We give a polynomial time attack on the McEliece public key cryptosystem  
based on algebraic geometry codes. Roughly speaking, this attacks runs in 
O(n^4) operations in GF(q), where n denotes the code length. Compared to 
previous attacks, allows to recover a decoding algorithm for the public 
key even for codes from high genus curves.
This is joint work of Alain Couvreur, Irene Marquez-Corbella and Ruud Pellikaan