Abstract
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.
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Buchmann, J., Cabarcas, D., Ding, J., Mohamed, M.S.E. (2010). Flexible Partial Enlargement to Accelerate Gröbner Basis Computation over \(\mathbb{F}_2\) . In: Bernstein, D.J., Lange, T. (eds) Progress in Cryptology – AFRICACRYPT 2010. AFRICACRYPT 2010. Lecture Notes in Computer Science, vol 6055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12678-9_5
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DOI: https://doi.org/10.1007/978-3-642-12678-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-12677-2
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