Distribution of Primitive Polynomials Over GF(2) with Respect to Their Weights

  • Prasanna Raghaw Mishra
  • Indivar Gupta
  • Navneet Gaba
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 139)


In this paper, we study the distribution of primitive polynomials over \(\textit{GF}(2)\) with respect to their weights and report some interesting empirical results which can help crypto-designers to select suitable primitive polynomials. We carry out an exhaustive study of primitive polynomials over \(\textit{GF}(2)\) for the degrees up to 30 and figure out the cases where this distribution is symmetrically placed about its mean. We then try to address the issue of effect on variability of primitive polynomials restricted to have certain minimum weight. Further, we propose an empirical lower bound on variability of primitive polynomials when the polynomials are restricted to have at least 40 % taps. We also propose a conjecture on the relationship of degree and the most probable weight of randomly generated primitive polynomials.


Primitive polynomial LFSR Finite fields Crypto-primitives 


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Copyright information

© Springer India 2015

Authors and Affiliations

  • Prasanna Raghaw Mishra
    • 1
  • Indivar Gupta
    • 1
  • Navneet Gaba
    • 1
  1. 1.Scientific Analysis Group, Defence Research and Development OrganizationDelhiIndia

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