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

We introduce a new class of irreducible pentanomials over F ₂ of the form f(x) = x ^{2 b + c}+ x ^{b + c}+ x ^b+ x ^c+ 1. Let m= 2 b+ 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 F ₂[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.