Although language model (LM) agents are demonstrating growing potential in many domains, their success in cybersecurity has been limited due to simplistic design and the lack of fundamental features for this domain. We present EnIGMA, an LM agent for autonomously solving Capture The Flag (CTF) challenges. EnIGMA introduces new Agent-Computer Interfaces (ACIs) to improve the success rate on CTF challenges. We establish the novel Interactive Agent Tool concept, which enables LM agents to run interactive command-line utilities essential for these challenges. Empirical analysis of EnIGMA on over 350 CTF challenges from three different benchmarks indicates that providing a robust set of new tools with demonstration of their usage helps the LM solve complex problems and achieves state-of-the-art results on the NYU CTF and Intercode-CTF benchmarks. Finally, we discuss insights on ACI design and agent behavior on cybersecurity tasks that highlight the need to adapt real-world tools for LM agents.