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In this paper, we propose two classes of 2k-variable Boolean functions, which have optimal algebraic immunity under the assumption that a general combinatorial conjecture is correct. These functions also have high algebraic degree and high nonlinearity. One class contain more bent functions , and the other class are balanced.
This paper is devoted to the existence and uniqueness results of solutions for fractional differential equations with integral boundary conditions. By means of the Banach contraction mapping principle, some new results on the existence and uniqueness are obtained. It is interesting to note that the sufficient conditions for the existence and uniqueness of(More)
  • Baofeng Wu
  • 2014
We propose new classes of quadratic bent functions in polynomial forms, coefficients of which are from extension fields of F<sub>2</sub>. Bentness of these functions is based on certain linearized permutation polynomials over finite fields of even characteristic, whose permutation properties are confirmed by virtue of arithmetics in skew-polynomial rings.(More)
Constructing 2m-variable Boolean functions with optimal algebraic immunity based on decomposition of additive group of the finite field F 2 2m seems to be a promising approach since Tu and Deng's work. In this paper, we consider the same problem in a new way. Based on polar decomposition of the multiplicative group of F 2 2m , we propose a new construction(More)
—We propose a general approach to construct cryptographic significant Boolean functions of (r + 1)m variables based on the additive decomposition F2rm × F2m of the finite field F 2 (r+1)m , where r is odd and m ≥ 3. A class of unbalanced functions are constructed first via this approach, which coincides with a variant of the unbalanced class of generalized(More)
Many modern block ciphers use maximum distance separate (MDS) matrices as their diffusion layers. In this paper, we propose a new method to verify a sort of MDS diffusion block matrices whose blocks are all polynomials in a certain primitive block over the finite field F 2. And then we discover a new kind of transformations that can retain MDS property of(More)