A differentially private security system communicatively coupled to a database storing restricted data receives a database query from a client. The database query includes a relation indicative of data to perform the query upon and at least one privacy parameter indicative of a level of differential privacy with which to perform the query. The differentially private security system determines a noise type for the query. The differentially private security system determines a representation of probabilistic privacy loss for the query based on the determined noise type. The differentially private security system determines a privacy spend for the query using the generated representation of probabilistic privacy loss. The differentially private security system determines whether the determined privacy spend exceeds a privacy budget associated with the client.