Patents play a critical role in driving technological innovation by granting inventors exclusive rights to their inventions. However the process of drafting a patent application is often expensive and time-consuming, making it a prime candidate for automation. Despite recent advancements in language models, several challenges hinder the development of robust automated patent drafting systems. First, the information within a patent application is highly confidential, which often prevents the use of closed-source LLMs for automating this task. Second, the process of drafting a patent application is difficult for even the most advanced language models due to their long context, technical writing style, and specialized domain knowledge. To address these challenges, we introduce AutoSpec, a secure, agentic framework for Automatically drafting patent Specification. Our approach decomposes the drafting process into a sequence of manageable subtasks, each solvable by smaller, open-source language models enhanced with custom tools tailored for drafting patent specification. To assess our system, we design a novel evaluation protocol in collaboration with experienced patent attorneys. Our automatic and expert evaluations show that AutoSpec outperforms existing baselines on a patent drafting task.