A Family of p-ary Binomial Bent Functions

• ZHENG Dabin

  Faculty of Mathematics and Computer Science, Hubei University

• ZENG Xiangyong

  Faculty of Mathematics and Computer Science, Hubei University

• HU Lei

  State Key Laboratory of Information Security, Graduate School of Chinese Academy of Sciences

Abstract

For a prime p with p ≡ 3(mod 4) and an odd number m, the Bentness of the p-ary binomial function $f_{a,b}(x)={\\rm Tr}_{1}^n(ax^{p^m-1})+{\\rm Tr}_{1}^2(bx^{\\frac{p^n-1}{4}})$ is characterized, where n=2m, $a\\in \\bF_{p^n}^*$, and $b\\in \\bF_{p^2}^*$. The necessary and sufficient conditions of ƒ_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 ƒ_a,b(x) by the Hamming weight of a sequence.

Journal

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E94-A (9), 1868-1872, 2011

  The Institute of Electronics, Information and Communication Engineers

Keywords

• <i>p</i>-ary binomial Bent functions
• exponential sum
• Hamming weight

Details

• CRID: 1390001206312138880
• NII Article ID: 10030190926
• NII Book ID: AA10826239
• DOI: 10.1587/transfun.e94.a.1868
• ISSN: 17451337
• ISSN: 09168508
• Web Site: http://www.jstage.jst.go.jp/article/transfun/E94.A/9/E94.A_9_1868/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed