  Blind quantum computation protocols allow a user to delegate a computation to
a remote quantum computer in such a way that the privacy of their computation
is preserved, even from the device implementing the computation. To date, such
protocols are only known for settings involving at least two quantum devices:
either a user with some quantum capabilities and a remote quantum server or two
or more entangled but noncommunicating servers. In this work, we take the first
step towards the construction of a blind quantum computing protocol with a
completely classical client and single quantum server. Specifically, we show
how a classical client can exploit the ambiguity in the flow of information in
measurement-based quantum computing to construct a protocol for hiding critical
aspects of a computation delegated to a remote quantum computer. This ambiguity
arises due to the fact that, for a fixed graph, there exist multiple choices of
the input and output vertex sets that result in deterministic measurement
patterns consistent with the same fixed total ordering of vertices. This allows
a classical user, computing only measurement angles, to drive a
measurement-based computation performed on a remote device while hiding
critical aspects of the computation.
