  Algebraic cryptanalysis usually requires to recover the secret key by solving
polynomial equations. Grobner bases algorithm is a well-known method to solve
this problem. However, a serious drawback exists in the Grobner bases based
algebraic attacks, namely, any information won't be got if we couldn't work out
the Grobner bases of the polynomial equations system. In this paper, firstly, a
generalized model of Grobner basis algorithms is presented, which provides us a
platform to analyze and solve common problems of the algorithms. Secondly, we
give and prove the degree bound of the polynomials appeared during the
computation of Grobner basis after field polynomials is added. Finally, by
detecting the temporary basis during the computation of Grobner bases and then
extracting the univariate polynomials contained unique solution in the
temporary basis, a heuristic strategy named Middle-Solving is presented to
solve these polynomials at each iteration of the algorithm. Farther, two
specific application mode of Middle-Solving strategy for the incremental and
non-incremental Grobner bases algorithms are presented respectively. By using
the Middle-Solving strategy, even though we couldn't work out the final Grobner
bases, some information of the variables still leak during the computational
process.
