Recent developments in multivariate polynomial solving algorithms have made algebraic cryptanalysis a plausible threat to many cryptosystems. However, theoretical complexity estimates have shown this kind of attack unfeasible for most realistic applications. In this paper we present a strategy for computing Gröbner basis that challenges those complexity estimates. It uses a flexible partial enlargement technique together with reduced row echelon forms to generate lower degree elements-mutants. This new strategy surpasses old boundaries and obligates us to think of new paradigms for estimating complexity of Gröbner basis computation. The new proposed algorithm computed a Gröbner basis of a degree 2 random system with 32 variables and 32 equations using 30 GB which was never done before by any known Gröbner bases solver. © 2010 Springer-Verlag.
CITATION STYLE
Buchmann, J., Cabarcas, D., Ding, J., & Mohamed, M. S. E. (2010). Flexible partial enlargement to accelerate Gröbner basis computation over double-struck F2. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6055 LNCS, pp. 69–81). https://doi.org/10.1007/978-3-642-12678-9_5
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