Distribution system topology identification has historically been accomplished by unencrypting the information that is received from the smart meters and then running a topology identification algorithm. Unencrypted smart meter data introduces privacy and security issues for utility companies and their customers. This paper introduces security aware machine learning algorithms to alleviate the privacy and security issues raised with un-encrypted smart meter data. The security aware machine learning algorithms use the information received from the Advanced Metering Infrastructure (AMI) and identifies the distribution systems topology without unencrypting the AMI data by using fully homomorphic NTRU and CKKS encryption. The encrypted smart meter data is then used by Linear Discriminant Analysis, Convolution Neural Network, and Support Vector Machine algorithms to predict the distribution systems real time topology. This method can leverage noisy voltage magnitude readings from smart meters to accurately identify distribution system reconfiguration between radial topologies during operation under changing loads.