Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter April 27, 2017

On 1-stable perfectly balanced Boolean functions

  • Stanislav V. Smyshlyaev EMAIL logo

Abstract

The paper is concerned with relations between the correlation-immunity (stability) and the perfectly balancedness of Boolean functions. It is shown that an arbitrary perfectly balanced Boolean function fails to satisfy a certain property that is weaker than the 1-stability. This result refutes some assertions by Markus Dichtl. On the other hand, we present new results on barriers of perfectly balanced Boolean functions which show that any perfectly balanced function such that the sum of the lengths of barriers is smaller than the length of variables, is 1-stable.


Originally published in Diskretnaya Matematika (2016) 28, №2, 117–126 (in Russian).


Award Identifier / Grant number: 16-01-00226-a and 16-01-00470-a

Funding statement: This work was supported by the Russian Fund for Basic Research, grant nos. 16-01-00226-a and 16-01-00470-a).

References

[1] Anderson R.J., “Searching for the optimum correlation attack”, FSE 1995, Lect. Notes Comput. Sci., 1008, 1995, 137–143.10.1007/3-540-60590-8_11Search in Google Scholar

[2] Dichtl M., “On nonlinear filter generators”, FSE 1997, Lect. Notes Comput. Sci., 1267, Springer, Heidelberg, 1997, 103–106.10.1007/BFb0052338Search in Google Scholar

[3] Gouget A., Sibert H., “Revisiting correlation-immunity in filter generators”, SAC 2007, Lect. Notes Comput. Sci., 4876, 2007, 378–395.10.1007/978-3-540-77360-3_24Search in Google Scholar

[4] Smyshlyaev S. V., “Perfectly balanced Boolean functions and Golić conjecture”, J. Cryptology, 25:3 (2012), 464–483.10.1007/s00145-011-9100-7Search in Google Scholar

[5] Logachev O. A., “On a class of perfectly balanced Boolean functions”, Mater. 3 Mezhdunar. nauchn. Konf. po probl. bezopasn. protivod. terror. (MCCME), 2008, 137–141 (in Russian).Search in Google Scholar

[6] Logachev O. A., Sal’nikov A. A., Smyshlyaev S. V., Yashchenko V. V., Boolean functions in the coding theory and cryptology, 3rd edition, M.: LENAND, 2015 (in Russian).Search in Google Scholar

[7] Logachev O. A., Smyshlyaev S. V., Yashchenko V. V., “New methods of investigation of perfectly balanced Boolean functions”, Discrete Math. Appl., 19:3 (2009), 237–262.10.1515/DMA.2009.014Search in Google Scholar

[8] Smyshlyaev S. V., “Barriers of perfectly balanced Boolean functions”, Discrete Math. Appl., 20:3 (2010), 321–336.10.1515/dma.2010.019Search in Google Scholar

[9] Smyshlyaev S. V., “Construction of classes of perfectly balanced Boolean functions without a barrier”, Prikladnaya diskretnaya matematika, 2010, ł 3(9), 41–50 (in Russian).10.17223/20710410/9/4Search in Google Scholar

[10] Smyshlyaev S. V., “Boolean functions without prediction”, Discrete Math. Appl., 21:2 (2011), 209–227.10.1515/dma.2011.013Search in Google Scholar

[11] Sumarokov S. N., “Inhibits of binary functions and reversibility for one class of coding devices”, Obozr. prikl. promyshl. matem., 1:1 (1994), 33–55 (in Russian).Search in Google Scholar

Received: 2016-4-19
Published Online: 2017-4-27
Published in Print: 2017-4-1

© 2017 Walter de Gruyter GmbH, Berlin/Boston

Downloaded on 28.3.2024 from https://www.degruyter.com/document/doi/10.1515/dma-2017-0013/html
Scroll to top button