Gustavo Banegas

Gustavo Banegas

Cryptography Researcher

A New Class of Irreducible Pentanomials for Polynomial-Based Multipliers in Binary Fields

Published in In *Journal of Cryptographic Engineering* (JCEN), 2018

We introduce a new class of irreducible pentanomials over ( \mathbb{F}_2 ) of the form
[ f(x) = x^{2b+c} + x^{b+c} + x^b + x^c + 1 ]
and use these polynomials to define finite field extensions of degree ( m = 2b + c ).

Highlights:

  • Exact operation count for reduction modulo ( f(x) )
  • Efficient Karatsuba-based multiplier in ( \mathbb{F}_2[x] )
  • Lower XOR and AND gate complexity in hardware
  • Competitive time delay compared to existing Karatsuba multipliers

This work supports the design of high-performance hardware for cryptographic binary field arithmetic.

Recommended citation: Gustavo Banegas, Ricardo Felipe Custodio, Daniel Panario. (2018). "A New Class of Irreducible Pentanomials for Polynomial-Based Multipliers in Binary Fields." In Journal of Cryptographic Engineering (JCEN).
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