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Globecom

Seed analysis of universal hash functions for physical layer security in the wiretap channel

Johannes Voichtleitner, Moritz Wiese, Holger Boche

Published Dec 8, 2025• 2 citations
Publisher

Abstract

In this study, we examine different functions for the security layer of a seeded modular coding scheme for semantic security. We investigated the separation of the seed set into dispersing and non-dispersing seeds. The separation exists for all five implemented security functions in combination with all three tested error correcting codes. We show a simple procedure to reduce the probability of dispersing seeds for all security functions in two of three error correcting codes. Additionally, it was shown that Eve has an advantage in extracting information from her channel output if dispersing seeds are used. The simulations showed that this advantage can lead in special cases to a better information extraction despite larger encoding randomness. To the best of the authors’ knowledge, this is the first analytic comparison of different security functions for a seeded modular coding scheme of this kind.

DOI
10.1109/globecom59602.2025.11432053

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In this study, we examine different functions for the security layer of a seeded modular coding scheme for semantic security. We investigated the separation of the seed set into dispersing and non-dispersing seeds. The separation exists for all five implemented security functions in combination with all three tested error correcting codes. We show a simple procedure to reduce the probability of dispersing seeds for all security functions in two of three error correcting codes. Additionally, it was shown that Eve has an advantage in extracting information from her channel output if dispersing seeds are used. The simulations showed that this advantage can lead in special cases to a better information extraction despite larger encoding randomness. To the best of the authors’ knowledge, this is the first analytic comparison of different security functions for a seeded modular coding scheme of this kind.
We experimentally verify the information-theoretic security of a seeded modular code for the AWGN wiretap channel consisting of a security layer, an error-correction layer and a modulation layer. The security layer is given by a universal family of hash functions. In the error-correction layer and the modulation layer we use polar codes and QAM, respectively. The eavesdropper uses the maximum likelihood (ML) test as an attack strategy. We analyze the security in different communication scenarios using simulations. We show that for small blocklengths the advantage (security measure) at the eavesdropper in the corresponding scenario can be close to 0 for suitable code parameters. Additional insights gathered from the simulation results include the impact of code parameters and seed choice on security.
In this paper we use a seeded modular coding scheme for implementing physical layer security in a wiretap scenario. This modular scheme consists of a traditional coding layer and a security layer. For the traditional coding layer, we use a polar code. We evaluate the performance of the seeded modular coding scheme in an experimental setup with software defined radios and compare these results to simulation results. In order to assess the secrecy level of the scheme, we employ the distinguishing security metric. In our experiments, we compare the distinguishing error rate for different seeds and block lengths.
We consider reversely-degraded secure-communication channels, for which the secrecy capacity is zero if there is no channel feedback. Specifically, we focus on a seeded modular code design for the block-fading Gaussian wiretap channel with channel-output feedback, combining universal hash functions for security and learned feedback-based codes for reliability. The trade-off between communication reliability and information leakage is studied, illustrating that feedback enables agreeing on a secret key shared between legitimate parties, overcoming the security advantage of the eavesdropper. Our findings motivate code designs for sensing-assisted secure communications in the context of integrated sensing and communication (ISAC).
This paper investigates the relation between the second-order coding rate, where the second-order turns out to be strictly larger than n\sqrt{n}n​, and the mutual information as the leaked information for a fixed error probability by using wiretap codes constructed by universal2_22​ hash functions. We first generalize the upper bound on εεε-smooth max information in \cite{tyagi} and use it in our analysis where we adopt the method in \cite{hayashi-tan}, which uses universal hashing for compressing a source and making it secure from another correlated source, and apply it to the wiretap channel. We prove first- and second-order achievability results by assuming that the conjecture we state holds true.
This paper examines the use of nonsystematic channel codes to obtain secure transmissions over the additive white Gaussian noise wire-tap channel. Unlike the previous approaches, we propose to implement nonsystematic coded transmission by scrambling the information bits, and characterize the bit error rate of scrambled transmissions through theoretical arguments and numerical simulations. We have focused on some examples of Bose-Chaudhuri-Hocquenghem and low-density parity-check codes to estimate the security gap, which we have used as a measure of physical layer security, in addition to the bit error rate. Based on a number of numerical examples, we found that such a transmission technique can outperform alternative solutions. In fact, when an eavesdropper (Eve) has a worse channel than the authorized user (Bob), the security gap required to reach a given level of security is very small. The amount of degradation of Eve's channel with respect to Bob's that is needed to achieve sufficient security can be further reduced by implementing scrambling and descrambling operations on blocks of frames, rather than on single frames. While Eve's channel has a quality equal to or better than that of Bob's channel, we have shown that the use of a hybrid automatic repeat-request protocol with authentication still allows achieving a sufficient level of security. Finally, the secrecy performance of some practical schemes has also been measured in terms of the equivocation rate about the message at the eavesdropper and compared with that of ideal codes.
We study semantic security for classical-quantum channels. Our security functions are functional forms of mosaics of combinatorial designs. We extend methods in [25] from classical channels to classical-quantum channels to demonstrate that mosaics of designs ensure semantic security for classical-quantum channels, and are also capacity achieving coding schemes. An advantage of these modular wiretap codes is that we provide explicit code constructions that can be implemented in practice for every channel, given an arbitrary public code.