Secure autonomous secret key distillation (SKD) systems traditionally depend on external common randomness (CR) sources, which often suffer from instability and limited reliability over long-term operation. In this work, we propose a novel SKD architecture that synthesizes CR by combining a keystream of a shared-key keystream generator KSG(KG) with locally generated binary Bernoulli noise. This construction emulates the statistical properties of the classical Maurer satellite scenario while enabling deterministic control over key parameters such as bit error rate, entropy, and leakage rate (LR). We derive a closed-form lower bound on the equivocation of the shared-secret key KG from the viewpoint of an adversary with access to public reconciliation data. This allows us to define an admissible operational region in which the system guarantees long-term secrecy through periodic key refreshes, without relying on advantage distillation. We integrate the Winnow protocol as the information reconciliation mechanism, optimized for short block lengths (N=8), and analyze its performance in terms of efficiency, LR, and final key disagreement rate (KDR). The proposed system operates in two modes: ideal secrecy, achieving secret key rates up to 22% under stringent constraints (KDR < 10−5, LR < 10−10), and perfect secrecy mode, which approximately halves the key rate. Notably, these security guarantees are achieved autonomously, without reliance on advantage distillation or external CR sources. Theoretical findings are further supported by experimental verification demonstrating the practical viability of the proposed system under realistic conditions. This study introduces, for the first time, an autonomous CR-based SKD system with provable security performance independent of communication channels or external randomness, thus enhancing the practical viability of secure key distribution schemes.
Secure autonomous secret key distillation (SKD) systems traditionally depend on external common randomness (CR) sources, which often suffer from instability and limited reliability over long-term operation. In this work, we propose a novel SKD architecture that synthesizes CR by combining a keystream of a shared-key keystream generator KSG(KG) with locally generated binary Bernoulli noise. This construction emulates the statistical properties of the classical Maurer satellite scenario while enabling deterministic control over key parameters such as bit error rate, entropy, and leakage rate (LR). We derive a closed-form lower bound on the equivocation of the shared-secret key KG from the viewpoint of an adversary with access to public reconciliation data. This allows us to define an admissible operational region in which the system guarantees long-term secrecy through periodic key refreshes, without relying on advantage distillation. We integrate the Winnow protocol as the information reconciliation mechanism, optimized for short block lengths (N=8), and analyze its performance in terms of efficiency, LR, and final key disagreement rate (KDR). The proposed system operates in two modes: ideal secrecy, achieving secret key rates up to 22% under stringent constraints (KDR < 10−5, LR < 10−10), and perfect secrecy mode, which approximately halves the key rate. Notably, these security guarantees are achieved autonomously, without reliance on advantage distillation or external CR sources. Theoretical findings are further supported by experimental verification demonstrating the practical viability of the proposed system under realistic conditions. This study introduces, for the first time, an autonomous CR-based SKD system with provable security performance independent of communication channels or external randomness, thus enhancing the practical viability of secure key distribution schemes.
This paper studies the problem of extracting common randomness (CR) or secret keys from correlated random sources observed by two legitimate parties, Alice and Bob, through public discussion in the presence of an eavesdropper, Eve. We propose a practical two-stage CR extraction framework. In the first stage, the variational probabilistic quantization (VPQ) step is introduced, where Alice and Bob employ probabilistic neural network (NN) encoders to map their observations into discrete, nearly uniform random variables (RVs) with high agreement probability while minimizing information leakage to Eve. This is realized through a variational learning objective combined with adversarial training. In the second stage, a secure sketch using code-offset construction reconciles the encoder outputs into identical secret keys, whose secrecy is guaranteed by the VPQ objective. As a representative application, we study physical layer key (PLK) generation. Beyond the traditional methods, which rely on the channel reciprocity principle and require two-way channel probing, thus suffering from large protocol overhead and being unsuitable in high mobility scenarios, we propose a sensing-based PLK generation method for integrated sensing and communications (ISAC) systems, where paired range-angle (RA) maps measured at Alice and Bob serve as correlated sources. The idea is verified through both end-to-end simulations and real-world software-defined radio (SDR) measurements, including scenarios where Eve has partial knowledge about Bob's position. The results demonstrate the feasibility and convincing performance of both the proposed CR extraction framework and sensing-based PLK generation method.
We study common randomness where two parties have access to i.i.d. samples from a known random source, and wish to generate a shared random key using limited (or no) communication with the largest possible probability of agreement. This problem is at the core of secret key generation in cryptography, with connections to communication under uncertainty and locality sensitive hashing. We take the approach of treating correlated sources as a critical resource, and ask whether common randomness can be generated resource-efficiently. We consider two notable sources in this setup arising from correlated bits and correlated Gaussians. We design the first explicit schemes that use only a polynomial number of samples (in the key length) so that the players can generate shared keys that agree with constant probability using optimal communication. The best previously known schemes were both non-constructive and used an exponential number of samples. In the amortized setting, we characterize the largest achievable ratio of key length to communication in terms of the external and internal information costs, two well-studied quantities in theoretical computer science. In the relaxed setting where the two parties merely wish to improve the correlation between the generated keys of length k, we show that there are no interactive protocols using o(k) bits of communication having agreement probability even as small as 2–o(k). For the related communication problem where the players wish to compute a joint function f of their inputs using i.i.d samples from a known source, we give a simultaneous message passing protocol using 2O(c) bits where c is the interactive randomized public-coin communication complexity of f. This matches the lower bound shown previously while the best previously known upper bound was doubly exponential in c. Our schemes reveal a new connection between common randomness and unbiased error-correcting codes, e.g., dual-BCH codes and their analogues in Euclidean space.
