# A Class of Perfectly Secret Autonomous Low-Bit-Rate Voice Communication Systems
## 2 System Architecture  
A generic secret low-bit-rate speech communication system is shown in Figure 1. According to the classification provided in [22], it belongs to the category of secure voice communication using modem-based cryptographic techniques. A key aspect of the information-theoretic approach to verifying the security level of a system is the amount of information an eavesdropper can obtain about the messages based on ciphertext observations. It is well known [1] that if \(C_{K}\) is generated using any cryptographic algorithm with a finite secret key \(K\), its equivocation from the attacker's perspective, \(H(K|Y)\), rapidly converges to zero after a sufficiently long ciphertext observation. Practically, this means that such a system is not information-theoretically secure, and its security depends on the computational power of the adversary. Once the amount of observed ciphertext satisfies the condition \(H(K|Y)=0\), the key \(K\) has a unique solution, meaning that, in cryptanalytic terms, the system is broken. However, if \(C_{K}\) is a purely random sequence independent of the messages \(X\), it can be shown that the mutual information \(I(Y;X)=0\). This implies that the attacker cannot retrieve the messages regardless of their computational resources, making the system perfectly secret. We selected a standard low-bit-rate vocoder MELPe with a speed of 1.2 kb/s [5,18]. Note that the MELPe vocoder can be replaced by any other standard vocoder with similar performance. The input speech signal \(S\) is sampled at 8 kHz, discretized with 16 bits per sample, and divided into frames lasting 67.5 ms (540 samples). In the MELPe analyzer, 81 bits are generated for each input frame, of which 80 bits code 10 LSP parameters of the LP speech production model, while the 81 st bit is the synchronization bit. This bit stream is encrypted by adding modulo 2 with the binary pseudorandom sequence \(C_{K}\) generated by key stream generator KSG(K) with secret key K, which must be shared between legitimate parties before the start of communication. The ciphertext \(Y\) is transmitted over the main channel after appropriate modulation. On the receiving side, after demodulation, decryption is performed. Decryption is done by adding modulo 2 with a synchronously generatedbinary sequence \(C_{K}\) on the receiving side. As a result, identical LSP parameters are obtained, which produce the reconstructed speech signal \(\hat{S}\) in the MELPe synthesizer block. With \(CR(S,\ \hat{S})\), we denoted our first candidate for the source of common randomness, formed from the input speech signal \(S\) on the transmitter side and the speech signal \(\hat{S}\) synthesized on the receiver side; see Figure 1.  
Figure 2 shows an extension of the generic scheme from Figure 1 with local MELPe synthesis on the transmitter side. \(CR(\hat{S}_{l},\ \hat{S})\) is denoted as our second candidate for the source of common randomness, formed from the locally synthesized speech signal \(\hat{S}_{l}\) on the transmitter side and the speech signal \(\hat{S}\) synthesized on the receiver side. If there are no transmission errors, the synthesis filters on the receiving and transmitting sides are equal, and the differences in the synthesized signals come from different local sources of randomness, which are used to form the complex excitation of the MELPe vocoder synthesizer. As is known [9], during the execution of the SKD protocol, in the advantage distillation (AD) and information reconciliation (IR) phases, the information exchanged between [PERSON] and [PERSON] over the public channel is available to [PERSON]. For example, if the bit parity (BP) protocol [31] is used in the AD phase, the number of parity bits of [PERSON]'s sequence that are available to [PERSON] is provided by following Lemma. Figure 1: Generic scheme of low-bit-rate secure communications using MELPe voice color.