arXiv subjects
Publications and source records attributed to Elise Barelli.
We present an efficient key recovery attack on code based encryption schemes using some quasi-dyadic alternant codes with extension degree 2. This attack permits to break the proposal DAGS recently submitted to NIST.
In this paper we study the security of the key of compact McEliece schemes based on alternant/Goppa codes with a non-trivial permutation group, in particular quasi-cyclic alternant codes. We show that it is possible to reduce the key-recovery problem on the original quasi-cyclic code to the same problem on a smaller code derived from the public key. This result is obtained thanks to the invariant code operation which gives the subcode whose elements are fixed by a permutation in Perm(C). The fundamental advantage is that the invariant subcode of an alternant code is an alternant code. This approach improves the technique of Faugere, Otmani, Tillich, Perret and Portzamparc which uses folded codes of alternant codes obtained by using supports globally stable by an affine map. We use a simpler approach with a unified view on quasi-cyclic alternant codes and we treat the case of automorphisms arising from a non affine homography. In addition, we provide an efficient algorithm to recover the full structure of the alternant code from the structure of the invariant code.
We improve previously known lower bounds for the minimum distance of certain two-point AG codes constructed using a Generalized Giulietti-Korchmaros curve (GGK). Castellanos and Tizziotti recently described such bounds for two-point codes coming from the Giulietti-Korchmaros curve (GK). Our results completely cover and in many cases improve on their results, using different techniques, while also supporting any GGK curve. Our method builds on the order bound for AG codes: to enable this, we study certain Weierstrass semigroups. This allows an efficient algorithm for computing our improved bounds. We find several new improvements upon the MinT minimum distance tables.