We propose the first general multiplication algorithm in GF(2^k) with a subquadratic area complexity of 0(k^8/5) = 0(k^1.6). Using the Chinese Remainder Theorem, we represent the elements of GF(2^k); i.e. the polynomials in GF(2)[X] of degree at most k - 1, by their remainder modulo a set of n pairwise prime trinomials, T₁, …, T_n, of degree d such that nd ≥ k. Our algorithm is based on Montgomery's multiplication applied to the ring formed by the direct product of the trinomials.