International Association
for Cryptologic Research

Over the past years, the so called Goppa Code Distinguishing (GD) problem has been studied. The GD problem asks at recognizing a generator matrix of a binary Goppa code from a random matrix. The main motivation for introducing the GD problem is the connection to the security of the McEliece public-key cryptosytem. A main contribution in addressing this problem is the so called syzygy distinguisher. In this article, we introduce another distinguisher. From a geometric perspective, the distinguisher considers certain invariants of the space of all homogeneous polynomials that vanish in higher order on the columns of the generator matrix. Based on heuristic arguments, the distinguisher described in this article might be favorable (but not practically computable) for specific practical parameters such as the combination (m = 12, s = 64, k =768, n = 3488) compared to the values given by the syzygy distinguisher.