A Family of <I>p</I>-ary Binomial Bent Functions

Dabin ZHENG; Xiangyong ZENG; Lei HU

doi:10.1587/transfun.E94.A.1868

A Family of p-ary Binomial Bent Functions

Dabin ZHENG, Xiangyong ZENG, Lei HU

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For a prime p with p≡3 (mod 4) and an odd number m, the Bentness of the p-ary binomial function f_a,b(x)=Tr₁ⁿ(ax^{p^m-1})+Tr₁² is characterized, where n=2m, a ∈ F^*_pⁿ, and b ∈ F^*_p². The necessary and sufficient conditions of f_a,b(x) being Bent are established respectively by an exponential sum and two sequences related to a and b. For the special case of p=3, we further characterize the Bentness of the ternary function f_a,b(x) by the Hamming weight of a sequence.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.9 pp.1868-1872

Publication Date: 2011/09/01

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Online ISSN: 1745-1337

DOI: 10.1587/transfun.E94.A.1868

Type of Manuscript: LETTER

Category: Cryptography and Information Security

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Dabin ZHENG, Xiangyong ZENG, Lei HU, "A Family of p-ary Binomial Bent Functions" in IEICE TRANSACTIONS on Fundamentals, vol. E94-A, no. 9, pp. 1868-1872, September 2011, doi: 10.1587/transfun.E94.A.1868.
Abstract: For a prime p with p≡3 (mod 4) and an odd number m, the Bentness of the p-ary binomial function f_a,b(x)=Tr₁ⁿ(ax^{p^m-1})+Tr₁² is characterized, where n=2m, a ∈ F^*_pⁿ, and b ∈ F^*_p². The necessary and sufficient conditions of f_a,b(x) being Bent are established respectively by an exponential sum and two sequences related to a and b. For the special case of p=3, we further characterize the Bentness of the ternary function f_a,b(x) by the Hamming weight of a sequence.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E94.A.1868/_p

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@ARTICLE{e94-a_9_1868,
author={Dabin ZHENG, Xiangyong ZENG, Lei HU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Family of p-ary Binomial Bent Functions},
year={2011},
volume={E94-A},
number={9},
pages={1868-1872},
abstract={For a prime p with p≡3 (mod 4) and an odd number m, the Bentness of the p-ary binomial function f_a,b(x)=Tr₁ⁿ(ax^{p^m-1})+Tr₁² is characterized, where n=2m, a ∈ F^*_pⁿ, and b ∈ F^*_p². The necessary and sufficient conditions of f_a,b(x) being Bent are established respectively by an exponential sum and two sequences related to a and b. For the special case of p=3, we further characterize the Bentness of the ternary function f_a,b(x) by the Hamming weight of a sequence.},
keywords={},
doi={10.1587/transfun.E94.A.1868},
ISSN={1745-1337},
month={September},}

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TY - JOUR
TI - A Family of p-ary Binomial Bent Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1868
EP - 1872
AU - Dabin ZHENG
AU - Xiangyong ZENG
AU - Lei HU
PY - 2011
DO - 10.1587/transfun.E94.A.1868
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E94-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2011
AB - For a prime p with p≡3 (mod 4) and an odd number m, the Bentness of the p-ary binomial function f_a,b(x)=Tr₁ⁿ(ax^{p^m-1})+Tr₁² is characterized, where n=2m, a ∈ F^*_pⁿ, and b ∈ F^*_p². The necessary and sufficient conditions of f_a,b(x) being Bent are established respectively by an exponential sum and two sequences related to a and b. For the special case of p=3, we further characterize the Bentness of the ternary function f_a,b(x) by the Hamming weight of a sequence.
ER -