Paper 2009/577

On the nonlinearity profile of the Dillon function

Claude Carlet

Abstract

The nonlinearity profile of a Boolean function is the sequence of its minimum Hamming distances $nl_r(f)$ to all functions of degrees at most $r$, for $r\geq 1$. The nonlinearity profile of a vectorial function is the sequence of the minimum Hamming distances between its component functions and functions of degrees at most $r$, for $r\geq 1$.The profile of the multiplicative inverse functions has been lower bounded in a previous paper by the same author. No other example of an infinite class of functions with unbounded algebraic degree has been exhibited since then, whose nonlinearity profile could be efficiently lower bounded. In this preprint, we lower bound the whole nonlinearity profile of the simplest Dillon bent function $(x,y)\mapsto xy^{2^{n/2}-2}$, $x,y\in F_{2^{n/2}}$.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Published elsewhere. Unknown where it was published
Contact author(s)
claude carlet @ inria fr
History
2009-12-01: received
Short URL
https://ia.cr/2009/577
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2009/577,
      author = {Claude Carlet},
      title = {On the nonlinearity profile of the Dillon function},
      howpublished = {Cryptology ePrint Archive, Paper 2009/577},
      year = {2009},
      note = {\url{https://eprint.iacr.org/2009/577}},
      url = {https://eprint.iacr.org/2009/577}
}
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