1-Resilient Boolean Function with Optimal Algebraic Immunity

Qingfang Jin; Zhuojun Liu; Baofeng Wu

Paper 2011/549

1-Resilient Boolean Function with Optimal Algebraic Immunity

Qingfang Jin, Zhuojun Liu, and Baofeng Wu

Abstract

In this paper, We propose a class of 2k-variable Boolean functions, which have optimal algebraic degree, high nonlinearity, and are 1-resilient. These functions have optimal algebraic immunity when k > 2 and u = -2^l; 0 =< l < k. Based on a general combinatorial conjecture, algebraic immunity of these functions is optimal when k > 2 and u = 2^l; 0 =< l < k. If the general combinatorial conjecture and a new assumption are both true, algebraic immunity of our functions is also optimal when k > 2, otherwise u.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): qfjin @ amss ac cn
History: 2011-10-11: received
Short URL: https://ia.cr/2011/549
License: CC BY

BibTeX

@misc{cryptoeprint:2011/549,
      author = {Qingfang Jin and Zhuojun Liu and Baofeng Wu},
      title = {1-Resilient Boolean Function with Optimal Algebraic Immunity},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/549},
      year = {2011},
      url = {https://eprint.iacr.org/2011/549}
}