Generalizations of bent functions. A survey

Tokareva, Natalia

doi:10.1134/s1990478911010133

Cited by 47 publications

(16 citation statements)

References 51 publications

(82 reference statements)

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“…Their definitions are given in the follows. We can see more results about the constructions of bent functions and near bent functions in the papers [14][15].…”

Section: Similar-bent Functionmentioning

confidence: 99%

New constructions of low-correlation sequences with high-linear complexity

Xiong¹,

Li²,

Dai³

et al. 2012

IET Communications

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Abstract. In this paper, we propose a new concept named similar-bent function and we present two general methods to construct balanced sequences with low correlation by using similar-bent functions and orthogonal similar-bent functions. We find that the bent sequence sets are special cases of our construction. We also investigate the linear complexity of the new constructed sequences. If a suitable similar-bent function is given, the sequences constructed by it can have high linear complexity. As examples, we construct two new low correlation sequence sets. One constructed based on Dobbertin's iterative function is asymptotically optimal with respect to Welch's bound and the other one is constructed based on Kasami function whose sequences have a high linear complexity.

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“…Their definitions are given in the follows. We can see more results about the constructions of bent functions and near bent functions in the papers [14][15].…”

Section: Similar-bent Functionmentioning

confidence: 99%

New constructions of low-correlation sequences with high-linear complexity

Xiong¹,

Li²,

Dai³

et al. 2012

IET Communications

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“…One of the simplest examples is Rothaus's bent function f (x) = x 1 x 2 + x 3 x 4 + · · · + x 2t−1 x 2t , where n = 2t. For m = 4 and m = 8, several constructions and existence results on GBFs have been found in [5,[8][9][10][11][12][13]. Generalized bent functions have been widely investigated since they are applied in many fields such as communication theory, cryptography and closely related to coding theory and combinatorial design theory.…”

Section: Introductionmentioning

confidence: 99%

Nonexistence of generalized bent functions from $$\mathbb {Z}_{2}^{n}$$ Z 2 n to $$\mathbb {Z}_{m}$$ Z m

Liu

Feng

2016

Des. Codes Cryptogr.

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“…A function with minimum absolute WHT values is called q-ary bent, i.e. f ∈ B n,q is q-ary bent if |W f (u)| = q n/2 for every u ∈ Z n q [9,11,15].…”

Section: Preliminariesmentioning

confidence: 99%

Constructions ofq-ary functions with good global avalanche characteristics

Singh

Bhaintwal

Singh

2014

International Journal of Computer Mathematics

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In this paper, we construct two classes of q-ary balanced functions which have good global avalanche characteristics (GAC) measured in terms of sum-of-squares-modulus indicator (SSMI), modulus indicator(MI), and propagation criterion (PC). We show that the SSMI, MI, and PC of q-ary functions are invariant under affine transformations. Also, we give a construction of q-ary s-plateaued functions and obtain their SSMI. We provide a relationship between the autocorrelation spectrum of a cubic Boolean function and the dimension of the kernel of the bilinear form associated with the derivative of the function. Using this result, we identify several classes of cubic semi-bent Boolean functions which have good bounds on their SSMI and MI, and hence show good behaviour with respect to the GAC.

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Generalizations of bent functions. A survey

Cited by 47 publications

References 51 publications

New constructions of low-correlation sequences with high-linear complexity

New constructions of low-correlation sequences with high-linear complexity

Nonexistence of generalized bent functions from $$\mathbb {Z}_{2}^{n}$$ Z 2 n to $$\mathbb {Z}_{m}$$ Z m

Constructions ofq-ary functions with good global avalanche characteristics

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