Quadratic Bent and Semi-bent Functions over Finite Fields of Odd Characteristic

ZHENG Dabin; YU Long; HU Lei

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Article Navigation > Chinese Journal of Electronics > 2014 > 23(4): 767-772

ZHENG Dabin, YU Long, HU Lei, “Quadratic Bent and Semi-bent Functions over Finite Fields of Odd Characteristic,” Chinese Journal of Electronics, vol. 23, no. 4, pp. 767-772, 2014,

Citation:

ZHENG Dabin, YU Long, HU Lei, “Quadratic Bent and Semi-bent Functions over Finite Fields of Odd Characteristic,” Chinese Journal of Electronics, vol. 23, no. 4, pp. 767-772, 2014,

ZHENG Dabin, YU Long, HU Lei, “Quadratic Bent and Semi-bent Functions over Finite Fields of Odd Characteristic,” Chinese Journal of Electronics, vol. 23, no. 4, pp. 767-772, 2014,

Citation:

ZHENG Dabin, YU Long, HU Lei, “Quadratic Bent and Semi-bent Functions over Finite Fields of Odd Characteristic,” Chinese Journal of Electronics, vol. 23, no. 4, pp. 767-772, 2014,

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Quadratic Bent and Semi-bent Functions over Finite Fields of Odd Characteristic

1.
Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China;
2.
School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China;
3.
State Key Laboratory of Information Security, Institute of Information Engineering, CAS, Beijing 100093, China

Funds: The work is supported by the National Natural Science Foundation of China (No.11101131), and the National Basic Research Program of China (No.2013CB834203).

Received Date: 2012-04-01
Rev Recd Date: 2013-05-01
Publish Date: 2014-10-05

Abstract

Abstract

Let n=me and p be an odd prime. Let F_p be a finite field and F_pⁿ be its nth field extension. By some polynomial GCD computations, this paper characterize the bentness and semi-bentness of two classes of p-ary quadratic functions from F_pⁿ to F_p with coefficients in F_p^e. Moreover, the enumeration formulas of constructed bent functions are obtained for some special cases of m. The results generalize some previous related work.
- Quadratic bent function,
- Quadratic semi-bent function,
- Greatest common divisor,
- Block cyclic matrix

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References(20)

References

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