Algebraic attack is used to study cryptosystems by solving equations.To lower the degrees of the equations is an important method to reduce the complexity to solve them.Annihilators is introduced to reach this aim

but there is not an efficient way to find the annihilators of a boolean function up to now.The article presents a kind of algorithm to work out the space of the annihilators of a given boolean function.We can find a basis of the annihilators set by the former two algorithms.Using the third algorithm

we can find the annihilators with lowest degree.The complexity is concerned with the number of monomials in the boolean function

and it is greatly reduced than that of the algorithms before in most cases for stream ciphers.We will present a toy example at the end of the article to show how the third algorithm works.