The problem of detecting a high-dimensional signal based on compressive measurements in the presence of an eavesdropper (Eve) is studied in this paper. We assume that a large number of sensors collaborate to detect the presence of sparse signals while the Eve has access to all the information transmitted by the sensors to the fusion center (FC). A strategy to ensure secrecy that has been used in the literature is the injection of artificial noise to the raw observations of some of the nodes. However, this strategy considers a clairvoyant case where it assumes that all the noise injection sensors are aware of the true hypothesis, which may not be practical in some situations. Different from this, we propose a new method, in which falsified data are produced by a fraction of the nodes based on their own observations and sent to the FC. Moreover, we determine the optimal parameters of this system to ensure perfect secrecy at the Eve and maximize the detection performance at the FC. Simulation results demonstrate the superior performance of the proposed method.