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

Selcuk Kavut; Subhamoy Maitra; Sumanta Sarkar; Melek D.  Yucel

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Paper 2006/249

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

Selcuk Kavut, Subhamoy Maitra, Sumanta Sarkar, and Melek D. Yucel

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 Yücel. 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.

Metadata

Available format(s): PDF PS
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Boolean Functions
Contact author(s): subho @ isical ac in
History: 2006-07-24: received
Short URL: https://ia.cr/2006/249
License: CC BY

BibTeX

@misc{cryptoeprint:2006/249,
      author = {Selcuk Kavut and Subhamoy Maitra and Sumanta Sarkar and Melek D.  Yucel},
      title = {Enumeration of 9-variable Rotation Symmetric Boolean Functions having Nonlinearity > 240},
      howpublished = {Cryptology ePrint Archive, Paper 2006/249},
      year = {2006},
      note = {\url{https://eprint.iacr.org/2006/249}},
      url = {https://eprint.iacr.org/2006/249}
}