Symmetric weak ternary quantum homomorphic encryption schemes

Abstract

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.