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An accurate sense of elapsed time is essential for the safe and correct operation of hardware, software, and networked systems. Unfortunately, an adversary can manipulate the system's time and violate causality, consistency, and scheduling properties of underlying applications. Although cryptographic techniques are used to secure data, they cannot ensure time security as securing a time source is much more challenging, given that the result of inquiring time must be delivered in a timely fashion. In this paper, we first describe general attack vectors that can compromise a system's sense of time. To counter these attacks, we propose a secure time architecture, TIMESEAL that leverages a Trusted Execution Environment (TEE) to secure time-based primitives. While CPU security features of TEEs secure code and data in protected memory, we show that time sources available in TEE are still prone to OS attacks. TIMESEAL puts forward a high-resolution time source that protects against the OS delay and scheduling attacks. Our TIMESEAL prototype is based on Intel SGX and provides sub-millisecond (msec) resolution as compared to 1-second resolution of SGX trusted time. It also securely bounds the relative time accuracy to msec under OS attacks. In essence, TIMESEAL provides the capability of trusted timestamping and trusted scheduling to critical applications in the presence of a strong adversary. It delivers all temporal use cases pertinent to secure sensing, computing, and actuating in networked systems.