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 $f(x) = x^{2b+c} + x^{b+c} + x^b + x^c + 1$. Let $m=2b+c$ 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 $F_2[x]$ 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.

In Journal of Cryptographic Engineering
Gustavo Banegas
Gustavo Banegas

My research interests include post-quantum cryptanalysis and its implementations.