Interactive PNR-KE without feedback: feasibility versus lower bounds

Determine whether there exist fully interactive pseudorandom noise-resilient key exchange (PNR-KE) protocols that do not rely on noiseless feedback and achieve substantially stronger security than non-interactive constructions, or alternatively extend the current lower bounds and quasipolynomial-time attacks for non-interactive PNR-KE to the interactive setting to demonstrate that such barriers are inherent rather than artifacts of non-interactivity.

Background

The paper introduces pseudorandom noise-resilient key exchange (PNR-KE) and gives two positive results: a construction based on learning sparse parities with noise (yielding plausible quasipolynomial security) and a stronger construction in a noiseless-feedback model sufficient for the main application. It also proves negative results, including impossibility of public pseudorandom codes under constant noise and quasipolynomial-time attacks on any non-interactive PNR-KE (or any protocol that yields a weakly correlated non-interactive hidden bit).

These findings leave open whether interaction—without assuming noiseless feedback—can evade the quasipolynomial attacks that apply to non-interactive protocols, yielding substantially stronger PNR-KE; conversely, it is unknown whether the lower bounds can be extended to the fully interactive setting, which would show that the obstacles identified for non-interactive protocols are fundamental. Resolving this would clarify the true feasibility and limits of PNR-KE without feedback.