A Class of New Quadratic Vectorial Bent Functions

PANG Tingting; ZENG Xiangyong; LI Nian; XU Yunge

doi:10.1049/cje.2020.08.002

Volume 29 Issue 5

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PANG Tingting, ZENG Xiangyong, LI Nian, XU Yunge. A Class of New Quadratic Vectorial Bent Functions[J]. Chinese Journal of Electronics, 2020, 29(5): 873-879. doi: 10.1049/cje.2020.08.002

Citation:

PANG Tingting, ZENG Xiangyong, LI Nian, XU Yunge. A Class of New Quadratic Vectorial Bent Functions[J]. Chinese Journal of Electronics, 2020, 29(5): 873-879. doi: 10.1049/cje.2020.08.002

PANG Tingting, ZENG Xiangyong, LI Nian, XU Yunge. A Class of New Quadratic Vectorial Bent Functions[J]. Chinese Journal of Electronics, 2020, 29(5): 873-879. doi: 10.1049/cje.2020.08.002

Citation:

PANG Tingting, ZENG Xiangyong, LI Nian, XU Yunge. A Class of New Quadratic Vectorial Bent Functions[J]. Chinese Journal of Electronics, 2020, 29(5): 873-879. doi: 10.1049/cje.2020.08.002

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A Class of New Quadratic Vectorial Bent Functions

doi: 10.1049/cje.2020.08.002

The Faculty of Mathematics and Statistics, Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan 430062, China

Funds: This work is supported by the National Natural Science Foundation of China (No.61761166010, No.61702166), the Major Technological Innovation Special Project of Hubei Province (No.2019ACA144), and National Natural Science Foundation of Hubei Province of China (No.2017CFB143).

More Information

Corresponding author: ZENG Xiangyong (corresponding author) was born in Hubei Province, China, in 1973. He received the B.S. degree from the Department of Mathematics, Hubei University in 1995, and received the M.S. and Ph.D. degrees from Beijing Normal University in 1998 and 2002 respectively. From 2002 to 2004, he was a postdoctoral member in the Computer School of Wuhan University. Since 2009, he has been a professor of Hubei University. His research interests include cryptography, sequence design and coding theory. (Email:xiangyongzeng@aliyun.com)
Received Date: 2019-09-03
Rev Recd Date: 2019-12-19
Publish Date: 2020-09-10

Abstract

Abstract

A class of quadratic vectorial bent functions having the form F (x)=Tr_mⁿ (ax^2s1 +1) + Tr₁ⁿ (bx^2s2 +1) is investigated, where n, m, s₁, s₂ are positive integers and the coefficients a, b belong to the finite field F_2ⁿ. Through some discussions on the permutation property of certain linearized polynomials over F_2ⁿ, several classes of quadratic vectorial bent functions are presented for special cases of n, and it is also verified by computer that some vectorial bent functions proposed are extended affine inequivalent to all known quadratic vectorial bent functions.
- Vectorial bent function,
- Permutation polynomial,
- Extended affine equivalence,
- Finite field

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References(33)

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