Privacy and security-related concerns are growing as machine learning reaches diverse application domains. The data holders want to train with private data while exploiting accelerators, such as GPUs, that are hosted in the cloud. However, Cloud systems are vulnerable to the attackers that compromise privacy of data and integrity of computations. This work presents DarKnight, a framework for large DNN training while protecting input privacy and computation integrity. DarKnight relies on cooperative execution between trusted execution environments (TEE) and accelerators, where the TEE provides privacy and integrity verification, while accelerators perform the computation heavy linear algebraic operations.