5 papers
Algebraic Modelings of the Supersingular Isogeny Problem
Alessio Caminata, Andrea Sanguineti, Silvia Sconza
We present a new algebraic modeling of the Supersingular Isogeny Problem as a system of multivariate polynomial equations, in the case where the elliptic curves are connected by an…
Solving Polynomial Systems with Gröbner Bases: An Introduction to F4 and FGLM
Anna Maria Bigatti, Alessio Caminata, Tor Kristian Ellingsen +3
These notes originate from a reading course held by the authors in the spring of 2024 at the Università di Genova. They provide a hands-on introduction to the F4 and FGLM algorithm…
Cryptanalysis of a multivariate CCZ scheme
Alessio Caminata, Elisa Gorla, Madison Mabe +2
We consider the multivariate scheme Pesto, which was introduced by Calderini, Caminata, and Villa. In this scheme, the public polynomials are obtained by applying a CCZ transformat…
A new multivariate primitive from CCZ equivalence
Marco Calderini, Alessio Caminata, Irene Villa
Multivariate Cryptography is one of the candidates for Post-quantum Cryptography. Multivariate schemes are usually constructed by applying two secret affine invertible transformati…
Quadratic Modelings of Syndrome Decoding
Alessio Caminata, Ryann Cartor, Alessio Meneghetti +2
This paper presents enhanced reductions of the bounded-weight and exact-weight Syndrome Decoding Problem (SDP) to a system of quadratic equations. Over , we improve o…