Cryptanalysis of a McEliece Cryptosystem Based on Cascaded Goppa-Ldpc Code Encryption

This paper provides a cryptanalysis of a recently-proposed cryptosystem that uses a cascade of McEliece cryptosystems, the first using Goppa codes and the second using low-density parity-check (LDPC) codes. This cryptosystem decreases the key size while presuming to be as secure against known attacks as the original McEliece cryptosystem with Goppa codes. We show that the security of this specific cryptosystem reduces to the security of the McEliece cryptosystem instantiated with an LDPC code, upon which a key-recovery attack can be applied. As demonstrated in this paper, this reduction in security is enabled by an efficient attack against the sum of two codewords from two different codes whose generator matrices are available to the attacker. Combining this attack with the key-recovery attack, a key assumed to have 172-bit security loses 125 bits of security.