Secretly Pruned Convolutional Codes: Security Analysis and Performance Results

Abstract

Constructions of secure channel encoders, based on secret pruning, are considered in this paper. The key defines how pruning is applied on a mother convolutional code. This results in a secret subspace that legitimate users are using to perform decoding, in contrast to an eavesdropper that employs the mother code. Both reliability and security aspects of the joint scheme are treated. We derive the expected weight enumerating function of the secret subcode and show that the legitimate users achieve a better performance (that depends on the pruning rate) in terms of word and bit error rate compared with the eavesdroppers. The security relies on the notion of indistinguishability against chosen plaintext attacks. The security proofs are given in the random oracle model, and it is shown that a randomized version of the proposed joint scheme is semantically secure by relying on the hardness of the learning parities with noise problem. The above-mentioned results are achieved by introducing a new model for physical encryption to consider the contribution of the channel noise to the system’s security.