  This paper describes our ongoing work on security verification against
inference attacks on data trees. We focus on infinite secrecy against inference
attacks, which means that attackers cannot narrow down the candidates for the
value of the sensitive information to finite by available information to the
attackers. Our purpose is to propose a model under which infinite secrecy is
decidable. To be specific, we first propose tree transducers which are
expressive enough to represent practical queries. Then, in order to represent
attackers' knowledge, we propose data tree types such that type inference and
inverse type inference on those tree transducers are possible with respect to
data tree types, and infiniteness of data tree types is decidable.
