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ASIACRYPT
2004
Springer

The XL-Algorithm and a Conjecture from Commutative Algebra

8 years 8 months ago
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
Claus Diem
Added 30 Jun 2010
Updated 30 Jun 2010
Type Conference
Year 2004
Where ASIACRYPT
Authors Claus Diem
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