Key reduction of McEliece's cryptosystem using list decoding

Different variants of the code-based McEliece cryptosystem were proposed to reduce the size of the public key. All these variants use very structured codes, which open the door to new attacks exploiting the underlying structure. In this paper, we show that the quasi-dyadic variant can be designed to resist all known attacks. In light of a new study on list decoding algorithms for binary Goppa codes, we explain, as already suggested by Bernstein, Lange and Peters, how to increase the security level for given public keysizes. Using the state-of-the-art list decoding algorithm instead of unique decoding, we exhibit a keysize gain of about 4% for the standard McEliece cryptosystem and up to 21% for the adjusted quasi-dyadic variant.