Protecting the privacy of input data is of growing importance as machine learning methods reach new application domains. In this paper, we provide a unified training and inference framework for large DNNs while protecting input privacy and computation integrity. Our approach called DarKnight uses a novel data blinding strategy using matrix masking to create input obfuscation within a trusted execution environment (TEE). Our rigorous mathematical proof demonstrates that our blinding process provides information-theoretic privacy guarantee by bounding information leakage. The obfuscated data can then be offloaded to any GPU for accelerating linear operations on blinded data. The results from linear operations on blinded data are decoded before performing non-linear operations within the TEE. This cooperative execution allows DarKnight to exploit the computational power of GPUs to perform linear operations while exploiting TEEs to protect input privacy. We implement DarKnight on an Intel SGX TEE augmented with a GPU to evaluate its performance.