Cryptanalysis of a new instance of McEliece cryptosystem based on QC-LDPC 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.