Subquadratic binary field multiplier in double polynomial system

We propose a new space efficient operator to multiply elements lying in a binary field F2k . Our approach is based on a novel system of representation called Double Polynomial System which set elements as a bivariate polynomials over F2. Thanks to this system of representation, we are able to use a Lagrange representation of the polynomials and then get a logarithmic time multiplier with a space complexity of O(k1:31) improving previous best known method.