New Results on the Boolean Functions That Can Be Expressed as the Sum of Two Bent Functions

Qu, Longjiang; Fu, Shaojing; Dai, Qingping; Li, Chao

doi:10.1587/transfun.e99.a.1584

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…Though it is only confirmed for a few classical constructions of Boolean functions that they are a sum of two bent functions (mostly seen straightforward, see [29]), the hypothesis is not falsified. In fact if this were true in general, then one would have quite precise (upper and lower) bounds for the number of Boolean bent functions in any dimension n.…”

Section: Coding-theoretic Approachmentioning

confidence: 99%

Linear codes and incidence structures of bent functions and their generalizations

Meidl¹,

Polujan²,

Pott³

2020

Preprint

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In this paper we consider further applications of (n, m)-functions for the construction of 2-designs. For instance, we provide a new application of the extended Assmus-Mattson theorem, by showing that linear codes of APN functions with the classical Walsh spectrum support 2-designs. On the other hand, we use linear codes and combinatorial designs in order to study important properties of (n, m)-functions. In particular, we give a new design-theoretic characterization of (n, m)-plateaued and (n, m)-bent functions and provide a coding-theoretic as well as a design-theoretic interpretation of the extendability problem for (n, m)-bent functions.

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Section: Coding-theoretic Approachmentioning

confidence: 99%

Linear codes and incidence structures of bent functions and their generalizations

Meidl¹,

Polujan²,

Pott³

2020

Preprint

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“…But till now this problem is unsolved. 4.15. P r o b l e m " S u p e r S -b o x " ( u n s o l v e d ) The problem is still unsolved.…”

Section: P R O B L E M " T H E M U S I C a L N O T A T I O N " ( 4 S mentioning

confidence: 99%

Problems, Solutions and Experience of the First International Student’s Olympiad in Cryptography

Agievich¹,

Gorodilova²,

Kolomeec³

et al. 2015

Prikladnaya Diskretnaya Matematika

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A detailed overview of the problems, solutions and experience of the first international student's Olympiad in cryptography, NSUCRYPTO'2014, is given. We start with the rules of participation and the description of rounds. All 15 mathematical problems of the Olympiad and their solutions are considered in detail. The problems are about differential characteristics of S-boxes, S-box masking, relations between cyclic rotation and additions modulo 2 and 2 n , special linear subspaces in F n 2 , the number of solutions of the equation F (x) + F (x + a) = b over the finite field F 2 n and APN functions. Some unsolved problems in symmetric cryptography are also considered.

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“…Для произвольного n доказан [4] ослабленный вариант гипотезы. Авторы [5] доказали, что в виде суммы двух бент-функций может быть представлена любая квадратичная булева функция, любая бент-функция Мак-Фарланда, произвольная функция частичного расщепления. В работе [6] отмечается связь гипотезы с открытыми вопросами о метрических свойствах класса бент-функций.…”

Section: Introductionunclassified

On decomposition of a dual bent function into sum of two bent functions

Tokareva¹

2014

Applied Discrete Mathematics

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New Results on the Boolean Functions That Can Be Expressed as the Sum of Two Bent Functions

Cited by 4 publications

References 27 publications

Linear codes and incidence structures of bent functions and their generalizations

Linear codes and incidence structures of bent functions and their generalizations

Problems, Solutions and Experience of the First International Student’s Olympiad in Cryptography

On decomposition of a dual bent function into sum of two bent functions

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