Analysis and simulation of cryptographic techniques based on sparse graph with application to satellite and airborne communication systems

In view of the future diffusion of quantum computers, many of the cryptographic systems currently in use must be rethought. This drastic but concrete preview has led us to reflect on a possible solution based on error correction code theory. In fact, many lines of thought are in agreement with the possibility of using error correctly codes not only for channel encoding, but also for encryption. In 1978 McEliece was the first to propose this idea, at those time not very much considered because with worse performance in the area of cryptography compared to other techniques, but today re-evaluated. The Low Density Parity Check codes (LDPC) are state-of-art in error correction since they can be decoded efficiently close to the Shannon capacity. Thanks to new advances in the algorithmic aspects of code theory and progress on linear-time encodable/decodable codes it is possible to achieve capacity even against adversarial noise. This thesis work mainly focuses on the decoding (or in terms of cryptography in the decryption) of LDPC codes through the implementation of Hard Decision Iterative Decoding with the aim of studying the performances for different codes belonging to the same LDPC family in terms of error correction capability.