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

TL;DR

This paper introduces four symmetric ternary quantum homomorphic encryption schemes based on the ternary quantum one-time pad, enabling secure quantum computations on ternary quantum data with proven security properties.

Contribution

The paper presents novel symmetric ternary quantum homomorphic encryption schemes for various quantum gates, extending security analysis and potential integration into quantum cloud computing.

Findings

Schemes protect user data with high probability of security against attackers.

Encryption schemes are applicable to multi-qutrit quantum transformations.

Security analysis confirms robustness of the proposed schemes.

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.