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We find a correspondence between quadratic APN functions and a special kind of matrices. Based on this result, we have developed efficient algorithms to construct quadratic APN functions. Up to now, we have found more than 470 classes of new CCZ-inequivalent quadratic APN functions on F 2 7 , which is 20 times more than known ones. And we also have found… (More)

Constructing S-boxes with low differential uniformity and high nonlinearity is of cardinal significance in cryptography. In the present paper, we show that numerous differentially 4-uniform permutations over F 2 2k can be constructed by composing the inverse function and cycles over F 2 2k. Two sufficient conditions are given, which ensure that the… (More)

It is observed that exchanging two values of a function over F 2 n , its differential uniformity and nonlinearity change only a little. Using this idea, we find permutations of differential 4-uniform over F 2 6 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… (More)

In a compartmented access structure, there are disjoint participants C1,. .. , Cm. The access structure consists of subsets of participants containing at least ti from Ci for i = 1,. .. , m, and a total of at least t0 participants. Tassa [2] asked: whether there exists an efficient ideal secret sharing scheme for such an access structure? Tassa and Dyn [5]… (More)

This paper mainly focuses on permutation polynomials over the residue class ring Z N , where N > 3 is composite. We have proved that for the polynomial f (x) = a 1 x

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