Cryptanalysis of public-key cryptosystems that use subcodes of algebraic   geometry codes
  We give a polynomial time attack on the McEliece public key cryptosystem based on subcodes of algebraic geometry (AG) codes. The proposed attack reposes on the distinguishability of such codes from random codes using the Schur product. Wieschebrink treated the genus zero case a few years ago but his approach cannot be extent straightforwardly to other genera. We address this problem by introducing and using a new notion, which we call the t-closure of a code. 
Alain Couvreur (INRIA Saclay - Ile de France), Irene   M\'arquez-Corbella (INRIA Saclay - Ile de France), Ruud Pellikaan
cs.IT cs.CR math.AG math.IT