The c-differential uniformity is recently proposed to reflect resistance against some variants of differential attack. Finding functions with low attracting attention from many researchers. For even characteristic, it known that permutations Carlitz rank have good cryptographic parameters, for example, uniformity, high nonlinearity, etc. In this paper we show uniformity. We also investigate 3 i...

It is observed that exchanging two values of a function over F2n , its differential uniformity and nonlinearity change only a little. Using this idea, we find permutations of differential 4-uniform over F26 whose number of the pairs of input and output differences with differential 4-uniform is 54, less than 63, which provides a solution for an open problem proposed by Berger et al. [1]. Moreov...

In this paper, for an odd prime p, the differential spectrum of the power function x pk+1 2 in Fpn is calculated. For an odd prime p such that p ≡ 3 mod 4 and odd n with k|n, the differential spectrum of the power function x pn+1 pk+1 + p n −1 2 in Fpn is also derived. From their differential spectrums, the differential uniformities of these two power functions are determined. We also find some...

Article history: Received 13 May 2013 Received in revised form 7 February 2014 Accepted 10 February 2014 Available online xxxx Communicated by Rudolf Lidl MSC: 12Y05 11T06 11T71

introduction: designing and management of sprinkler irrigation systems depend on the situation and location of its implementation and often rely on professional and long-term tests (9). having a good irrigation system depends on knowledge of the relationship between soil, water, plants, irrigation scheduling, the required amount of irrigation water to the water-holding capacity of soil, climate...

The two most important criteria for vectorial Boolean functions used as S-boxes in block ci-phers are differential uniformity and nonlinearity. Previous work in this field has focused onlyon nonlinearity and a different criterion, autocorrelation. In this paper, we describe the resultsof experiments in using simulated annealing, memetic algorithms, and ant colony optimisation to...

The differential uniformity of a mapping F : F2n → F2n is defined as the maximum number of solutions x for equations F (x+a)+F (x) = b when a ̸= 0 and b run over F2n . In this paper we study the question whether it is possible to determine the differential uniformity of a mapping by considering not all elements a ̸= 0, but only those from a special proper subset of F2n \ {0}. We show that the ans...