# A Class of Perfectly Secret Autonomous Low-Bit-Rate Voice Communication Systems
## 4 LSP-Based LP Synthesizer
Since this fact will affect her optimal strategy, and thus the length of the distilled keys, in the general case \(\left|K_{i}^{*}\right|\
eq\left|K_{i}\right|\). The optimal PA strategy must, therefore, rely on [PERSON]'s conditional Renyi entropy, which is  
\[A(z)=1-\sum_{i=1}^{p}a_{i}z^{-i}. \tag{8}\]8  
or in terms of their minimal values  
\[A(z)=1-\sum_{i=1}^{p}a_{i}z^{-i}. \tag{8}\]9  
**Remark 5**. : _If the conditional Renyi entropies \(R(w_{i}|e_{i})\) and \(R^{*}(w_{i}|e_{i},K_{i-1})\) were identical or slightly different \((c\approx c^{*})\), this would mean that [PERSON]'s information about the key \(K_{i-1}\) does not affect her information about the distilled key \(K_{i}\), and that, according to (28) and (29), this information decreases exponentially in the excess compression \(c^{*}-\left|K_{i}^{*}\right|\approx c-\left|K_{i}\right|\)._  
Whether this is true or not for APS-VCS, we have tested empirically, estimating these two distributions in an experiment with 1000 locally synthesized signals \(\hat{S}_{IA}\) and \(\hat{S}_{IB}\) of length 540 samples encoded with 16 bits. The SKD protocol consists of the BP algorithm for the AD phase, the Winnow algorithm for the IR phase followed by the optimal Huffman encoder and Universal hashing; see Figure 9:0 The selection and optimization of algorithms and parameters for the SKD protocol are thoroughly discussed in the works [14; 42]. In this paper, we use parameters from those works that resulted in the highest key rate with minimal information leakage. Specifically, we use the AD algorithm for two iterations, after which the error becomes sufficiently small to be corrected by the Winnow algorithm. For the IR phase, we have chosen the 8-bit Winnow algorithm, which has been shown in [31] to be optimal in terms of minimizing the information that an eavesdropper can gain during the IR phase. For the universal class of hash functions, a binary matrix with a Toeplitz structure is used since its complexity is \(O(n\cdot logn)\). Figure 13 shows the distributions of conditional Renyi entropies \(R(w_{i}|e_{i})\) and \(R^{*}(w_{i}|e_{i},K_{i-1})\), and Table 1 shows their means and variances. We can conclude that the distributions are almost identical and that extremely small differences originate from the inherent properties of random experiments on finite samples. \begin{table}
\begin{tabular}{c c} \hline
**Renyi Entropy** & **Mean \(\pm\) Std** \\ \hline \(R^{*}(w_{i}|e_{i},K_{i-1})\) & 1244.01 \(\pm\) 97.84 \\ \(R(w_{i}|e_{i})\) & 1246.66 \(\pm\) 101.49 \\ \hline \end{tabular}
\end{table} 
Table 1: Mean values and standard deviations of corresponding Renyi entropies from Figure 13.  
**Remark 6**. : _The presented theoretical analysis and experimental verification make it possible to conclude that the proposed APS-VCS system is resistant to attacks on the contents of the FIFO memories. This property logically follows from the properties of PA based on universal hash functions, as well as a sufficient amount of innovative entropy that refreshes the information content of the synthesized signals \(\hat{S}_{IA}\) and \(\hat{S}_{IB}\). Therefore, the answer to the question of whether there is an Eve strategy that provides it an advantage over SKD systems based on classical CR sources is negative._