Advancements in DeepFake (DF) audio models pose a significant threat to voice authentication systems, leading to unauthorized access and the spread of misinformation. We introduce a defense mechanism, SecureSpectra, addressing DF threats by embedding orthogonal, irreversible signatures within audio. SecureSpectra leverages the inability of DF models to replicate high-frequency content, which we empirically identify across diverse datasets and DF models. Integrating differential privacy into the pipeline protects signatures from reverse engineering and strikes a delicate balance between enhanced security and minimal performance compromises. Our evaluations on Mozilla Common Voice, LibriSpeech, and VoxCeleb datasets showcase SecureSpectra's superior performance, outperforming recent works by up to 71% in detection accuracy. We open-source SecureSpectra to benefit the research community.