In this talk, I will present a novel algebraic approach for attacking the McEliece cryptosystem which is currently at the 4-th round of the NIST post-quantum standardization process. The contributions are twofold.
(1) A new distinguisher on alternant and Goppa codes working in a much broader range of parameters than previous distinguishers is introduced and its complexity analysed;
(2) With this approach, a polynomial-time key recovery attack on alternant and Goppa codes of high-rate and under some conditions on their field size and degree is also provided.