We consider the framework of the McEliece cryptosystem based on low-density parity-check (LDPC) codes, which is a promising post-quantum alternative to classical public key cryptosystems. The use of LDPC codes in this context allows to achieve good security levels with very compact keys, which is an important advantage over the classical McEliece cryptosystem based on Goppa codes. However, only regular LDPC codes have been considered up to now, while some further improvement can be achieved by using irregular LDPC codes, which are known to achieve better error correction performance than regular LDPC codes. This is shown in this paper, for the first time at our knowledge. The possible use of irregular transformation matrices is also investigated, which further increases the efficiency of the system, especially in regard to the public key size.

In this paper, we carry out a practical assessment of the performance of finite-length LDPC codes over the wiretap channel with fast Rayleigh fading. Classical metrics for physical layer security, like the secrecy capacity, are based on information theoretic arguments, and provide the ultimate security bounds for these schemes. However, it is difficult to design practical schemes, using some specific finite-length code, able to approach such a performance. Then we use a more practical metric, based on the error probability, which allows assessing the performance achieved in terms of both reliability and security over the fast Rayleigh fading wire-tap channel.

In this paper, we provide a tight estimation of the security gap for the wiretap channel with fast Rayleigh fading. The error rate has already been used as a practical physical layer security metric, and the security gap has been defined to exploit such a metric over the wiretap channel with additive white Gaussian noise. We study two different approaches for estimating the security gap also over a fast fading wiretap channel. The first approach is quite conservative, and tends to overestimate the security gap. The second approach instead allows to perform a more realistic evaluation, and to highlight the gain achievable through information scrambling and coding, even when both the legitimate receiver and the eavesdropper channels are known only in statistical terms.

We investigate and compare different options for updating the error correcting code currently used in space mission telecommand links. Taking as a reference the solutions recently emerged as the most promising ones, based on Low-Density Parity-Check codes, we explore the behavior of alternative schemes, based on parallel concatenated turbo codes and soft-decision decoded BCH codes. Our analysis shows that these further options can offer similar or even better performance.

In the context of public key cryptography, the McEliece cryptosystem represents a very smart solution based on the hardness of the decoding problem, which is believed to be able to resist the advent of quantum computers. Despite this, the original McEliece cryptosystem based on Goppa codes, has encountered limited interest in practical applications, partly because of some constraints imposed by this very special class of codes. The authors have recently introduced a variant of the McEliece cryptosystem including low‐density parity‐check codes, that are state‐of‐the‐art codes, now used in many telecommunication standards and applications. In this study, the authors discuss the possible use of a bit‐flipping decoder in this context, which gives a significant advantage in terms of complexity. The authors also provide theoretical arguments and practical tools for estimating the trade‐off between security and complexity, in such a way to give a simple procedure for the system design.

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.

Binary linear [n,k] codes that are proper for error detection are known for many combinations ofnandk. For the remaining combinations, existence of proper codes is conjectured. In this paper, a particular class of [n,k] codes is studied in detail. In particular, it is shown that these codes are proper for many combinations ofnandkwhich were previously unsettled.

This paper is a first study on the usage of non-systematic codes based on scrambling matrices for physical layer security. The chance of implementing transmission security at the physical layer is known since many years, but it is now gaining an increasing interest due to its several possible applications. It has been shown that channel coding techniques can be effectively exploited for designing physical layer security schemes, in such a way that an unauthorized receiver, experiencing a channel different from that of the authorized receiver, is not able to gather any information. Recently, it has been proposed to exploit puncturing techniques in order to reduce the security gap between the authorized and unauthorized channels. In this paper, we show that the security gap can be further reduced by using non-systematic codes, able to scramble information bits within the transmitted codeword.