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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 F27 , we have found more than 470 classes of new(More)
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(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 F22k can be constructed by composing the inverse function and cycles over F22k . Two sufficient conditions are given, which ensure that the(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(More)
This paper mainly focuses on permutation polynomials over the residue class ring ZN , where N > 3 is composite. We have proved that for the polynomial f(x) = a1x 1 + · · · + akx with integral coefficients, f(x) mod N permutes ZN if and only if f(x) mod N permutes Sμ for all μ | N , where Sμ = {0 < t < N : gcd(N, t) = μ} and SN = S0 = {0}. Based on it, we(More)
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