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Federated learning (FL) has increasingly been deployed, in its vertical form, among organizations to facilitate secure collaborative training over siloed data. In vertical FL (VFL), participants hold disjoint features of the same set of sample instances. Among them, only one has labels. This participant, known as the active party, initiates the training and interacts with the other participants, known as the passive parties. Despite the increasing adoption of VFL, it remains largely unknown if and how the active party can extract feature data from the passive party, especially when training deep neural network (DNN) models. This paper makes the first attempt to study the feature security problem of DNN training in VFL. We consider a DNN model partitioned between active and passive parties, where the latter only holds a subset of the input layer and exhibits some categorical features of binary values. Using a reduction from the Exact Cover problem, we prove that reconstructing those binary features is NP-hard. Through analysis, we demonstrate that, unless the feature dimension is exceedingly large, it remains feasible, both theoretically and practically, to launch a reconstruction attack with an efficient search-based algorithm that prevails over current feature protection techniques. To address this problem, we develop a novel feature protection scheme against the reconstruction attack that effectively misleads the search to some pre-specified random values. With an extensive set of experiments, we show that our protection scheme sustains the feature reconstruction attack in various VFL applications at no expense of accuracy loss.