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基于迹函数的negabent函数构造

赵海霞 李文宇 韦永壮

赵海霞, 李文宇, 韦永壮. 基于迹函数的negabent函数构造[J]. 电子与信息学报, 2024, 46(1): 335-343. doi: 10.11999/JEIT230001
引用本文: 赵海霞, 李文宇, 韦永壮. 基于迹函数的negabent函数构造[J]. 电子与信息学报, 2024, 46(1): 335-343. doi: 10.11999/JEIT230001
ZHAO Haixia, LI Wenyu, WEI Yongzhuang. Construction of Negabent Function Based on Trace Function over Finite Field[J]. Journal of Electronics & Information Technology, 2024, 46(1): 335-343. doi: 10.11999/JEIT230001
Citation: ZHAO Haixia, LI Wenyu, WEI Yongzhuang. Construction of Negabent Function Based on Trace Function over Finite Field[J]. Journal of Electronics & Information Technology, 2024, 46(1): 335-343. doi: 10.11999/JEIT230001

基于迹函数的negabent函数构造

doi: 10.11999/JEIT230001
基金项目: 国家自然科学基金(62162016),广西自然科学基金(2019GXNSFGA245004)
详细信息
    作者简介:

    赵海霞:女,副教授,研究方向为密码函数、对称密码算法设计与分析

    李文宇:男,硕士生,研究方向为密码函数、对称密码分析

    韦永壮:男,教授,研究方向为密码函数,对称密码算法设计与分析,侧信道攻击与防御科技

    通讯作者:

    韦永壮 walker_wyz@guet.edu.cn

  • 中图分类号: TN918.2

Construction of Negabent Function Based on Trace Function over Finite Field

Funds: The National Natural Science Foundation of China (62162016), Guangxi Natural Science Foundation (2019GXNSFGA245004)
  • 摘要: Negabent函数是一种具有最优自相关性、较高非线性度的布尔函数,在密码学、编码理论及组合设计中都有着广泛的应用。该文基于有限域上的迹函数,将其与置换多项式相结合,提出两种构造negabent函数的方法。所构造的两类negabent函数均具备${\text{Tr}}_1^k(\lambda {x^{{2^k} + 1}}) + {\text{Tr}}_1^n(ux){\text{Tr}}_1^n(vx) + {\text{Tr}}_1^n(mx){{\rm{Tr}}} _1^n(dx)$形式:构造方法1通过调整$\lambda ,{\text{ }}u,{\text{ }}v,{\text{ }}m$中的3个参数来获得negabent函数,特别地,当$\lambda $≠1时,能得到$({2^{n - 1}} - 2)({2^n} - 1)({2^n} - 4)$个negabent函数;构造方法2通过调整$\lambda ,{\text{ }}u,{\text{ }}v,{\text{ }}m,{\text{ }}d$中的4个参数来获得negabent函数,特别地,当$\lambda$≠1时,至少能够得到${2^{n - 1}}[({2^{n - 1}} - 2)({2^{n - 1}} - 3) + {2^{n - 1}} - 4]$个negabent函数。
  • 表  1  不同调参方案所构造函数数量

