Recursive Lower Bounds on the Nonlinearity Profile of Boolean Functions and Their Applications

@article{Carlet2006RecursiveLB,
  title={Recursive Lower Bounds on the Nonlinearity Profile of Boolean Functions and Their Applications},
  author={Claude Carlet},
  journal={IEEE Transactions on Information Theory},
  year={2006},
  volume={54},
  pages={1262-1272}
}
The nonlinearity profile of a Boolean function (i.e., the sequence of its minimum Hamming distances nlr(f) to all functions of degrees at most r, for r ges 1) is a cryptographic criterion whose role against attacks on stream and block ciphers has been illustrated by many papers. It plays also a role in coding theory, since it is related to the covering radii of Reed-Muller codes. We introduce a method for lower-bounding its values and we deduce bounds on the second-order nonlinearity for… CONTINUE READING