Highly Nonlinear Resilient Functions Optimizing Siegenthaler's Inequality

  title={Highly Nonlinear Resilient Functions Optimizing Siegenthaler's Inequality},
  author={Subhamoy Maitra and Palash Sarkar},
Siegenthaler proved that an n input 1 output, m-resilient (balanced mth order correlation immune) Boolean function with algebraic degree d satisfies the inequality : m + d ≤ n - 1. We provide a new construction method using a small set of recursive operations for a large class of highly nonlinear, resilient Boolean functions optimizing Siegenthaler's inequality m + d = n - 1. Comparisons to previous constructions show that better nonlinearity can be obtained by our method. In particular, we… 
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