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 adopt a class of quasi-cyclic low-density parity-check codes that allow to overcome the main limitations of the original McEliece cryptosystem based on Goppa codes, that are large key size and low transmission rate. The codes are designed by using a new algorithm based on "random difference families" that permits to construct very large sets of equivalent codes. An extensive cryptanalysis is developed to verify the security level achievable through a selected choice of the system parameters. While previous versions of the McEliece cryptosystem based on LDPC codes are vulnerable to the considered attacks, a new scheme is proposed that ensures satisfactory system robustness with reduced key size and increased transmission rate. Moreover, it is established that the new cryptosystem can be fast enough to justify its adoption as an alternative to widespread solutions, like RSA.

In this paper, a new variant of the McEliece cryptosystem, based on quasi-cyclic low-density parity-check (QC-LDPC) codes, is studied. In principle, such codes can substitute Goppa codes, originally used by McEliece; their adoption, however, is subject to cryptanalytic evaluation to ensure sufficient system robustness. The authors conclude that some families of QC-LDPC codes, based on circulant permutation matrices, are inapplicable in this context, due to security issues, whilst other codes, based on the "difference families" approach, can be able to ensure a good level of security against intrusions, even if very large lengths are needed.

In this paper, we deal with time-invariant spatially coupled low-density parity-check convolutional codes (SC-LDPC-CCs). Classic design approaches usually start from quasi-cyclic low-density parity-check block codes and exploit suitable unwrapping procedures to obtain SC-LDPC-CCs. We show that the direct design of the SC-LDPC-CCs syndrome former matrix or, equivalently, the symbolic parity-check matrix, leads to codes with smaller syndrome former constraint lengths with respect to the best solutions available in the literature. We provide theoretical lower bounds on the syndrome former constraint length for the most relevant families of SC-LDPC-CCs, under constraints on the minimum length of cycles in their Tanner graphs. We also propose new code design techniques that approach or achieve such theoretical limits.