The problem we study in this paper is the key recovery problem on the C* schemes and generalizations where the quadratic monomial of C* (the product of two linear monomials) is replaced by a product of three or more linear monomials. This problem has been further generalized to any multivariate polynomial hidden by two invertible linear maps and named the Isomorphism of Polynomials (I P ) problem by Patarin et al. Some cryptosystems have been built on this appearing hard problem such as a traitor tracing scheme proposed by Billet and Gilbert. Here we show that if the hidden multivariate monomial is a quadratic monomial, as in SFLASH, or a cubic (or higher) monomial as in the traitor tracing scheme, then it is possible to recover an equivalent secret key in polynomial time O(nd ) where n is the number of variables and d is the degree of the public polynomials.