Description
The McEliece cryptosystem is based on classical Goppa codes over F_2. Generalizations of the McEliece cryptosystem using Goppa codes over larger fields F_q were investigated but not found to offer advantages for small q. We showed that codes over F_31 offer advantages in key size compared to codes over F_2 while maintaining the same security level against all attacks known. However, codes over smaller fields such as F_3 were still not competitive in key size with binary codes.<br/> The "wild McEliece cryptosystem" uses wild Goppa codes over finite fields to achieve smaller public key sizes compared to the original McEliece cryptosystem. This proposal makes "larger tiny fields" attractive and bridges the gap between F_2 and F_31. We added an extra shield to the wild McEliece cryptosystem, slightly increasing key sizes but drastically increasing the pool of Goppa polynomials to choose from.