As more applications are built on top of blockchain and public ledger, different approaches are developed to improve the performance of blockchain construction. Recently Intel proposed a new concept of proof-of-elapsed-time (PoET), which leverages trusted computing to enforce random waiting times for block construction. However, trusted computing component may not be perfect and 100% reliable. It is not clear, to what extent, blockchain systems based on PoET can tolerate failures of trusted computing component. The current design of PoET lacks rigorous security analysis and a theoretical foundation for assessing its strength against such attacks. To fulfill this gap, we develop a theoretical framework for evaluating a PoET based blockchain system, and show that the current design is vulnerable in the sense that adversary can jeopardize the blockchain system by only compromising Θ (log log n/log n) fraction of the participating nodes, which is very small when n is relatively large. Based on our theoretical analysis, we also propose methods to mitigate these vulnerabilities.