A post-quantum signature scheme from the secant variety of the Grassmannian

We propose a new digital signature scheme. This scheme is based on a new problem: determine a point in a shifted Grassmannian variety or on its secant variety using the knowledge of its defining polynomials. An advantage of using the secant variety of the Grassmannian is that it is defined by cubic equations, which are, in general, more difficult to solve than quadratic ones. Moreover, these equations are sparse, therefore they can be represented efficiently.