# Synthesis of Sources of Common Randomness Based on Keystream Generators with Shared Secret Keys
## 6 From Ideal Security Towards Perfect Security by SKD Based on CR KSG and Winnow IR Protocol
: _Starting from (84) and (85), we can derive expressions that relate the maximum \(\left|\widetilde{K}_{s}\right|_{max}\) and the length of the basic block \(n_{IR0}\) with \(\left|K_{G}\right|\) and the security margin \(t\)_  
\[H(W_{i}|S=s)\geq R(W_{i}|S=s)\, \tag{93}\]4  
\[H(W_{i}|S=s)\geq R(W_{i}|S=s)\, \tag{93}\]5  
_where the constants \(C_{1}\) and \(C_{2}\) are given by (83), see \[H(W_{i}|S=s)\geq R(W_{i}|S=s)\, \tag{93}\]6 For sufficiently large \(|K_{G}|\), from (106), we conclude that the asymptotic value of the maximal effective secrecy capacity is equal to \(\left|\widetilde{K}_{s}\right|_{max}=\frac{1}{2}(C_{2}-C_{1})=0.1136\), or \(11.36\%\)._  
The synthesis is straightforward and consists first of selecting \(|K_{G}|\) and \(t\), which then uniquely determine \(n_{IR0}\). Note from Figure 12a, that once \(|K_{G}|>400\), we enter the saturation region where \(\left|\widetilde{K}_{s}\right|_{max}\) does not increase by more than \(10\%\). Table 2 provides an overview of these values for standard \(|K_{G}|\) settings. **Example 2**. : _By selecting the optimal parameters \(\varepsilon_{max}=0.0525\), \(t=34\), \(\left|K_{G}\right|=512\), \(n_{IR0}=1833\), we synthesized a perfectly secret autonomous encryption system capable of protecting an information source with a rate up to \(\left|\widetilde{K}_{s}\right|_{max}=0.1043\), with \(\ KDR<2.5822\cdot 10^{-5}\), and a key leakage rate \(I(K_{s},\ K_{G};Z,S)<10^{-10}\)._  
The selection of the system's operational mode fundamentally depends on the operational environment and the prioritized security requirements. If it is assessed that the adversary does not possess computational capabilities sufficient to feasibly analyze all \(2^{\lambda_{K_{G}}}\) hypotheses regarding the applied secret key \(K_{G}\) within an acceptable timeframe, then the ideal security mode, with the corresponding equivocation bound on the secret keys, becomes the logical choice. Here, the acceptable analysis time is practically defined by the period during which the protected information retains its relevance. However, if the system is required to provide forward secrecy and ensure the impossibility of decryption regardless of the adversary's computational resources, including quantum computing, then the secret key \(K_{G}\) is not a good candidate for the secret key \(K_{G}\). \[H(W_{i}|S=s)\geq R(W_{i}|S=s)\, \tag{93}\]7 **(a)** Maximum effective secrecy capacity \(\left|\widetilde{K}_{s}\right|_{max}\) as a function of the secret key length \(\left|K_{G}\right|\) (top). The asymptotic value \(0.5\cdot(C2-C1)=0.1136\) is also shown. **(b)** Required basic data block length \(n_{IR0}\) as a function of the secret key length \(\left|K_{G}\right|\). The security margin \(t\) defining the compression rate of the applied universal hash function \(G\) is fixed at \(t=34\). the perfect secrecy mode should be selected. The trade-off in this case is a reduction in the secret key distillation rate. In the subsequent Example 3, we present two practical scenarios in which each operational mode offers distinct advantages. **Example 3**. : _Mode Selection for Secure Communications._  
Consider a secure messaging system in a high-latency environment (e.g., satellite communication). The system requires key updates every 60 s and operates with a constrained public channel. In this context, the ideal secrecy mode is appropriate--it enables higher secret key rates by tolerating a strictly bounded (but non-zero) leakage rate, ensuring timely key availability. In contrast, a critical infrastructure application (e.g., defense-grade secure storage) may prioritize zero leakage over key throughput. For such use cases, the perfect secrecy mode is preferred, despite halving the key rate, as it guarantees zero information disclosure to an adversary even under full public observation.