摘要： 对XL算法中的方程组约简过程进行改进，提出一种更有效的求解算法。改进算法中充分利用各单项式之间的约束关系对方程组进行约简，消去其中次数较高的单项式。采用分步扩展及约简的思想消去扩展过程中添加的冗余等式，有效降低XL算法的计算复杂度及存储复杂度。此外，改进的算法还可用于构建布尔函数的低次零化子。

关键词: 密码学, 代数攻击, XL算法, 多元方程组的求解问题

Abstract: In this paper, the process of reducing systems of equations is improved, and a more efficient algorithm for solving systems is developed. The improved algorithm uses the relation of all the monomials sufficiently for reducing systems of equations, and removes the high-degree monomials. Simultaneously, the systems are expanded and reduced step by step in order to remove the redundant equations, decrease the computing and saving complexity of the XL algorithm. And more, the improved algorithm can be applied to constructing the low-degree Annihilators of Boolean function.

Key words: cryptography, algebraic attacks, XL algorithm, MQ problem

中图分类号: 

• TP301.6