Results on Bent Functions

Hou, Xiang‐dong; Langevin, Philippe

doi:10.1006/jcta.1997.2804

Cited by 46 publications

(22 citation statements)

References 8 publications

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“…(2.5) Equation (2.5) with k = 2 has been obtained in [14]. We remark that several previous computer searches for bent functions can be made much easier using Corollary 2.2 ( [12], [19]).…”

Section: The Main Theoremmentioning

confidence: 89%

On the coefficients of binary bent functions

Hou

1999

Proc. Amer. Math. Soc.

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“…(2.5) Equation (2.5) with k = 2 has been obtained in [14]. We remark that several previous computer searches for bent functions can be made much easier using Corollary 2.2 ( [12], [19]).…”

Section: The Main Theoremmentioning

confidence: 89%

On the coefficients of binary bent functions

Hou

1999

Proc. Amer. Math. Soc.

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“…In [5] and later in [2] several interesting results where derived concerning the ANF of a bent function. It was shown that the ANF of a bent function has to fulfill several criteria.…”

Section: Detailed Description Of Our Methodsmentioning

confidence: 99%

“…The first is the above recalled classification of RM * (4, 8) and the second is a result from [5], see Theorem 1 below, that restricts the ANF of a bent functions in term of equations that are fulfilled by the ANF coefficients. An important detail of these equations is, that the equations involving degree m coefficients become affine when all coefficients of higher degree than m are fixed (see Lemma 1 for details).…”

Section: Outline Of Our Approachmentioning

confidence: 98%

Counting all bent functions in dimension eight 99270589265934370305785861242880

Langevin¹,

Leander²

2010

Des. Codes Cryptogr.

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Based on the classification of the homogeneous Boolean functions of degree 4 in 8 variables we present the strategy that we used to count the number of all bent functions in dimension 8. There are 99270589265934370305785861242880 ≈ 2 106 such functions in total. Furthermore, we show that most of the bent functions in dimension 8 are nonequivalent to Maiorana-McFarland and partial spread functions.

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“…Bent functions played many important roles in design theory, coding theory and cryptography. Binary bent functions, studied extensively over a long time, turn out to be a very intricate topic with many open questions [1,2,4,10,11]. Although q-ary bent functions are beginning to receive attention [5,6], not very much is known about them.…”

Section: Introductionmentioning

confidence: 99%