The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. The classical algorithm for solving such a system is Buchberger's algorithm for constructing Gröbner bases. Another algorithm for solving such a system is XL algorithm. For sparse system, Buchberger's algorithm benefits from sparsity of the system, but its complexity is impractical and hard to determine. XL could not make a good use of sparse structure of the system, since XL has no good strategy of choosing the multiply monomials. In this paper, based on..
