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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)

—We find a one to one correspondence between quadratic APN functions without linear and constant terms and a special kind of matrices (We call such matrices as QAMs). Based on the nice mathematical structures of the QAMs, we have developed efficient algorithms to construct quadratic APN functions. On F 2 7 , we have found more than 470 classes of new… (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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