The present invention relates to security systems for communication networks. More precisely, the invention relates to a method for generating a shared key between a first node (D1) and a second node (D2) for secure communication in a network (1), the first node storing a first node keying material share based on a root keying material and the method comprising the following steps: a) the first node receiving an identifier of the second node, b) the first node evaluating the first node keying material share at a second node's identifier, to generate the shared key, wherein the first node keying material share is a polynomial-based keying material over a finite field Fq and step b) comprises: b1) the first node applying a Horner's rule to factorize the first node keying material under the form of a combination of monomials, b2) the first node computing the result of each monomial operation by evaluating at a predetermined point a polynomial of degree r−1 with coefficients in a sub-field of Fq. The invention also relates to a network and a computer program thereof.