Economic Confidentiality without Secrets: Making Intercepted LLM-Agent Communications Unusable

We study whether LLM agents can exchange useful information over a public channel without secrets (no keys, no TEEs) while making unauthorized decoding economically impractical. We formalize an “economic confidentiality” objective and design a stochastic “private language” ${L_r}$ whose parameters-embedding dimension $d$, flavor multiplicity $f$, and dilution $k$-disperse recoverable signal $S$ across long sequences with low per-token correlation. We analyze attackers that observe traffic and, in stronger scopes, possess agent weights, and we propose a back-of-the-envelope scaling law$n \approx \tfrac{k f}{S^2}\, d\log_2 d$for learning the inverse mapping to the "original legible language" ${L_u}$ represented as ${L_r}\to\{L_u}$. This scaling law is accompanied by back-of-the-envelope budget calculations to illustrate parameter trade-offs. This paper is a theoretical exploration and analysis-only: no significant system implementation or empirical evaluation are reported. While weaker than cryptographic secrecy, our conceptual modeling quantifies regimes where inverting ${L_r}$ exceeds realistic budgets-aligning with the goal of making unauthorized use uneconomical-and clarify utility-cost trade-offs in secret-less settings.