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**2012/335**

**Title:**

Constructing Vectorial Boolean Functions with High Algebraic Immunity Based on Group Decomposition

**Authors:**
Yu Lou, Huiting Han, Chunming Tang, Maozhi Xu

**Abstract:**

In this paper, we construct a class of vectorial Boolean functions over \mathbb{F}_{2^{n}} with high algebraic immunity based on the decomposition of the multiplicative group of \mathbb{F}_{2^n}. By viewing \mathbb{F}_{2^{n}} as G_1G_2\bigcup \{0\} (where G_1 and G_2 are subgroups of \mathbb{F}_{2^{n}}^{*},~(\#G_1,\#G_2)=1 and \#G_1\times \#G_2=2^{2k}-1), we give a generalized description for constructing vectorial Boolean functions with high algebraic immunity. Moreover, when n is even, we provide two special classes of vectorial Boolean functions with high(sometimes optimal) algebraic immunity, one is hyper-bent, and the other is of balancedness and optimal algebraic degree .

**ePrint:**
https://eprint.iacr.org/2012/335

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