Fast Squaring in TypeI All One Polynomial Field

In this paper, the authors propose a fast squaring on all one polynomial field and show some simulation results with characteristic p = 256-bit prime and extension degree k ∈ {2, 4, 6, 10, 12} implemented on a PentiumIV (2.6㎓) using the C programming language. The computer simulations showed that, on average, the proposed algorithm accelerated about 30% in F p² , 12% in F p⁴ and 6% in F p? compared to the conventional squaring.