Paper 2011/083

On the number of bent functions from iterative constructions: lower bounds and hypotheses

Natalia Tokareva

Abstract

In the paper we study lower bounds on the number of bent functions that can be obtained by iterative constructions, namely by the construction proposed by A.Canteaut and P.Charpin in 2003. The number of bent iterative functions is expressed in terms of sizes of finite sets and it is shown that evaluation of this number is closely connected to the problem of decomposing Boolean function into sum of two bent functions. A new lower bound for the number of bent iterative functions that is supposed to be asymptotically tight is given. Applying Monte-Carlo methods the number of bent iterative functions in 8 variables is counted. Based on the performed calculations several hypotheses on the asymptotic value of the number of all bent functions are formulated.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Print variant. It is publushed in Advances in Mathematics of Communications (AMC). 2011. V. 5, N 4. P. 609-621.
Keywords
boolean functionsbent functionlower bound
Contact author(s)
tokareva @ math nsc ru
History
2012-02-16: last of 2 revisions
2011-02-20: received
See all versions
Short URL
https://ia.cr/2011/083
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2011/083,
      author = {Natalia Tokareva},
      title = {On the number of bent functions from iterative constructions: lower bounds and hypotheses},
      howpublished = {Cryptology ePrint Archive, Paper 2011/083},
      year = {2011},
      note = {\url{https://eprint.iacr.org/2011/083}},
      url = {https://eprint.iacr.org/2011/083}
}
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