  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.
