Maiorana-McFarland Functions with High Second-Order Nonlinearity

Nicholas Kolokotronis; Konstantinos Limniotis

Paper 2011/212 Original: eprint.iacr.org/2011/212 ↗

Maiorana-McFarland Functions with High Second-Order Nonlinearity

Nicholas Kolokotronis

Konstantinos Limniotis

Abstract

The second-order nonlinearity, and the best quadratic approximations, of Boolean functions are studied in this paper. We prove that cubic functions within the Maiorana-McFarland class achieve very high second order nonlinearity, which is close to an upper bound that was recently proved by Carlet et al., and much higher than the second order nonlinearity obtained by other known constructions. The structure of the cubic Boolean functions considered allows the efficient computation of (a subset of) their best quadratic approximations.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Preprint.
History: 2011-05-06: last updated; 2011-05-06: published
Short URL: https://ia.cr/2011/212
License: https://creativecommons.org/licenses/by/4.0/

BibTeX

@misc{cryptoeprint:2011/212,
      author = {Nicholas Kolokotronis and Konstantinos Limniotis},
      title = {Maiorana-McFarland Functions with High Second-Order Nonlinearity},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/212},
      year = {2011},
      url = {https://eprint.iacr.org/2011/212}
}