We investigate the integration of Conformal Prediction (CP) with supervised learning on deterministically encrypted data, aiming to bridge the gap between rigorous uncertainty quantification and privacy-preserving machine learning. Using AES-encrypted variants of the MNIST dataset, we demonstrate that CP methods remain effective even when applied directly in the encrypted domain, owing to the preservation of data exchangeability under fixed-key encryption. We test traditional $p$-value-based against $e$-value-based conformal predictors. Our empirical evaluation reveals that models trained on deterministically encrypted data retain the ability to extract meaningful structure, achieving 36.88\% test accuracy -- significantly above random guessing (9.56\%) observed with per-instance encryption. Moreover, $e$-value-based CP achieves predictive set coverage of over 60\% with 4.3 loss-threshold calibration, correctly capturing the true label in 4888 out of 5000 test cases. In contrast, the $p$-value-based CP yields smaller predictive sets but with reduced coverage accuracy. These findings highlight both the promise and limitations of CP in encrypted data settings and underscore critical trade-offs between prediction set compactness and reliability. %Our work sets a foundation for principled uncertainty quantification in secure, privacy-aware learning systems.