    调整的参数计数
    文献[12]$ u,v $$({2^{n - 1}} - 2)({2^n} - 1)$
    定理2$ u,v,m $$({2^{n - 1}} - 2)({2^n} - 1)({2^n} - 4)$
    定理3$ u,v,m,d $$\ge {2^{n - 1} }[({2^{n - 1} } - 2)({2^{n - 1} } - 3) + {2^{n - 1} } - 4]$
    下载: 导出CSV
    定理3中$\lambda \ne 1$时$\left( {A,B,C,D,E,F,G,H,I,J} \right)$不取的10元向量
    11000000001100000100111101000111000000011111110001110000010111111101101100000111111000000011100001001111001100
    11111100001111101100111110010111111011111111111011000000001011010000011111000100111110010011110111011111001110
    11111010111111111010000000010100000000111110110101111110000111110110101111000110111101111111111101010000001101
    00000001101110101001111100001011110110001110101101111101010111111011010000010101000000111011100100101110111000
    11110011111110100110111100110111111010010000011010000001001111100100011110110001111100001111100110111111000101
    11111000100000011101000010010111100011101110100111111011110011010111011110110011111100011100010000100000111010
    11100000101110100010111011100111010110101110101000111011110100010010000000111101110111011111100110011110110010
    11010110011110011101111011011100010100000001000011110100010011100000011110101110110101001011100101101110110110
    00011000000001000110110001111111011100001110011100110100010111100011111110101111000111110000010010011100010010
    11011001011110001000110011011111100001101110000111001000001000010100011100000010110110001011100000111100101111
    11011111111101111101001000011000011001001011111010110100001011011010111100100110110110100111011110110010010000
    00011011001011011100110011110011010111101100010100110100011011011110100010100001000111011110110100111100101011
    11010101101100001001110001011011011011110010101101000111110110110010101100100010110101000010111110111100000110
    11011011010010111001001000001110100111101100010000110100001110111101011011111101110110101000110000000010101111
    10100111001100001000110011001010111001011011010111110101010000110000100010111101101001101110111111001100011101
    10111000111011001011110011110100110001010011000011101001001010111101001100011010101100111010101100111100111010
    00110001110011100000101000101010111001111100000011101011110110100111111100110110001101101000111001001001100101
    10111000101011111110101011010110100101101100100101001101110100111001011001011111101101110110111101101010101111
    10100010111011111111001110011000111001111001010101101101101010111100111010101110100111101010111101110100000000
    00111110101001001010101100010110111010101010100110100110110110111011110100001000001111110110000111101010111001
    10110100001010100011100100101110111010110100010000010000000110000100101010110100101100100010100101001000111000
    10110010010100011000010000100110000100011010100010101011111010011111011000010111101100011001001000000100010001
    10000011001010010000101011101110011101111000010110101011111101001010000100011100100000101010011111001010110010
    10011000111000001011101011011101001100000100100100011111001010011101101010101100100100100101111111011010110110
    01001110000100101000011101101010011011001010101010100011110101111110101010101011010100000001001011000111000100
    10011000101010011000100011101001111001011001101111011000000001001101000110111100100101010010100011101000100110
    01111000101001101011011001000001001111000110010010100100100010011011101000100101011101101110010111100111000000
    01010001000110001000100010010010011010101000100011011100010110001111110111011000010100100101100000101000100010
    10010111010111110001011010111010001101101000000010011000010001011110011000011101100101101001111011100110010110
    10001010111000100000011001000101011101011000011100100011001001111011000110010011100010011110001010010111000001
    01011010111000011010100010101001110111010110001001011111111110001101110111011001010101000010000010001000001110
    01110000110110000110011111100010010000101000000011010100101010000001010111101001011010011001011111110111110110
    10010001011000000110010100100001111101000111011110011001010101011011110111101011100101100010001000010101000010
    01111001110111000110011000010101010101000111011111100110000110001010000100111010011110000001101100100101100100
    01010010110111000111100110100010001100110100110010011101110001100000110101100001010100011001101110011001110001
    10010000110100101010011100001001011100000101001101010011101101101101101010000010100110000001001000100110100010
    01011010000101000101010011001101101010101010000101100110100101000110100110010100010100111001001111010100101011
    01100101111010001001101000001101000100100110000001010100001101001101010100100011011000011110100100011010000110
    01000010100101100000010011111001001011010100011011010111111010101001111010001111010000001001010011000100110110
    01001001010100010101010111010010101100001010010111001111110001010000010100101110010001110101000011010101101001
    10110000101010101001001111100101001110010100100110010001011001000001010101001111101101010010101100010011110110
    01001100010100011110010000111000111101110101000111101110000010110000110011010001010010100101000100110100000011
    00111011110100111111101111100010110001110011010000010010000101000010110011111111001101101101001101111100011000
    10110101010011001111010001100101000001100011111000001101010001001011111100101100101111100100110011010100010100
    00111010100011101110001100101101001001111100110001111000110000110010100100001100001101111100111000110011001001
    01000111111101000000111000110100110010000100000100001101100000101100010011000110010001011111100010011111000001
    00100110010011100010001011001000101011000010111011010000111111110000000001110110001001001000101000100010101010
    00101001100010010110010000011100001001100001101011001000101000100101010010100111001010001100100100110011101011
    00001000110000111110000101100000011100000010001000001001100000100010110010111100111000010100001110110001010010
    00011000100001111000001000111100010110010010110110000011001100001101100001001010000101111100011100100001110001
    00010101100010101011000010111000001010110000110101000101101100011010100001100110000100101100100111110000010110
    11010001110000101101000101011100001100100001100011000001111000011111100000001010000010001000000100100001001101
    00001010100001000101000001101100011110010000001011
    下载: 导出CSV
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出版历程
  • 收稿日期:  2023-01-09
  • 修回日期:  2023-06-09
  • 网络出版日期:  2023-06-14
  • 刊出日期:  2024-01-17

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