An algorithm for solving over-determined multivariate quadratic systems over finite fields is given. It is more efficient than other known algorithms over finite fields of relatively large size in terms of both performance and memory comsumption. It is also simpler for computer programming. The complexity estimate of our algorithm can be used to estimate the security level of multivariate cryptosystems by solving the multivariate quadratic systems induced by the cryptosystems.

中文翻译：

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一种求解有限域上超定多元二次系统的算法

给出了一种求解有限域上超定多元二次系统的算法。在性能和内存消耗方面，它在相对较大的有限域上比其他已知算法更有效。计算机编程也更简单。我们算法的复杂度估计可用于通过求解由密码系统诱导的多元二次系统来估计多元密码系统的安全级别。