16 citations · 16 across the 7 of their papers we have counts for
9 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…
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…
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…
The complexity of solving Weil restriction systems
Alessio Caminata, Michela Ceria, Elisa Gorla
The solving degree of a system of multivariate polynomial equations provides an upper bound for the complexity of computing the solutions of the system via Groebner bases methods.…
Solving degree, last fall degree, and related invariants
Alessio Caminata, Elisa Gorla
In this paper we study and relate several invariants connected to the solving degree of a polynomial system. This provides a rigorous framework for estimating the complexity of sol…
The complexity of MinRank
Alessio Caminata, Elisa Gorla
In this note, we leverage some of our results from arXiv:1706.06319 to produce a concise and rigorous proof for the complexity of the generalized MinRank Problem in the under-defin…
Solving multivariate polynomial systems and an invariant from commutative algebra
Alessio Caminata, Elisa Gorla
The complexity of computing the solutions of a system of multivariate polynomial equations by means of Groebner bases computations is upper bounded by a function of the solving deg…