New cyclic difference sets with Singer parameters

Dillon, John F.; Dobbertin, Hans

doi:10.1016/j.ffa.2003.09.003

Cited by 239 publications

(174 citation statements)

References 31 publications

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“…Note that r i 's are computed by the rules given in [4] for making t(x) a permutation, and the exponents r i 's are different from the exponents q i 's in Eq. (1) which are taken from [17].…”

Section: The New Results On the Wg Transformationsmentioning

confidence: 99%

Optimal parameters for the WG stream cipher family

et al. 2013

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Abstract. In this paper, we first present some new results about the Welch-Gong (WG) transformations, followed by a description of the WG stream cipher family which is built upon an LFSR and a WG transformation over an extension field. The randomness properties of keystreams produced by a decimated WG cipher are derived based on the new results. We also discuss the selection criteria for choosing the optimal parameters for a WG cipher in order to achieve the maximum level of security. Finally, we present the optimal parameters for the WG transformations over F2m , 7 ≤ m ≤ 16 based on the proposed criteria.

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Section: The New Results On the Wg Transformationsmentioning

confidence: 99%

Optimal parameters for the WG stream cipher family

et al. 2013

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“…Our next construction is based on a class of functions from the construction of cyclic Hadamard difference sets by Dillon and Dobbertin [8].…”

Section: Lemma 2 (Kasami-dillonmentioning

confidence: 99%

“…C f (λ) = P x∈GF (2 n ) (−1) f (x)+f (λx) = 0 for all λ = 1 [7][8][9], for applications in pseudorandom number generation and communication systems.…”

Section: Lemma 2 (Kasami-dillonmentioning

confidence: 99%

“…We present some functions used in the construction of certain Hadamard difference sets, which achieve these properties. They include the Kasami functions, the Dillon-Dobbertin functions, the Segre hyperoval functions and the Welch-Gong Transformation functions [7][8][9]11]. Moreover, some of these functions have high algebraic degree (for algebraic complexity) and large linear span (which offers protection against an interpolation attack [13]).…”

Section: Introductionmentioning

confidence: 99%

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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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“…Due to their good randomness properties and simple implementation [9] [10], Ñ-sequences have been widely used for communication systems. Besides Ñ-sequences, several other inequivalent classes of binary sequences with ideal two-level autocorrelation have been constructed and discovered [4] [13] [20] [22] [24].…”

Section: Introductionmentioning

confidence: 99%

New Binary Sequences With Optimal Autocorrelation Magnitude

Gong

2008

IEEE Trans. Inform. Theory

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New binary sequences of period AE 3 Ñ ½µ for even Ñ are found. These sequences can be described by a ¢´¾ Ñ ½µ interleaved structure. The new sequences are almost balanced and have four-valued autocorrelation, i.e., AE ¼ ¦ , which is optimal with respect to autocorrelation magnitude.Complete autocorrelation distribution and exact linear complexity of the sequences are mathematically derived. From the simple implementation with a small number of shift registers and a connector, the sequences have a benefit of obtaining large linear complexity.

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New cyclic difference sets with Singer parameters

Cited by 239 publications

References 31 publications

Optimal parameters for the WG stream cipher family

Optimal parameters for the WG stream cipher family

Additive Autocorrelation of Resilient Boolean Functions

New Binary Sequences With Optimal Autocorrelation Magnitude

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