Power functions with low uniformity on odd characteristic finite fields

Science China Mathematics - Tập 53 - Trang 1931-1940 - 2010
ZhengBang Zha1,2, XueLi Wang3
1School of Mathematical Sciences, Luoyang Normal University, Luoyang, China
2State Key Laboratory of Information Security, Graduate University of Chinese Academy of Sciences, Beijing, China
3School of Mathematical Sciences, South China Normal University, Guangzhou, China

Tóm tắt

In this paper, we give some new low differential uniformity of some power functions defined on finite fields with odd characteristic. As corollaries of the uniformity, we obtain two families of almost perfect nonlinear functions in GF(3 n ) and GF(5 n ) separately. Our results can be used to prove the Dobbertin et al.’s conjecture.

Tài liệu tham khảo

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