# A Class of Perfectly Secret Autonomous Low-Bit-Rate Voice Communication Systems
## 1 Introduction
### Related Works  
To focus on relevant research, it is essential to recall the fundamental requirements that a highly secure voice protection system must meet [21]. Security Requirements:  
* Strong end-to-end encryption--only legitimate parties should be able to encrypt and decrypt the communication. * Key management procedures must be designed in a way that does not compromise the declared security level of the system. * A secure key agreement must be ensured. * The choice of encryption algorithm and secret key length must support the proclaimed security level. Functionality Requirements:  
* The system must be resistant to distortions introduced by GSM codecs, which are designed for speech transmission over mobile networks rather than encrypted speech, which is inherently a data stream. * Minimization of transmission error rates--this requirement is crucial for low-bit-rate vocoders. The analytical-synthetic approach of vocoders inherently reduces the quality of synthesized speech on the receiving side, meaning that additional transmission errors must be minimized. According to the classification provided in [22], most research falls into two distinct categories:  
* Secure voice communication using modem-based cryptographic techniques
* Secure voice communication based on chaotic cryptographic techniques  
Due to the generic structure of modem-based cryptographic techniques, the vPCP-V system belongs to this category [22; 23]. Therefore, our primary focus will be on this class of systems. Table 2 in ref. [22] summarizes the performance of 22 systems published up to 2022. Without exception, all solutions are based on standard cryptographic algorithms with finite secret keys (AES, RC4, TEA) and rely on conventional public key infrastructure (PKI) for key generation and distribution. As a result, these systems do not ensure autonomy, as they depend on a Trusted Third Party (TTP), nor do they achieve perfect secrecy, since their secret key rates are far below the speech data rate they encrypt. In [24], a practical implementation of a lightweight AES algorithm (128-bit key) in FPGA technology for peer-to-peer voice encryption was analyzed. It is evident that this work falls within the same category of non-autonomous and non-perfectly secret systems. Similarly, ref. [25] proposes a new VoIPChain system for authentication in Voice over IP using Ethereum Blockchain technology [26]. While this decentralized system overcomes many security issues associated with traditional single-server PKI infrastructures, it still requires a security infrastructure, including maintaining a shared ledger. Consequently, this system also falls under the category of non-autonomous, non-perfectly secret voice transmission systems. Furthermore, ref. [27] presents various security concepts and communication systems proposed by NATO Research Task Group IST-174, titled \"Secure Underwater Communications for Heterogeneous Network-enabled Operations\". These efforts contribute to standardization in the field. Recognizing that key allocation and management remain major challenges in symmetric cryptographic systems, the study identifies SKD protocols over appropriate sources of common randomness as one of the most promising technologies, which is fully aligned with our findings. However, it is important to note that this workdoes not discuss the use of SKD for real-time perfectly secret systems, but only in the context of traditional non-perfect cryptographic systems. In the category of secure voice communication based on chaotic cryptographic techniques, seven solutions published up to 2019 were analyzed in [22]. Additionally, we incorporated the latest studies [28; 29; 30] into this review. Secure voice communication systems based on chaotic cryptographic techniques leverage chaotic algorithms due to their sensitivity to initial conditions and their ability to generate pseudo-randomness, both of which are essential for secure encryption.