2021/12/20 by A. Caminata, Caminata, Alessio, Michela Ceria +3
Computer Science · Mathematics · #Coding theory and cryptography #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.2112.10506
openalex publication_date 2021/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. In this paper, we consider polynomial systems that are obtained via Weil restriction of scalars. The latter is an arithmetic construction which, given a finite Galois field extension k\hookrightarrow K, associates to a system F defined over K a system Weil(F) defined over k, in such a way that the solutions of F over K and those of Weil(F) over k are in natural bijection. In this paper, we find upper bounds for the complexity of solving a polynomial system Weil(F) obtained via Weil restriction in terms of algebraic invariants of the system F.