4 papers · 1 filter
On the matrix code of quadratic relationships for a Goppa code
Rocco Mora
In this article, we continue the analysis started in \cite{CMT23} for the matrix code of quadratic relationships associated with a Goppa code. We provide new sparse and low-rank el…
Polynomial time key-recovery attack on high rate random alternant codes
Magali Bardet, Rocco Mora, Jean-Pierre Tillich
A long standing open question is whether the distinguisher of high rate alternant codes or Goppa codes \cite{FGOPT11} can be turned into an algorithm recovering the algebraic struc…
On the dimension and structure of the square of the dual of a Goppa code
Rocco Mora, Jean-Pierre Tillich
The Goppa Code Distinguishing (GD) problem asks to distinguish efficiently a generator matrix of a Goppa code from a randomly drawn one. We revisit a distinguisher for alternant an…
Decoding Reed-Solomon codes by solving a bilinear system with a Gröbner basis approach
Magali Bardet, Rocco Mora, Jean-Pierre Tillich
Decoding a Reed-Solomon code can be modeled by a bilinear system which can be solved by Gröbner basis techniques. We will show that in this particular case, these techniques are mu…