On Plateaued Functions and Their Constructions

Carlet, Claude; Prouff, Emmanuel

doi:10.1007/978-3-540-39887-5_6

Cited by 62 publications

(53 citation statements)

References 33 publications

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“…Carlet and Prouff present another way of concatenating quadratic functions in [6].We denote the class by Q. Definition 3 [6] For any positive integers r and s such that n=r+s, an Q function f is defined by…”

Section: Q's Functionsmentioning

confidence: 99%

“…As a result, the study of Plateaued functions becomes necessary and important. As for the construction of Plateaued functions, there only exist three main classes (see [4][5][6]). The class in [7] is in fact a subclass of [4].…”

Section: Introductionmentioning

confidence: 99%

“…We call λ the amplitude [6] of Plateaued functions. The study of the Walsh spectrum of quadratic function can be found in [16,17].…”

Section: Introductionmentioning

confidence: 99%

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On primary construction of Plateaued functions

Sun¹,

Hu²,

Liu³

et al. 2015

Proceedings of the 3rd International Conference on Material, Mechanical and Manufacturing Engineering

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Abstract. To resist different kinds of attacks, Boolean functions used in the cryptosystem should have good cryptographic properties. The Plateaued functions, a large class of Boolean functions containing Bent functions and Partial-Bent functions, are good choices. Therefore, the study of construction and cryptographic properties of Plateaued functions has received wide attention. However, until now, there are few primary constructions known to us, in which one does not assume the existence of previously defined functions to define new ones. Moreover, most of them have some drawbacks. In this paper, a new primary construction of Plateaued functions is given. And we show in particular that most of the existing primary constructions of Plateaued functions can be reduced to ours.

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Section: Q's Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On primary construction of Plateaued functions

Sun¹,

Hu²,

Liu³

et al. 2015

Proceedings of the 3rd International Conference on Material, Mechanical and Manufacturing Engineering

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show abstract

“…This is an important class of functions with many applications in cryptography, for example see [2,4,5,20,27]. We give several new constructions of resilient Boolean functions with high nonlinearity and optimally low additive autocorrelation.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, the Maiorana-McFarland function in equation (4) becomes linear when we fix (n − 1)/2 input bits y. Our construction can avoid this possible weakness:…”

mentioning

confidence: 99%

Additive Autocorrelation of Resilient Boolean Functions

Gong

Khoo

2004

Selected Areas in Cryptography

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Abstract. In this paper, we introduce a new notion called the dual function for studying Boolean functions. First, we discuss general properties of the dual function that are related to resiliency and additive autocorrelation. Second, we look at preferred functions which are Boolean functions with the lowest 3-valued spectrum. We prove that if a balanced preferred function has a dual function which is also preferred, then it is resilient, has high nonlinearity and optimal additive autocorrelation. We demonstrate four such constructions of optimal Boolean functions using the Kasami, Dillon-Dobbertin, Segre hyperoval and Welch-Gong Transformation functions. Third, we compute the additive autocorrelation of some known resilient preferred functions in the literature by using the dual function. We conclude that our construction yields highly nonlinear resilient functions with better additive autocorrelation than the Maiorana-McFarland functions. We also analysed the saturated functions, which are resilient functions with optimized algebraic degree and nonlinearity. We show that their additive autocorrelation have high peak values, and they become linear when we fix very few bits. These potential weaknesses have to be considered before we deploy them in applications.

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Plateaued functions, partial geometric difference sets, and partial geometric designs

2019

J of Combinatorial Designs

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Plateaued functions on finite fields have been studied in many papers in recent years. As a generalization of plateaued functions on finite fields, we introduce the notion of a plateaued function on a finite abelian group. We will give a characterization of a plateaued function in terms of an equation of the matrix associated to the function. Then we establish a one‐to‐one correspondence between the Z2‐valued plateaued functions and partial geometric difference sets (with specific parameters) in finite abelian groups. We will also discuss two general methods (extension and lifting) for the construction of new partial geometric difference sets from old ones in (abelian or nonabelian) finite groups, and construct many partial geometric difference sets and plateaued functions. A one‐to‐one correspondence between partial geometric difference sets (in arbitrary finite groups) and partial geometric designs will be proved.

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On Plateaued Functions and Their Constructions

Cited by 62 publications

References 33 publications

On primary construction of Plateaued functions

On primary construction of Plateaued functions

Additive Autocorrelation of Resilient Boolean Functions

Plateaued functions, partial geometric difference sets, and partial geometric designs

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