Can a Large Language Model Serve as a Covert Channel? A Trilemma of Signal-to-Noise, Kripkenstein Rules, and Asociality

Imagine you want an LLM to secretly answer "yes" or "no" when direct answers are forbidden. You agree on a code word. This paper argues it cannot be done reliably while staying hidden. Three things get in the way. First, plain information theory: a common code is ambiguous, a rare one is easy to detect. Second, Kripke's paradox of following rules: the LLM has no fact of the matter that would fix the code's meaning on a new question. Third, the model lacks the social practice – the shared form of life – that lets humans resolve that paradox. Put together, these three conditions make a reliable covert one‑bit channel impossible. I use basic math (Shannon, Zipf) and a simple linear detector to show why.