摘要
In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that the proposed functions over the finite field Fq are permutations if and only if q≡3(mod 4).
In this paper, we propose a construction of functions with low differential uniformity based on known perfect nonlinear functions over finite fields of odd characteristic. For an odd prime power q, it is proved that the proposed functions over the finite field Fq are permutations if and only if q = 3 （mod 4）.
基金
supported by National Natural Science Foundation of China(Grant Nos.61070172,10990011 and 61170257)
the External Science and Technology Cooperation Program of Hubei Province(Grant No.2012IHA01402)
National Key Basic Research Program of China(Grant No.2013CB834203)
the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA06010702)
