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Machine learning models are vulnerable to data inference attacks, such as membership inference and model inversion attacks. In these types of breaches, an adversary attempts to infer a data record's membership in a dataset or even reconstruct this data record using a confidence score vector predicted by the target model. However, most existing defense methods only protect against membership inference attacks. Methods that can combat both types of attacks require a new model to be trained, which may not be time-efficient. In this paper, we propose a differentially private defense method that handles both types of attacks in a time-efficient manner by tuning only one parameter, the privacy budget. The central idea is to modify and normalize the confidence score vectors with a differential privacy mechanism which preserves privacy and obscures membership and reconstructed data. Moreover, this method can guarantee the order of scores in the vector to avoid any loss in classification accuracy. The experimental results show the method to be an effective and timely defense against both membership inference and model inversion attacks with no reduction in accuracy.