Maiorana-McFarland Functions with High Second-Order Nonlinearity

Nicholas Kolokotronis; Konstantinos Limniotis

Paper 2011/212

Maiorana-McFarland Functions with High Second-Order Nonlinearity

Nicholas Kolokotronis and 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: Published elsewhere. An extended version of this work has been submitted to IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessible.
Keywords: boolean functions
Contact author(s): nkolok @ uop gr
History: 2011-05-06: received
Short URL: https://ia.cr/2011/212
License: CC BY

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}
}