Characterizing Negabent Boolean Functions over Finite Fields

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• 作者：Sumanta Sarkar (1) sarkas@ucalgary.ca
• 关键词：negabent function – Bent function – quadratic Boolean function – Maiorana ; McFarland function – permutation
• 刊名：Lecture Notes in Computer Science
• 出版年：2012
• 出版时间：2012
• 年：2012
• 卷：7280
• 期：1
• 页码：77-88
• 全文大小：218.2 KB
• 参考文献：1. Dillon, J.: Elementary Hadamard Difference sets, Ph.D. dissertation, Univ. of Maryland (1974)
  2. Dobbertin, H., Leander, G.: A Survey of Some Recent Results on Bent Functions. In: Helleseth, T., Sarwate, D., Song, H.-Y., Yang, K. (eds.) SETA 2004. LNCS, vol. 3486, pp. 1–29. Springer, Heidelberg (2005)
  3. Helleseth, T., Kholosha, A.: and related affine polynomials over GF(2 k ). Cryptography and Communications 2(1), 85–109 (2010)
  4. Parker, M.G.: Constabent properties of Golay-Davis-Jedwab sequences. In: Int. Symp. Information Theory, p. 302. IEEE, Sorrento (2000)
  5. Parker, M.G., Pott, A.: On Boolean Functions Which are Bent and Negabent. In: Golomb, S.W., Gong, G., Helleseth, T., Song, H.-Y. (eds.) SSC 2007. LNCS, vol. 4893, pp. 9–23. Springer, Heidelberg (2007)
  6. Riera, C., Parker, M.G.: One and Two-Variable Interlace Polynomials: A Spectral Interpretation. In: Ytrehus, ?. (ed.) WCC 2005. LNCS, vol. 3969, pp. 397–411. Springer, Heidelberg (2006)
  7. Rothaus, O.S.: On bent functions. Journal of Combinatorial Theory Series A 20, 300–305 (1976)
  8. Sarkar, S.: On the Symmetric Negabent Boolean Functions. In: Roy, B., Sendrier, N. (eds.) INDOCRYPT 2009. LNCS, vol. 5922, pp. 136–143. Springer, Heidelberg (2009)
  9. Schmidt, K.-U., Parker, M.G., Pott, A.: Negabent Functions in the Maiorana–McFarland Class. In: Golomb, S.W., Parker, M.G., Pott, A., Winterhof, A. (eds.) SETA 2008. LNCS, vol. 5203, pp. 390–402. Springer, Heidelberg (2008)
  10. St?nic?, P., Gangopadhyay, S., Chaturvedi, A., Gangopadhyay, A.K., Maitra, S.: Nega–Hadamard Transform, Bent and Negabent Functions. In: Carlet, C., Pott, A. (eds.) SETA 2010. LNCS, vol. 6338, pp. 359–372. Springer, Heidelberg (2010)
• 作者单位：1. Department of Computer Science, University of Calgary, Canada
• ISSN：1611-3349

文摘

We consider negabent Boolean functions that have Trace representation. To the best of our knowledge, this is the first ever work on negabent functions with such representation. We completely characterize negabent quadratic monomial functions. We also present necessary and sufficient condition for a Maiorana-McFarland bent function to be a negabent function. As a consequence of that result we present a nice characterization of a bent-negabent Maiorana-McFarland function which is based on the permutation x ? x2ix \mapsto x^{2^i}.