# Synthesis of Sources of Common Randomness Based on Keystream Generators with Shared Secret Keys
## 2 Related Works and Contributions  
The foundation of secret key agreement from correlated random sources was laid by works of [PERSON] [2], [PERSON] [3], and [PERSON] [1], who introduced the satellite scenario to formalize secrecy generation in the presence of an eavesdropper. This model has since inspired significant research, particularly in quantum key distribution (QKD) and physical layer security, where the main sources of CR are different observable and measurable characteristics of the wireless communication channels between legitimate parties [4; 5; 6; 7; 8; 9; 10; 11].  
A principal limitation of secret key extraction from wireless channels lies in its strong dependence on channel dynamics and fluctuations, which significantly constrains the achievable secret key rate. Under conditions of frequent fading or deliberate jamming by an adversary, the volume of extractable secret key material typically becomes negligible, thereby rendering practical deployment infeasible [8; 12].  
Subsequent research has broadened the applicability of SKD beyond the physical layer, incorporating diverse CR source models, including those based on biometric signals [13; 14; 15; 16]. However, a critical limitation of biometric signals as CR sources stems from the intrinsically bounded entropy of biometric patterns. In operational contexts requiring continuous and reliable real-time secret key generation, such sources are generally unsuitable or restricted to a limited subset of communication modalities--most notably, voice-based systems [16].  
Artificial generation of common randomness via pseudorandom constructs has also been investigated, yet with limited attention to closed-form entropy analysis or integration with adaptive SKD protocols [12; 17]. Notably, prior designs often depend on unstable or external entropy sources with inconsistent long-term performance.  
Recent surveys have comprehensively analyzed key agreement and authentication protocols in IoT environments [18] and the use of intelligent reflecting surfaces to enhance physical layer secret key generation [19], emphasizing the practical challenges of secure key establishment under varying physical conditions. In parallel, advances in quantum information processing and integrated photonic platforms have led to high-performance heterodyne receivers supporting secure quantum random number generation and continuous-variable quantum key distribution (CV-QKD) with high secret key rates [20]. Techniques for establishing common randomness through round-trip travel times in packet data networks have been explored as a novel frontier in physical layer security, enabling secrecy level adaptation based on the similarity of common randomness [21]. Furthermore, random modulation has been utilized to enhance secret key generation over atmospheric optical channels, demonstrating practical improvements in the robustness and efficiency of key distribution schemes [22]. These developments collectively underscore the growing interest in autonomous and adaptable secret key generation mechanisms across classical, quantum, and hybrid environments, aligning with the motivation of the present study to design a scalable SKD system with bounded leakage and autonomous operation.  
More recently, equivocation-based analysis, following [PERSON]'s original concept of ideal secrecy, has been used to evaluate the robustness of cryptographic protocols against adversaries observing public exchanges [23]. However, existing systems rarely incorporate mechanisms to ensure a quantifiable lower bound on equivocation over time.  
This paper addresses these gaps by proposing a theoretically grounded and practically implementable system for CR synthesis based on deterministic keystream generators. It further integrates a high-efficiency, short-block Winnow protocol for reconciliation, optimized for minimal communication overhead and robustness under constrained bit error rate (BER) conditions.