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 \(\dim A_k \lambda\) where A k 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.
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Ding, J., Hodges, T.J., Kruglov, V. (2010). Growth of the Ideal Generated by a Quadratic Boolean Function. In: Sendrier, N. (eds) Post-Quantum Cryptography. PQCrypto 2010. Lecture Notes in Computer Science, vol 6061. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12929-2_2
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DOI: https://doi.org/10.1007/978-3-642-12929-2_2
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