Boolean Functions with Multiple-Valued Walsh Spectra

SUN Tianfeng; HU Bin

doi:10.1049/cje.2019.07.004

Volume 28 Issue 6

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Article Navigation > Chinese Journal of Electronics > 2019 > 28(6): 1165-1169

SUN Tianfeng and HU Bin, “Boolean Functions with Multiple-Valued Walsh Spectra,” Chinese Journal of Electronics, vol. 28, no. 6, pp. 1165-1169, 2019, doi: 10.1049/cje.2019.07.004

Citation:

SUN Tianfeng and HU Bin, “Boolean Functions with Multiple-Valued Walsh Spectra,” Chinese Journal of Electronics, vol. 28, no. 6, pp. 1165-1169, 2019, doi: 10.1049/cje.2019.07.004

SUN Tianfeng and HU Bin, “Boolean Functions with Multiple-Valued Walsh Spectra,” Chinese Journal of Electronics, vol. 28, no. 6, pp. 1165-1169, 2019, doi: 10.1049/cje.2019.07.004

Citation:

SUN Tianfeng and HU Bin, “Boolean Functions with Multiple-Valued Walsh Spectra,” Chinese Journal of Electronics, vol. 28, no. 6, pp. 1165-1169, 2019, doi: 10.1049/cje.2019.07.004

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Boolean Functions with Multiple-Valued Walsh Spectra

doi: 10.1049/cje.2019.07.004

Information Engineering University, Zhengzhou 450000, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61502532).

Received Date: 2018-04-26
Rev Recd Date: 2018-08-21
Publish Date: 2019-11-10

Abstract

Abstract

Compared with the method by Zhang in 2017, an extended one for constructing Boolean functions with multiple-valued Walsh spectra is given, which is derived from a bent function by complementing the values at some points. Based on which, new classes of Boolean functions with four-valued and five-valued Walsh spectra are presented, and some of their cryptographic properties are studied.
- Boolean function,
- Bent function,
- Multiple-valued Walsh spectra,
- Algebraic degree

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References(18)

References

O. Rothaus, "On bent functions", Journal of Combinatorial Theory, Vol.20, No.3, pp.300-305, 1976.

C. Carlet and S. Mesnager, "Four decades of research on bent functions", Designs, Codes and Cryptography, Vol.78, No.1, pp.5-50, 2016.

F.R. Zhang, C. Carlet, Y.P. Hu, et al., "New secondary constructions of bent functions", Applicable Algebra in Engineering, Communication and Computing, Vol.27, No.5, pp.413-434, 2016.

G.H. Sun and C.K. Wu, "Construction of semi-bent Boolean functions in even number of variables", Chinese Journal of Electronics, Vol.18, No.2, pp,231-237, 2009.

D.B. Zheng, L. Yu and L. Hu, "Quadratic bent and semibent functions over finite fields of odd characteristic", Chinese Journal of Electronics, Vol.23, No.4, pp.767-772, 2014.

F.R. Zhang, E. Pasalic, Y.Z. Wei, et al., "Constructing bent functions outside the Maiorana-McFarland class using a general form of Rothaus", IEEE Transactions on Information Theory, Vol.63, No.8, pp.5336-5349, 2017.

S. Mesnager, F.R. Zhang and Y. Zhou, "On construction of bent functions involving symmetric functions and their duals", Advances in Mathematics of Communications, Vol.11, No.2, pp.347-352, 2017.

W.Y. Zhang, Z.H. Xing and K.Q. Feng, "A construction of Bent functions with optimal algebraic degree and large symmetric group", https://eprint.iacr.org/2017/197.pdf,2017-2-27.

Z. Tu, D. Zheng, X. Zeng and L. Hu, "Boolean functions with two distinct Walsh coefficients", Applicable Algebra in Engineering, Communication and Computing, Vol.22, No,5-6, pp.359-366, 2011.

Y. Zheng and X.M. Zhang, "On plateaued functions", IEEE Transactions on Information Theory, Vol.47, No.3, pp.1215-1223, 2001.

C. Carlet, "A larger class of cryptographic Boolean functions via a study of the Marorana-McFarland construction", Cryptology-CRYPTO 2002, California, USA, pp.549-564, 2002.

C. Carlet and E. Prouff, "On plateaued functions and their construction", Fast Software Encryption, Lund, Sweden, pp.54-73, 2003.

T.W. Cusick, "Highly nonlinear plateaued functions", IET Information Security, Vol.11, No.2, pp.78-81, 2017.

J.Y. Hyun, J. Lee and Y. Lee, "Explicit criteria for construction of plateaued functions", IEEE Transactions on Information Theory, Vol.62, No.12, pp.7555-7565, 2016.

Z.Q. Sun and L. Hu, "Boolean functions with four-valued Walsh spectra", Journal of Systems Science and Complexity, Vol.28, No.3, pp.743-754, 2015.

Z.Q. Sun and L. Hu, "Two Boolean functions with fivevalued Walsh spectra and high nonlinearity", International Journal of Foundations of Computer Science, Vol.26, No.5, pp.537-556, 2015.

S. Mesnager and F.R. Zhang, "On constructions of bent, semi-bent and five valued spectrum functions from old bent functions", Advances in Mathematics of Communications, Vol.11, No.2, pp.339-345, 2017.

S. Maitra and P. Sarkar, "Cryptographically significant Boolean functions with five valued Walsh spectra", Theoretical Computer Science, Vol.276, No.1-2, pp.133-146, 2002.

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