The XL-Algorithm and a Conjecture from Commutative Algebra

The “XL-algorithm” is a computational method to solve overdetermined systems of polynomial equations which is based on a generalization of the well-known method of linearization; it was introduced to cryptology at Eurocrypt 2000. In this paper, we prove upper bounds on the dimensions of the spaces of equations in the XL-algorithm. These upper bounds provide strong evidence that for any fixed finite field K and any fixed c ∈ N the median of the running times of the original XL-algorithm applied to systems of m = n+c quadratic equations in n variables over K which have a solution

• Type: Conference
• Year: 2004
• Where: ASIACRYPT
• Authors: Claus Diem
• Keywords: ASIACRYPT 2004, Computational Method, Cryptology, Polynomial Equations, Upper Bounds