Growth of the Ideal Generated by a Quadratic Boolean Function

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 and Chen [YC] concerning the efficiency of the XL algorithm in cryptography.

• Type: Conference
• Year: 2010
• Where: PQCRYPTO
• Authors: Jintai Ding, Timothy J. Hodges, Victoria Kruglov
• Keywords: Boolean Functions, Cryptology, Exact Formulas, PQCRYPTO 2010, Quadratic Element