moreover, these schemes can be well integrated into the future quantum remote server architecture, and thus the computational security of the users’ private quantum information can be well protected in a distributed computing environment.
The significant advantage of the quantum homomorphic encryption scheme is to ensure the perfect security of quantum private data. In this paper, a novel secure multiparty quantum homomorphic encryption scheme is proposed, which can complete arbitrary quantum computation on the private data of multiple clients without decryption by an almost dishonest server. Firstly, each client obtains a secure encryption key through the measurement device independent quantum key distribution protocol and encrypts the private data by using the encryption operator and key. Secondly, with the help of the almost dishonest server, the non-maximally entangled states are pre-shared between the client and the server to correct errors in the homomorphic evaluation of T gates, so as to realize universal quantum circuit evaluation on encrypted data. Thirdly, from the perspective of the application scenario of secure multi-party computation, this work is based on the probabilistic quantum homomorphic encryption scheme, allowing multiple parties to delegate the server to perform the secure homomorphic evaluation. The operation and the permission to access the data performed by the client and the server are clearly pointed out. Finally, a concrete security analysis shows that the proposed multiparty quantum homomorphic encryption scheme can securely resist outside and inside attacks.
Suppose some data have been encrypted, can you compute with the data without decrypting them? This problem has been studied as homomorphic encryption and blind computing. We consider this problem in the context of quantum information processing, and present the definitions of quantum homomorphic encryption (QHE) and quantum fully homomorphic encryption (QFHE). Then, based on quantum one-time pad (QOTP), we construct a symmetric QFHE scheme, where the evaluate algorithm depends on the secret key. This scheme permits any unitary transformation on any nnn-qubit state that has been encrypted. Compared with classical homomorphic encryption, the QFHE scheme has perfect security. Finally, we also construct a QOTP-based symmetric QHE scheme, where the evaluate algorithm is independent of the secret key.
Secure multi-party computation has been playing a fundamental role in terms of classical cryptography. Quantum homomorphic encryption (QHE) could compute the encrypted data without decryption. At present, most protocols use a semi-honest third party (TP) to protect participants’ secrets. We use a quantum homomorphic encryption scheme instead of TP to protect the privacy of parties. Based on quantum homomorphic encryption, a secure multi-party quantum summation scheme is proposed in which N participants can delegate a server with strong quantum computing power to assist computation. By delegating the computation and key update processes to a server and a semi-honest key center, participants encrypt their private information data using Pauli operators to get the sum. Besides, the server can design and optimize the summation lines itself, and the correct results can be obtained even if the secret information is negative. The correctness analysis showed that the participants could correctly obtain the results of the calculation. The security analysis proves the scheme is resistant to both outside attack and participant’s attack, and is secure against collusive attack by up to N-2 participants. From the theoretical point of view, our protocol can extend to other secure multi-party computing problems.
Homomorphic encryption has giant advantages in the protection of privacy information. In this paper, we present a new kind of probabilistic quantum homomorphic encryption scheme for the universal quantum circuit evaluation. Firstly, the pre-shared non-maximally entangled states are utilized as auxiliary resources, which lower the requirements of the quantum channel, to correct the errors in non-Clifford gate evaluation. By using the set synthesized by Clifford gates and T gates, it is feasible to perform the arbitrary quantum computation on the encrypted data. Secondly, our scheme is different from the previous scheme described by the quantum homomorphic encryption algorithm. From the perspective of application, a two-party probabilistic quantum homomorphic encryption scheme is proposed. It is clear what the computation and operation that the client and the server need to perform respectively, as well as the permission to access the data. Finally, the security of probabilistic quantum homomorphic encryption scheme is analyzed in detail. It demonstrates that the scheme has favorable security in three aspects, including privacy data, evaluated data and encryption and decryption keys.
Abstract Quantum homomorphic encryption is the corresponding technology of classical homomorphic encryption in the quantum field. Due to its ability to ensure the correctness of computation and the security of data, it is particularly suitable for delegated computation in quantum cloud networks. However, previous schemes were unable to simultaneously handle the volatility problem of servers dynamically and eliminate the error caused by homomorphic evaluation of T-gate non-interactively. Therefore, a multi-party dynamic quantum homomorphic encryption scheme based on rotation operators is proposed in this paper. Firstly, the proposed scheme uses the rotation operators to solve the phase gate error that occurs during the homomorphic evaluation of T-gate non-interactively. Secondly, the scheme can dynamically deal with instability of servers, such as adding a server or removing a server. Then, the trusted key center is introduced, which is responsible for key updating and circuit replacement, which lowers the requirements for quantum capabilities on the client. Finally, this scheme extends the single-client multi-server model to the multi-client multi-server model, making it more suitable for quantum distributed networks and enhancing its practicality. In addition, we theoretically prove the correctness and fully homomorphic property of the proposed scheme, and verify it through the simulation conducted on the IBM Quantum Experience. Security analysis and efficiency analysis further demonstrate that the proposed scheme is information-theoretically secure and possesses high qubit efficiency.