Section: New Results
Compact McEliece Keys from Algebraic-geometry codes
In 1978, McEliece [31], introduced a public key
cryptosystem based on linear codes and suggested to use classical
Goppa codes which belong to the family of alternant codes. This
proposition remains secure but leads to very large public keys
compared to other public-key cryptosystems. Many proposals have been
made in order to reduce the key size, in particular quasi-cyclic
alternant codes. Quasi-cyclic alternant codes refer to alternant
codes admitting a generator matrix made of severals cyclic
bloks. These alternant codes contains weakness because they have a
non-trivial automorphism group. Thanks to this property we can
build, from a quasi-cyclic alternant code, an alternant code with
smaller parameters which has almost same private elements than the
original code. Faugère, Otmani, Tillich, Perret and Portzamparc
[29] showed this fact for alternant codes
obtained by using supports
In order to suggest compact keys for the McEliece cryptosystem E. Barelli and A. Couvreur studied quasi-cyclic alternant gemeotric codes. Alternant geometric codes means a subfield subcode of an algebraic-geometry codes. To build these codes, we need curves with automorphisms. In particular, we studied Kummer cover of plane curves.