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**2013/166**

**Title:**

On generalized semi-bent (and partially bent) Boolean functions

**Authors:**
Brajesh Kumar Singh

**Abstract:**

In this paper, we obtain a characterization of generalized Boolean functions based on spectral analysis. We investigate a relationship between the Walsh-Hadamard spectrum and \sigma_f, the sum-of-squares-modulus indicator (SSMI) of the generalized Boolean function. It is demonstrated that \sigma_f = 2^{2n + s} for every s-plateaued generalized Boolean function in n variables. Two classes of generalized semi-bent Boolean functions are constructed.% and it is demonstrated that their SSMI is over generalized s-plateaued Boolean functions is 2^{2n + s}. We have constructed a class of generalized semi-bent functions in (n+1) variables from generalized semi-bent functions in n variables and identify a subclass of it for which \sigma_f and \triangle_{f} both have optimal value. Finally, some construction on generalized partially bent Boolean functions are given.

**ePrint:**
https://eprint.iacr.org/2013/166

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