Stronger bounds on the cost of computing Gröbner bases for HFE systems. (March 2022)

• Record Type: Journal Article
• Authors: Gorla, Elisa; Mueller, Daniela; Petit, Christophe
• Is Part Of: Journal of symbolic computation. Volume 109(2022)
• Page Start: 386
• Page End: 398
• Publication Date: 2022-03
• Subjects: Multivariate cryptography -- Gröbner bases -- HFE -- (Fake) Weil descent -- Last fall degree -- Solving degree; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2020.07.011
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We give upper bounds for the solving degree and the last fall degree of the polynomial system associated to the HFE (Hidden Field Equations) cryptosystem. Our bounds improve the known bounds for this type of systems. We also present new results on the connection between the solving degree and the last fall degree and prove that, in some cases, the solving degree is independent of coordinate changes.