Abstract
We give exact formulas for the growth of the ideal Aλ for λ a quadratic element of the algebra of Boolean functions over the Galois field GF(2). That is, we calculate dim Akλ where Ak is the subspace of elements of degree less than or equal to k. These results clarify some of the assertions made in the article of Yang, Chen and Courtois [22,23] concerning the efficiency of the XL algorithm. © 2010 Springer-Verlag.
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CITATION STYLE
Ding, J., Hodges, T. J., & Kruglov, V. (2010). Growth of the ideal generated by a quadratic Boolean function. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6061 LNCS, pp. 13–27). https://doi.org/10.1007/978-3-642-12929-2_2
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