We propose a new high-speed secret key distillation system via public discussion based on the common randomness contained in the speech signal of the protocol participants. The proposed system consists of subsystems for quantization, advantage distillation, information reconciliation, an estimator for predicting conditional Renyi entropy, and universal hashing. The parameters of the system are optimized in order to achieve the maximum key distillation rate. By introducing a deep neural block for the prediction of conditional Renyi entropy, the lengths of the distilled secret keys are adaptively determined. The optimized system gives a key rate of over 11% and negligible information leakage to the eavesdropper, while NIST tests show the high cryptographic quality of produced secret keys. For a sampling rate of 16 kHz and quantization of input speech signals with 16 bits per sample, the system provides secret keys at a rate of 28 kb/s. This speed opens the possibility of wider application of this technology in the field of contemporary information security.
This paper presents a system for secure digital voice signal transmission over the GSM mobile network (Global System for Mobile Communication). The cryptographic part of the system is based on Vernam cipher, which requires the same speed of generating secret symmetric keys as the basic information flow in the main channel. The system for generating and distributing secret keys for Vernam cipher is realized based on the correlation properties of the locally synthesized speech signal of the transmitter and the corresponding receiving speech signal. By applying the method of sequential distillation of secret keys (SKD) on the mentioned source of common randomness, the generation speed of up to 34 kb/s is ensured, which is more than enough to maintain the absolute secrecy of Vernam cipher. The price that needs to be paid is the necessity of having an additional authenticated public channel through which the SKD protocol is performed. The privacy amplification block, as a necessary part of the SKD protocol, was implemented using machine learning methods, in order to reliably estimate the conditional Renyi entropy of the second order. According to our knowledge, this is the first autonomous, perfectly secret system for voice transmission over the GSM network without explicit prior generation and distribution of secret keys.
Secret key agreement in distributed low-power networks, such as Internet of Things (IoT) networks, is a major requirement for deploying cryptographic protocols to protect the security of sensitive data. However, due to the distributed nature of such networks, the devices need to be able to generate secret keys locally from some common source of randomness. The randomness in the characteristics of the physical layer channel provides such sources, however, this can be quite limited if the devices operate in a static environment and experience static or very slow fading channel. Therefore, fast secret key generation in such environments while keeping a low complexity architecture for the network nodes, such as IoT devices, remains a challenging task. We design a low-complexity protocol for fast secret key generation in static environments. To this end, we propose to use a limited number of random bits independently generated by the legitimate parties, referred to as Alice and Bob, in combination with the fading parameter to create a common source of randomness. In the proposed protocol, Alice and Bob share their random bits over the public channel, assumed to be a fading channel, and then construct a common random sequence. Then they perform several steps for recovery from errors in the shared sequence, privacy amplification to limit the chances of a successful attack, and consistency checking by exploiting universal hash functions. We characterize the reliability of the proposed protocol and provide an upper bound on the probability of accepting a mismatched key by Alice and Bob. The eavesdropper Eve is assumed to be passive and a successful attack by her is the event of guessing the key right based on her observations. We provide an analytical upper bound, that can be numerically evaluated, on the probability of a successful attack by Eve using the cryptographic notion of semantic security. In the simulations, the proposed protocol achieves a bit generation rate of 64-96 bits/packet, bit mismatch rate of 11-24%, bit error rate of 0.005%, 50% randomness efficiency, the probability of successful attack of at most 2-31, and the probability of consistency checking failure of at most 2-16.
This paper presents an autonomous perfectly secure low-bit-rate voice communication system (APS-VCS) based on the mixed-excitation linear prediction voice coder (MELPe), Vernam cipher, and sequential key distillation (SKD) protocol by public discussion. An authenticated public channel can be selected in a wide range, from internet connections to specially leased radio channels. We found the source of common randomness between the locally synthesized speech signal at the transmitter and the reconstructed speech signal at the receiver side. To avoid information leakage about open input speech, the SKD protocol is not executed on the actual transmitted speech signal but on artificially synthesized speech obtained by random selection of the linear spectral pairs (LSP) parameters of the speech production model. Experimental verification of the proposed system was performed on the Vlatacom Personal Crypto Platform for Voice encryption (vPCP-V). Empirical measurements show that with an adequate selection of system parameters for voice transmission of 1.2 kb/s, a secret key rate (KR) of up to 8.8 kb/s can be achieved, with a negligible leakage rate (LR) and bit error rate (BER) of order 10−3 for various communications channels, including GSM 3G and GSM VoLTE networks. At the same time, by ensuring perfect secrecy within symmetric encryption systems, it further highlights the importance of the symmetry principle in the field of information-theoretic security. To our knowledge, this is the first autonomous, perfectly secret system for low-bit-rate voice communication that does not require explicit prior generation and distribution of secret keys.