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Hardware components can contain hidden backdoors, which can be enabled with catastrophic effects or for ill-gotten profit. These backdoors can be inserted by a malicious insider on the design team or a third-party IP provider. In this paper, we propose techniques that allow us to build trustworthy hardware systems from components designed by untrusted designers or procured from untrusted third-party IP providers. We present the first solution for disabling digital, design-level hardware backdoors. The principle is that rather than try to discover the malicious logic in the design -- an extremely hard problem -- we make the backdoor design problem itself intractable to the attacker. The key idea is to scramble inputs that are supplied to the hardware units at runtime, making it infeasible for malicious components to acquire the information they need to perform malicious actions. We show that the proposed techniques cover the attack space of deterministic, digital HDL backdoors, provide probabilistic security guarantees, and can be applied to a wide variety of hardware components. Our evaluation with the SPEC 2006 benchmarks shows negligible performance loss (less than 1% on average) and that our techniques can be integrated into contemporary microprocessor designs.