A Conjecture on Binary String and Its Applications on Constructing Boolean Functions of Optimal Algebraic Immunity

Ziran Tu; Yingpu Deng

Paper 2009/272

A Conjecture on Binary String and Its Applications on Constructing Boolean Functions of Optimal Algebraic Immunity

Ziran Tu and Yingpu Deng

Abstract

In this paper, we propose a combinatoric conjecture on binary string, on the premise that our conjecture is correct we mainly obtain two classes of functions which are both algebraic immunity optimal: the first class of functions are also bent, moreover, from this fact we conclude that the algebraic immunity of bent functions can take all possible values except one. The second class are balanced functions, which have optimal algebraic degree and the best nonlinearity up to now.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: boolean function algebraic immunity bent function balanced nonlinearity algebraic degree
Contact author(s): naturetu @ gmail com
dengyp @ amss ac cn
History: 2009-06-09: received
Short URL: https://ia.cr/2009/272
License: CC BY

BibTeX

@misc{cryptoeprint:2009/272,
      author = {Ziran Tu and Yingpu Deng},
      title = {A Conjecture on Binary String and Its Applications on Constructing Boolean Functions of Optimal Algebraic Immunity},
      howpublished = {Cryptology {ePrint} Archive, Paper 2009/272},
      year = {2009},
      url = {https://eprint.iacr.org/2009/272}
}