Abstract
<p style='text-indent:20px;'>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.</p>
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