摘要
In this paper, the possible value of the differential uniformity of a function over finite fields is discussed. It is proved that, the differential uniformity of a function over Fq can be any even integer between 2 and q when q is even; and it can be any integer between 1 and q except q-1 when q is odd. Moreover, for any possible differential uniformity t, an explicit construction of a differentially t-uniform function is given.
In this paper, the possible value of the differential uniformity of a function over finite fields is discussed. It is proved that, the differential uniformity of a function over Fq can be any even integer between 2 and q when q is even; and it can be any integer between 1 and q except q - 1 when q is odd. Moreover, for any possible differential uniformity t, an explicit construction of a differentially t-uniform function is given.
基金
supported by National Natural Science Foundation of China(Grant Nos.61070215 and 61272484)
the National Basic Research Program of China(Grant No.2013CB338002)
the open research fund of Science and Technology on Information Assurance Laboratory(Grant No.KJ-12-02)
