# Synthesis of Sources of Common Randomness Based on Keystream Generators with Shared Secret Keys  
[PERSON]  
1 Vlatacom Institute of High Technology, Milutina Milankovica 5, 11070 Belgrade, Serbia;  
[EMAIL_ADDRESS] (D.C.); [EMAIL_ADDRESS] (M.M.);  
[EMAIL_ADDRESS] (N.L.); [EMAIL_ADDRESS] (T.U.);  
[EMAIL_ADDRESS] (M.V.);  
[PERSON]  
1 Vlatacom Institute of High Technology, Milutina Milankovica 5, 11070 Belgrade, Serbia;  
[EMAIL_ADDRESS] (D.C.); [EMAIL_ADDRESS] (M.M.);  
[EMAIL_ADDRESS] (M.N.L.); [EMAIL_ADDRESS] (T.U.);  
miljan.  
proposed CR source is based on a shared-key keystream generator \(KSG(K_{G})\), combined with locally injected Bernoulli noise. This construction ensures equivalence with the classical Maurer satellite scenario [1] while affording precise and deterministic control over critical parameters, including key disagreement rate (KDR), secret key rate, and information leakage rate (LR). To fulfill these requirements, the synthesized CR source is required to satisfy the following conditions:  
1. General Accessibility: Both parties ([PERSON] and [PERSON]) can implement and observe the CR source efficiently.
2. Integrity: An adversary ([PERSON]) cannot influence or manipulate the generation parameters of the CR source.
3. Optimality: The CR synthesis mechanism must be designed to maximize the achievable secrecy capacity of the SKD system, thereby operating at theoretical efficiency bounds.
4. Key Security: The integration of the CR source with the SKD protocol must ensure provably secure key generation with rigorously bounded information LR, under the assumption that the adversary employs an optimal inference strategy based on complete knowledge of the public discussion and system specifications.  
A key contribution of this work is the derivation of a closed-form lower bound on the equivocation of the secret key \(K_{G}\), ensuring provable secrecy even in the presence of public reconciliation data. This analytical result facilitates the rigorous characterization of an admissible operational region wherein long-term secrecy can be maintained through periodic key refresh without relying on traditional advantage distillation (AD) techniques.  
The remainder of this paper is organized as follows:  
Section 2 provides an overview of related works and discusses the key contributions and innovations of this study.  
Section 3 presents the overall system architecture, detailing each component and their interactions within the SKD framework.  
Section 4 provides an information-theoretic analysis of the proposed CR source, including the derivation of equivocation bounds and operation constraints.  
Section 5 describes the design and performance analysis of the optimized CR KSG and Winnow reconciliation protocol with emphasis on secrecy performance and implementation feasibility.  
Section 6 introduces two system operating modes of SKD based on CR KSG and Winnow reconciliation protocol: ideal secure and perfect secure mode.  
Section 7 presents a computational complexity analysis of the proposed system and highlights its advantages compared to traditional SKD systems that rely on natural sources of common randomness.  
Section 8 presents experimental verification to validate the theoretical analysis developed in Sections 4-6.  
Section 9 provides security analysis and discusses practical considerations, implementation trade-offs, and design guidelines for deployment in real-world settings.  
Section 10 concludes the paper with a summary of results and directions for future research.