# Synthesis of Sources of Common Randomness Based on Keystream Generators with Shared Secret Keys
## 10 Conclusions  
This paper introduces a new SKD paradigm using synthetic CR based on KSG with shared secret key and locally generated binary Bernoulli noise. We have shown that the introduced source of CR meets all the requirements mentioned in the introduction of the paper: general accessibility, integrity, optimality, and key security. This paradigm offers a comprehensive approach to secure key distribution, combining theoretical rigor with practical applicability. The proposed design has been both theoretically analyzed and practically validated, demonstrating the following key features:  
* Parameter-controlled equivocation: The system allows for adjustable equivocation levels, enabling fine-tuning of security parameters to meet specific requirements. * High-efficiency Winnow-based reconciliation: By implementing the Winnow protocol, the design achieves efficient error reconciliation with reduced communication overhead, enhancing overall system performance. * Autonomous key refresh: The architecture supports automatic key renewal processes, ensuring sustained security without manual intervention. * Secure operation without AD: The system maintains robust security standards without relying on AD techniques, simplifying the implementation. * Explicit optimal design: The framework is explicitly optimized to maximize the secrecy capacity of distilled keys while minimizing potential information leakage to eavesdroppers. * Dual modes of operation: The system can operate in two distinct modes--ideal and perfect secrecy--providing flexibility to adapt to various security scenarios. Based on the experimental verification, the proposed SKD system reliably achieves secret key rates close to the theoretical secrecy capacity while maintaining low BER and high collision entropy. The consistent high levels of entropy across repeated simulations confirm that the system remains secure against passive eavesdroppers even under finite-length conditions, thus making it suitable for practical lightweight secure communication systems. As a direction for future work, we aim to extend the current framework to support adaptive SKD systems that dynamically adjust key generation parameters in response to real-time system conditions, such as varying bit error rates and entropy availability. Another promising direction involves exploring hardware implementations of the proposedarchitecture under resource-constrained settings, including IoT and edge computing environments. Additionally, integrating post-quantum primitives with the CR KSG model could enhance resilience against future quantum adversaries while maintaining the system's autonomous operation and bounded leakage guarantees. Finally, we note that proposed general system design is readily applicable to other information reconciliation protocols, including those based on BCH, LDPC, and Polar Codes (PC) [57], with the potential to extend the optimization methodologies demonstrated here using the Winnow protocol. Conceptualization, D.C. and M.M. ; methodology, D.C. and M.M. ; software, J.R., N.L., T.U. and M.V. ; validation, M.M., J.R., N.L., T.U. and M.V. ; formal analysis, D.C. and M.M. ; investigation, D.C., M.M., J.R. and N.L. ; resources, J.R. and M.V. ; data curation, D.C., J.R., N.L., T.U. and M.V. ; writing--original draft preparation, D.C.; writing--review and editing, M.M. and J.R.; visualization, M.M. and J.R.; supervision, M.M. and M.V. ; project administration, D.C., J.R. and N.L. ; funding acquisition, D.C., M.M., T.U. and M.V. All authors have read and agreed to the published version of the manuscript. The research is funded by the Vlatacom Institute of High Technologies under Project #164 EEG_Keys. The raw data supporting the conclusions of this article will be made available by the authors on request. [PERSON] would like to thank his wife [PERSON] for her long-standing support and patience. He dedicates the first five theorems in Sections 3 and 4 to his five grandchildren: [PERSON], [PERSON], [PERSON], [PERSON], and [PERSON]. The authors declare no conflicts of interest.