This paper presents our extensive investigation of the security aspects of control plane procedures based on dynamic testing of the control components in operational Long Term Evolution (LTE) networks. For dynamic testing in LTE networks, we implemented a semi-automated testing tool, named LTEFuzz, by using open-source LTE software over which the user has full control. We systematically generated test cases by defining three basic security properties by closely analyzing the standards. Based on the security property, LTEFuzz generates and sends the test cases to a target network, and classifies the problematic behavior by only monitoring the device-side logs. Accordingly, we uncovered 36 vulnerabilities, which have not been disclosed previously. These findings are categorized into five types: Improper handling of (1) unprotected initial procedure, (2) crafted plain requests, (3) messages with invalid integrity protection, (4) replayed messages, and (5) security procedure bypass. We confirmed those vulnerabilities by demonstrating proof-of-concept attacks against operational LTE networks. The impact of the attacks is to either deny LTE services to legitimate users, spoof SMS messages, or eavesdrop/manipulate user data traffic. Precise root cause analysis and potential countermeasures to address these problems are presented as well. Cellular carriers were partially involved to maintain ethical standards as well as verify our findings in commercial LTE networks.