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 functionsAlgebraic immunityFast algebraic attacksProbabilistic 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
Creative Commons Attribution
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},
      note = {\url{https://eprint.iacr.org/2012/212}},
      url = {https://eprint.iacr.org/2012/212}
}
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