Synthesis of Sources of Common Randomness Based on Keystream Generators with Shared Secret Keys - Dejan Cizelj; Milan Milosavljević; Jelica Radomirović; Nikola Latinović; Tomislav Unkašević; Miljan Vučetić (Mathematics)
Secure autonomous secret key distillation (SKD) systems traditionally depend on external common randomness (CR) sources, which often suffer from instability and limited reliability over long-term operation. In this work, we propose a novel SKD architecture that synthesizes CR by combining a keystream of a shared-key keystream generator <semantics>KSG(KG)</semantics> with locally generated binary Bernoulli noise. This construction emulates the statistical properties of the classical Maurer satellite scenario while enabling deterministic control over key parameters such as bit error rate, entropy, and leakage rate (LR). We derive a closed-form lower bound on the equivocation of the shared-secret key <semantics> KG</semantics> from the viewpoint of an adversary with access to public reconciliation data. This allows us to define an admissible operational region in which the system guarantees long-term secrecy through periodic key refreshes, without relying on advantage distillation. We integrate the Winnow protocol as the information reconciliation mechanism, optimized for short block lengths (<semantics>N=8</semantics>), and analyze its performance in terms of efficiency, LR, and final key disagreement rate (KDR). The proposed system operates in two modes: ideal secrecy, achieving secret key rates up to 22% under stringent constraints (KDR < 10−5, LR < 10−10), and perfect secrecy mode, which approximately halves the key rate. Notably, these security guarantees are achieved autonomously, without reliance on advantage distillation or external CR sources. Theoretical findings are further supported by experimental verification demonstrating the practical viability of the proposed system under realistic conditions. This study introduces, for the first time, an autonomous CR-based SKD system with provable security performance independent of communication channels or external randomness, thus enhancing the practical viability of secure key distribution schemes.