A new class of irreducible pentanomials for polynomial-based multipliers in binary fields

We introduce a new class of irreducible pentanomials over F2F2 of the form f(x)=x2b+c+xb+c+xb+xc+1f(x)=x2b+c+xb+c+xb+xc+1. Let m=2b+cm=2b+c and use f to define the finite field extension of degree m. We give the exact number of operations required for computing the reduction modulo f. We also provide a multiplier based on Karatsuba algorithm in F2[x]F2[x]combined with our reduction process. We give the total cost of the multiplier and found that the bit-parallel multiplier defined by this new class of polynomials has improved XOR and AND complexity. Our multiplier has comparable time delay when compared to other multipliers based on Karatsuba algorithm