Joint channel coding-cryptography based on random insertions and deletions in quasi-cyclic-low-density parity check codes

In this paper, a new secure channel coding scheme is presented which randomly inserts and deletes bits in a codeword of a quasi-cyclic-low-density parity check (QC-LDPC) code. It is shown that the key size is smaller than other code-based cryptosystems based on permutation and scrambling matrices. The positions of the inserted and deleted bits are determined using a secret key. It is shown that the error performance of the resulting code after the insertions and deletions is better than a random low-density parity check code with similar parameters. An important advantage of this cryptosystem is that even if the QC-LDPC code is revealed, the system remains secure. Furthermore, the proposed approach using insertions and deletions can be employed with other classes of error correcting codes.