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Paper: Enumeration of 9-variable Rotation Symmetric Boolean Functions having Nonlinearity > 240

Authors:
Selçuk Kavut
Melek D. Yücel
Subhamoy Maitra
Sumanta Sarkar
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URL: http://eprint.iacr.org/2006/249
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Abstract: The existence of $9$-variable Boolean functions having nonlinearity strictly greater than $240$ has been shown very recently (May 2006) by Kavut, Maitra and Y{\"u}cel. The functions with nonlinearity 241 have been identified by a heuristic search in the class of Rotation Symmetric Boolean Functions (RSBFs). In this paper we efficiently perform the exhaustive search to enumerate the 9-variable RSBFs having nonlinearity $> 240$ and found that there are such functions with nonlinearity 241 only and there is no RSBF having nonlinearity $> 241$. Our search enumerates $8 \times 189$ many 9-variable RSBFs having nonlinearity 241. We further show that there are only two functions which are different up to the affine equivalence. Towards the end we explain the coding theoretic significance of these functions.
BibTeX
@misc{eprint-2006-21742,
  title={Enumeration of 9-variable Rotation Symmetric Boolean Functions having Nonlinearity > 240},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / Boolean Functions},
  url={http://eprint.iacr.org/2006/249},
  note={ subho@isical.ac.in 13349 received 19 Jul 2006},
  author={Selçuk Kavut and Melek D. Yücel and Subhamoy Maitra and Sumanta Sarkar},
  year=2006
}