Growth of the ideal generated by a quadratic multivariate function
Jíntai Ding, Victoria Kruglov · 2010
We find exact formulas for the growth of the ideal λA k, where λ is a quadratic element of the algebra of functions over the Galois field Fq for q = 2 and q = 3. More precisely, we calculate dim(λAk), where Ak is the subspace of elements of degree less than or equal to k. The results clarify some of the assertions made in the articles of Yang, Chen, and Courtois [YC], [YCC] regarding the complexity of the XL algorithm.