Paper 2006/180

Divisibility of the Hamming Weight by $2^k$ and Monomial Criteria for Boolean Functions

Dmitry Khovratovich

Abstract

In this paper we consider the notions of the Hamming weight and the algebraic normal form. We solve an open problem devoted to checking divisibility of the weight by $2^k$. We generalize the criterion for checking the evenness of the weight in two ways. Our main result states that for checking whether the Hamming weight of $f$ is divisible by $2^k, \,k>1$, it is necessary and sufficient to know its algebraic normal form accurate to an additive constant.

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. The Russian version was submitted to the workshop on discrete mathematics in Russia in 2006
Keywords
boolean functionsHamming weightalgebraic normal formcoding theory
Contact author(s)
diho @ rnt ru
History
2006-05-30: received
Short URL
https://ia.cr/2006/180
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2006/180,
      author = {Dmitry Khovratovich},
      title = {Divisibility of the Hamming Weight by $2^k$ and Monomial Criteria for Boolean Functions},
      howpublished = {Cryptology ePrint Archive, Paper 2006/180},
      year = {2006},
      note = {\url{https://eprint.iacr.org/2006/180}},
      url = {https://eprint.iacr.org/2006/180}
}
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