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