Patent ID: 8495373

Claim:
A method for generating a shared key between a first node (D 1 ) and a second node (D 2 ) for secure communication in a network, 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 F q and step b) comprises: b1) the first node factorizing the first node keying material under the form of a reduced polynomial over the field F q modulo an irreducible polynomial of degree r with coefficients in a sub-field of F q , the reduced polynomial being arranged so that evaluating the first node keying material at the second node's identifier includes iteratively evaluating and combining monomials at the second node's identifier, over the field F q , modulo the irreducible polynomial, 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 F q modulo the irreducible polynomial of degree r in a sub-field of F q , the coefficient polynomial being arranged so that evaluating the coefficient polynomial corresponds to iteratively evaluating and combining monomials at the predetermined point over the sub-field of F q modulo the irreducible polynomial.