Consider the Gaussian wiretap channel, where a transmitter wishes to send a confidential message to a legitimate receiver in the presence of an eavesdropper. It is well known that if the eavesdropper experiences less channel noise than the legitimate receiver, then it is impossible for the transmitter to achieve positive secrecy rates. A known solution to this issue consists in involving a second transmitter, referred to as a helper, to help the first transmitter to achieve security. While such a solution has been studied for the asymptotic blocklength regime and via non-constructive coding schemes, in this paper, for the first time, we design explicit and short blocklength codes using deep learning and cryptographic tools to demonstrate the benefit and practicality of cooperation between two transmitters over the wiretap channel. Specifically, our proposed codes show strict improvement in terms of information leakage compared to existing codes that do not consider a helper. Our code design approach relies on a reliability layer, implemented with an autoencoder architecture based on the successive interference cancellation method, and a security layer implemented with universal hash functions. We also propose an alternative autoencoder architecture that significantly reduces training time by allowing the decoders to independently estimate messages without successively canceling interference by the receiver during training. Additionally, we show that our code design is also applicable to the multiple access wiretap channel with helpers, where two transmitters send confidential messages to the legitimate receiver.

Consider the Gaussian wiretap channel, where a legitimate transmitter wishes to send a confidential message to a legitimate receiver in the presence of an eavesdropper. Unfortunately, in this setting, it is well known that if the eavesdropper experiences less channel noise than the legitimate receiver, then it is impossible for the transmitter to achieve positive secrecy rates. A known solution to this issue consists in involving a second transmitter, referred to as a helper, to help the first transmitter to achieve security. While such a solution has been studied for the asymptotic blocklength regime and via non-constructive coding schemes, in this paper, for the first time, we design explicit and short blocklength codes using deep learning and cryptographic tools to demonstrate the benefit and practicality of cooperation between two transmitters over the wiretap channel. Specifically, our proposed codes show strict improvement in terms of information leakage compared to existing point-to-point codes that do not consider a helper, even when the transmitter has adverse channel conditions, in the sense that the eavesdropper experiences less channel noise than the legitimate receiver. Our code design approach relies on a reliability layer, implemented with an autoencoder architecture inspired by the successive interference cancellation method developed for broadcast channels, and a security layer implemented with universal hash functions.

Consider a secret sharing model where a dealer shares a secret with several participants through a Gaussian broadcast channel such that predefined subsets of participants can reconstruct the secret and all other subsets of participants cannot learn any information about the secret. Our first contribution is to show that, in the asymptotic blocklength regime, it is optimal to consider coding schemes that rely on two coding layers, namely, a reliability layer and a secrecy layer, where the reliability layer is a channel code for a compound channel without any security constraint. Our second contribution is to design such a two-layer coding scheme at short blocklength. Specifically, we design the reliability layer via an autoencoder, and implement the secrecy layer with hash functions. To evaluate the performance of our coding scheme, we empirically evaluate the probability of error and information leakage, which is defined as the mutual information between the secret and the unauthorized sets of users channel outputs. We empirically evaluate this information leakage via a neural network-based mutual information estimator. Our simulation results demonstrate a precise control of the probability of error and leakage thanks to the two-layer coding design.

We design short blocklength codes for the Gaussian wiretap channel under information-theoretic security guarantees. Our approach consists in decoupling the reliability and secrecy constraints in our code design. Specifically, we handle the reliability constraint via an autoencoder, and handle the secrecy constraint with hash functions. For blocklengths smaller than or equal to 128, we evaluate through simulations the probability of error at the legitimate receiver and the leakage at the eavesdropper for our code construction. This leakage is defined as the mutual information between the confidential message and the eavesdropper’s channel observations, and is empirically measured via a neural network-based mutual information estimator. Our simulation results provide examples of codes with positive secrecy rates that outperform the best known achievable secrecy rates obtained non-constructively for the Gaussian wiretap channel. Additionally, we show that our code design is suitable for the compound and arbitrarily varying Gaussian wiretap channels, for which the channel statistics are not perfectly known but only known to belong to a pre-specified uncertainty set. These models not only capture uncertainty related to channel statistics estimation, but also scenarios where the eavesdropper jams the legitimate transmission or influences its own channel statistics by changing its location.

In this paper, we study an information-theoretic secret sharing problem, where a dealer distributes shares of a secret among a set of participants under the following constraints: (i) authorized sets of users can recover the secret by pooling their shares, and (ii) non-authorized sets of colluding users cannot learn any information about the secret. We assume that the dealer and participants observe the realizations of correlated Gaussian random variables and that the dealer can communicate with participants through a one-way, authenticated, rate-limited, and public channel. Unlike traditional secret sharing protocols, in our setting, no perfectly secure channel is needed between the dealer and the participants. Our main result is a closed-form characterization of the fundamental trade-off between secret rate and public communication rate.

We design short blocklength codes for the Gaussian wiretap channel under information-theoretic security guarantees. Our approach consists in decoupling the reliability and secrecy constraints in our code design. Specifically, we handle the reliability constraint via an autoencoder, and handle the secrecy constraint via hash functions. For blocklengths smaller than 16, we evaluate through simulations the probability of error at the legitimate receiver and the leakage at the eavesdropper of our code construction. This leakage is defined as the mutual information between the confidential message and the eavesdropper’s channel observations, and is empirically measured via a recent mutual information neural estimator. Simulation results provide examples of codes with positive rates that achieve a leakage inferior to one percent of the message length.

We study a secret sharing problem, where a dealer distributes shares of a secret among a set of participants under the constraints that (i) authorized sets of users can recover the secret by pooling their shares, (ii) non-authorized sets of colluding users cannot learn any information about the secret. We assume that the dealer and the participants observe the realizations of correlated Gaussian random variables and that the dealer can communicate with the participants through a one-way, authenticated, rate-limited, and public channel. Our main result is a closed-form characterization of the trade-off between secret rate and public communication rate. Unlike traditional secret sharing protocols, in our setting, no perfectly secure channel is needed between the dealer and the participants, and the size of the shares does not depend exponentially but rather linearly on the number of participants and the size of the secret for arbitrary access structures.