Propagation Characteristics and Correlation-Immunity of Highly Nonlinear Boolean Functions

Canteaut, Anne; Carlet, Claude; Charpin, Pascale; Fontaine, Caroline

doi:10.1007/3-540-45539-6_36

Cited by 70 publications

(59 citation statements)

References 28 publications

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“…We refer throughout the rest of this paper to the value p (n+1)/2 as F max (w). Thus: Theorem 5: (Generalization of theorem 3 in (Canteaut et al, 2000)) Let f(x) be a function defined over GF(p) with n variables. Then, the dimension k of the linear space V n is such that k ≤ 1.…”

Section: ∑ ∑mentioning

confidence: 99%

Generalization of Boolean Functions Properties to Functions Defined over GF(p)

`Hamed¹

2012

Journal of Computer Science

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Problem statement: Traditionally, cryptographic applications designed on hardware have always tried to take advantage of the simplicity of implementation functions over GF(p), p = 2, to reduce costs and improve performance. On the contrast, functions defined over GF(p); p > 2, possess far better cryptographic properties than GF(2) functions. Approach: We generalize some of the previous results on cryptographic Boolean functions to functions defined over GF(p); p > 2. Results: We generalize Siegenthaler's construction to functions defined over finite field. We characterize the linear structures of functions over GF(p) in terms of their Walsh transform values. We then investigate the relation between the autocorrelation coefficients of functions over GF(p) and their Walsh spectrum. We also derive an upper bound for the dimension of the linear space of the functions defined over GF(p). Finally, we present a method to construct a bent function from semi-bent functions. Conclusion: Functions defined over GF(p) can achieve better cryptographic bounds than GF(2) functions. In this paper we gave a generalization of several of the GF(2) cryptographic properties to functions defined over GF(p), where p is an odd prime.

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Section: ∑ ∑mentioning

confidence: 99%

Generalization of Boolean Functions Properties to Functions Defined over GF(p)

`Hamed¹

2012

Journal of Computer Science

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“…Thus, derivatives play also a role with respect to the notion of confusion, since they permit a characterization of bent functions; recent results [5] show that they play more generally a role with respect to nonlinearity, even for non-bent functions. We denote the second-…”

Section: Preliminariesmentioning

confidence: 99%

“…Annex A.2) and by Canteaut, Carlet, Charpin and Fontaine [5,6]. In the standard model of stream ciphers, a Boolean function is used to combine the outputs of n linear feedback shift registers.…”

Section: Plateaued Functionsmentioning

confidence: 99%

On Plateaued Functions and Their Constructions

Carlet

Prouff

2003

Fast Software Encryption

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Abstract. We use the notion of covering sequence, introduced by C. Carlet and Y. Tarannikov, to give a simple characterization of bent functions. We extend it into a characterization of plateaued functions (that is bent and three-valued functions). After recalling why the class of plateaued functions provides good candidates to be used in cryptosystems, we study the known families of plateaued functions and their drawbacks. We show in particular that the class given as new by Zhang and Zheng is in fact a subclass of Maiorana-McFarland's class. We introduce a new class of plateaued functions and prove its good cryptographic properties.

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“…Therefore, constructing the balanced Boolean function f with SAC property, which is called balanced SAC Boolean function in this paper for short, high nonlinearity N f and very good GAC property (low absolute indicator ∆ f and low sum-of-squares indicator σ f ) is very desirable. Addressing this problem, many works have been done, for instance [1,7,9,11,8], which are summarized in Table 1.…”

Section: Introductionmentioning

confidence: 99%

Construction of balanced Boolean functions with high nonlinearity and good autocorrelation properties

Tang

Zhang

Tang

2011

Des. Codes Cryptogr.

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Boolean functions with high nonlinearity and good autocorrelation properties play an important role in the design of block ciphers and stream ciphers. In this paper, we give a method to construct balanced Boolean functions on n variables, where n ≥ 10 is an even integer, satisfying strict avalanche criterion (SAC). Compared with the known balanced Boolean functions with SAC property, the constructed functions possess the highest nonlinearity and the best global avalanche characteristics (GAC) property.

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Propagation Characteristics and Correlation-Immunity of Highly Nonlinear Boolean Functions

Cited by 70 publications

References 28 publications

Generalization of Boolean Functions Properties to Functions Defined over GF(p)

Generalization of Boolean Functions Properties to Functions Defined over GF(p)

On Plateaued Functions and Their Constructions

Construction of balanced Boolean functions with high nonlinearity and good autocorrelation properties

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