Explicit formulae of polynomial basis squarer for pentanomials using weakly dual basis

I present a new method to compute a bit-parallel polynomial basis squarer for GF(2m)GF(2m) generated by an arbitrary irreducible polynomial using weakly dual basis. I apply the proposed method to irreducible pentanomial and derive the explicit formulae for squarer. It is the first time that gives the explicit formulae and an upper complexity bound of squarer for irreducible pentanomials. Moreover, such formulae permit one to choose pentanomial for any odd m∈[19,2000]m∈[19,2000] whose multiplier, as well as squarer, can be performed more efficiently.

► I propose a new method to compute a bit-parallel squarer for finite field.
► I present the explicit formulae of squarer for pentanomials for the first time.
► The explicit formulae permit one to choose optimal pentanomial for application.