Post-Quantum Stateless Steganography: Uniform Key Encapsulation under Strict MTU Bounds

While Stateless Steganography resolves the Authentication Trilemma and neutralizes active probing in classical elliptic-curve overlays via unilateral Zero Round-Trip Time (0-RTT) encapsulation, transitioning this paradigm to the post-quantum era introduces severe algebraic and transport-layer contradictions. In this paper, we demonstrate that a naive drop-in replacement of Elliptic Curve Diffie--Hellman (ECDH) and classical signatures with standardized post-quantum primitives (such as ML-KEM and ML-DSA) catastrophically breaks steganographic deniability under two distinct vectors. First, we formalize the Modulo Bias Invariant: standard bit-packing of lattice ciphertexts over prime moduli q ≠ 2ᵏ induces a macroscopic statistical distance from uniform noise (Δ(P, U) → 1), which compiles directly into a zero-cost O(1) passive distinguisher under the Invariant Boundary Theorem. Second, we prove the MTU Fragmentation Trap: because composite post-quantum 0-RTT envelopes exceed standard transport Maximum Transmission Unit (MTU) bounds, they force the responder to allocate stateful reassembly buffers prior to Authenticated Encryption with Associated Data (AEAD) verification, re-introducing asymmetric memory-exhaustion vulnerabilities and multi-packet dimensional invariants. To resolve both traps, we introduce Post-Quantum Stateless Steganography, combining constant-time inverse rejection sampling (or native power-of-two Learning With Rounding lattices) with two sub-MTU 0-RTT envelope architectures that strictly preserve O(1) kernel-bypass Silent Drop () and Silent Session Transition guarantees.