# A Class of Perfectly Secret Autonomous Low-Bit-Rate Voice Communication Systems
## 1 Introduction  
In this paper, we asked the following question: Is it possible to design an autonomous, perfectly secret speech communication system whose integral part is the subsystem for the generation and distribution of the required amount of secret keys in real time? As is known [1], the Vernam cipher [2] or One-Time-Pad (OTP) [3] satisfies the condition of perfect secrecy, and the price to be paid is that the secret key rate is equal to the message rate. The need for secret keys decreases proportionally with the message rate, justifying the use of low-bit-rate voice coders in practical implementations [4, 5, 6]. However,the problem of efficient generation and distribution of secret keys in the case of the Vernam cipher is still open. While physical key distribution remains the simplest but impractical option over long distances, more modern approaches, such as quantum key distribution and the use of physical entropy sources, provide promising methods for future systems. Quantum key distribution stands out for its provably secure nature, though it requires significant infrastructure [7]. In the group of methods that use physical entropy sources, a special place is occupied by the methods of generating and distributing secret keys using sequential key distillation (SKD) protocols by public discussion [8; 9; 10]. Their application requires two prerequisites:  
* Sources of common randomness with sufficient capacity shared by communication parties (Alice, Bob)
* An additional authenticated communication channel of appropriate capacity, which may be public, and which is assumed to be wiretapped by an attacker (Eve). By far, most solutions in this category take the wireless channel itself as a physical source of common randomness [11; 12; 13]. However, we exclude this approach due to our requirement for system autonomy, which implies independence from the used communication channel. A small number of remaining papers are dominantly related to various biometric signals as sources of common randomness [14; 15; 16]. However, there are no solutions that would be based on common randomness sources independent of the used telecommunication channels while guaranteeing the secret key generation speed equal to low-bit-rate vocoder speeds of 1.2 kb/s or 2.4 kb/s. While most existing works investigate key generation protocols in a particular environment, very few of them focus on the joint design of key generation and OTP. A straightforward way is cascading or parallel key generation and OTP, but more complex constructions appear in the literature. For example, in [17], it was proved that using a non-reconciled key for OTP outperforms classical identical key OTP. In the first step of the proposed system's design, we select a standard low-bit-rate vocoder MELPe with a speed of 1.2 kb/s [5; 18] and an appropriate authenticated public channel, which must be available during system operation. In the second step, based on extensive tests of this vocoder in real working conditions within the vPCP-V system [19], we identify a source of common randomness suitable for generating and distributing secret keys at speeds far higher than 1.2 kb/s. This source consists of a locally synthesized speech signal on the transmitting side (Alice) and a corresponding synthesized signal on the receiving side (Bob). The differences between these signals come from different local sources of randomness, which are used to form the complex excitation of the MELP vocoder synthesizer. This source of shared randomness can be used in the open speech mode, which, as a rule, precedes the phase of secure voice communication. All information about input voice that flows through the public channel to Eve during the execution of the SKD protocol is of no importance since communication is also open through the main channel. However, in the phase of protected communication on the main channel, this information will significantly reduce the uncertainty of the input voice.