16 citations · 16 across the 7 of their papers we have counts for
6 papers · 1 filter
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…
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…