Basics of secrecy coding

Abstract

Linear system theory over finite fields has played a major role in unveiling the properties of linear error correction codes, thus providing essential insights into key design parameters and features, such as minimal realizations, distance spectra, trapping sets, and efficient decoder structures, among others. A more recent thrust in error correction coding (linear or otherwise) is in secrecy systems, in the form of physical layer security that can complement, and in certain cases even replace, classical cryptography in specific communication settings. This chapter reviews the basic principles of secrecy coding, focusing on the properties of linear codes that approach secrecy capacity, as a precursor to understanding design strategies that attain these properties, as offered in the references. Applications beyond secure communications of these same coding techniques, notably in watermarking and steganography, are also outlined.