Balanced Boolean Function on 13-variables having Nonlinearity strictly greater than the Bent Concatenation Bound

Subhamoy Maitra

Paper 2007/309

Balanced Boolean Function on 13-variables having Nonlinearity strictly greater than the Bent Concatenation Bound

Subhamoy Maitra

Abstract

Very recently, Kavut and Yucel identified 9-variable Boolean functions having nonlinearity 242, which is currently the best known. However, any of these functions do not contain any zero in the Walsh spectrum and that is why they cannot be made balanced. We use these functions to construct 13-variable balanced Boolean function having nonlinearity $2^{13 - 1} - 2^{\frac{13 - 1}{2}} + 2 = 4034$ which is strictly greater than the bent concatenation bound. This is the first demonstration of balanced Boolean functions on odd number of variables having nonlinearity strictly greater than the bent concatenation bound for number of input variables less than 15.

Note: Nonlinearity improved to 4036 (by Kavut and Melek using systematic search) from 4034 in the first version.

Metadata

Available format(s): PDF
Category: Secret-key cryptography
Publication info: Published elsewhere. Unknown where it was published
Keywords: Balancedness Boolean Function Nonlinearity.
Contact author(s): subho @ isical ac in
History: 2007-08-27: revised; 2007-08-16: received; See all versions
Short URL: https://ia.cr/2007/309
License: CC BY

BibTeX

@misc{cryptoeprint:2007/309,
      author = {Subhamoy Maitra},
      title = {Balanced Boolean Function on 13-variables having Nonlinearity strictly greater than the Bent Concatenation Bound},
      howpublished = {Cryptology {ePrint} Archive, Paper 2007/309},
      year = {2007},
      url = {https://eprint.iacr.org/2007/309}
}