Perfect Algebraic Immune Functions

Meicheng Liu; Yin Zhang; Dongdai Lin

Paper 2012/212

Perfect Algebraic Immune Functions

Meicheng Liu, Yin Zhang, and Dongdai Lin

Abstract

A perfect algebraic immune function is a Boolean function with perfect immunity against algebraic and fast algebraic attacks. The main results are that for a perfect algebraic immune balanced function the number of input variables is one more than a power of two; for a perfect algebraic immune unbalanced function the number of input variables is a power of two. Also the Carlet-Feng functions on $2^s+1$ variables and the modified Carlet-Feng functions on $2^s$ variables are shown to be perfect algebraic immune functions. Furthermore, it is shown that a perfect algebraic immune function behaves good against probabilistic algebraic attacks as well.

Note: The proof of the "only if" direction of Theorem 8 has been corrected.

Metadata

Available format(s): PDF
Publication info: Published elsewhere. Unknown where it was published
Keywords: Boolean functions Algebraic immunity Fast algebraic attacks Probabilistic algebraic attacks
Contact author(s): meicheng liu @ gmail com
History: 2012-08-08: last of 3 revisions; 2012-04-22: received; See all versions
Short URL: https://ia.cr/2012/212
License: CC BY

BibTeX

@misc{cryptoeprint:2012/212,
      author = {Meicheng Liu and Yin Zhang and Dongdai Lin},
      title = {Perfect Algebraic Immune Functions},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/212},
      year = {2012},
      url = {https://eprint.iacr.org/2012/212}
}