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This paper describes the design, implementation, and evaluation of Otak, a system that allows two non-colluding cloud providers to run machine learning (ML) inference without knowing the inputs to inference. Prior work for this problem mostly relies on advanced cryptography such as two-party secure computation (2PC) protocols that provide rigorous guarantees but suffer from high resource overhead. Otak improves efficiency via a new 2PC protocol that (i) tailors recent primitives such as function and homomorphic secret sharing to ML inference, and (ii) uses trusted hardware in a limited capacity to bootstrap the protocol. At the same time, Otak reduces trust assumptions on trusted hardware by running a small code inside the hardware, restricting its use to a preprocessing step, and distributing trust over heterogeneous trusted hardware platforms from different vendors. An implementation and evaluation of Otak demonstrates that its CPU and network overhead converted to a dollar amount is 5.4$-$385$\times$ lower than state-of-the-art 2PC-based works. Besides, Otak's trusted computing base (code inside trusted hardware) is only 1,300 lines of code, which is 14.6$-$29.2$\times$ lower than the code-size in prior trusted hardware-based works.