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 functionalgebraic immunitybent functionbalancednonlinearityalgebraic degree
Contact author(s)
naturetu @ gmail com
dengyp @ amss ac cn
History
2009-06-09: received
Short URL
https://ia.cr/2009/272
License
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2009/272}},
      url = {https://eprint.iacr.org/2009/272}
}
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