About: Bent function

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In the mathematical field of combinatorics, a bent function is a special type of Boolean function which is maximally non-linear; it is as different as possible from the set of all linear and affine functions when measured by Hamming distance between truth tables. Concretely, this means the maximum correlation between the output of the function and a linear function is minimal. In addition, the derivatives of a bent function are a balanced Boolean functions, so for any change in the input variables there is a 50 percent chance that the output value will change.

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rdfs:label	Bent function (en) Fonction courbe (fr) Бент-функция (ru) Бент-функція (uk)
rdfs:comment	In the mathematical field of combinatorics, a bent function is a special type of Boolean function which is maximally non-linear; it is as different as possible from the set of all linear and affine functions when measured by Hamming distance between truth tables. Concretely, this means the maximum correlation between the output of the function and a linear function is minimal. In addition, the derivatives of a bent function are a balanced Boolean functions, so for any change in the input variables there is a 50 percent chance that the output value will change. (en) Une fonction booléenne avec un nombre pair de variables est dite fonction courbe — bent dans la terminologie anglosaxonne — si sa non-linéarité est maximale. Cela correspond à être à distance maximale — pour la distance de Hamming — de l'ensemble des fonctions booléennes linéaires, encore appelé code de Reed et Müller d'ordre 1. On dispose d'une borne générale sur la non-linéarité des fonctions booléennes, mais cette borne ne peut être atteinte que lorsque le nombre de variables est pair. De plus, dans ce cas, on sait construire des fonctions atteignant cette borne, par exemple la fonction (fr) Бент-функция (от англ. bent — «изогнутый, наклонённый», ) — булева функция с чётным числом переменных, для которой расстояние Хэмминга от множества аффинных булевых функций с тем же числом переменных максимально. Бент-функции в этом смысле обладают максимальной степенью нелинейности среди всех функций с данным числом переменных и благодаря этому широко применяются в криптографии для создания шифров, максимально устойчивых к методам линейного и дифференциального криптоанализа. (ru)
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dcterms:subject	Combinatorics Symmetric-key cryptography Boolean algebra Theory of cryptography
Wikipage page ID	24465207 (xsd:integer)
Wikipage revision ID	1097443528 (xsd:integer)
Link from a Wikipage to another Wikipage	Monomial Algebraic normal form Degree of a polynomial Interpolation attack Column vector Cryptographic hash function Cryptography Mathematics Modular arithmetic Block ciphers Confusion and diffusion Correlation attack Correlation coefficient Correlation immunity Cross-correlation Equivalence class Combinatorial design Combinatorics Hamming weight Spread spectrum Autocorrelation CDMA CRC Press Truth table HAVAL Linear cryptanalysis Linear map Absolute value Combinatorics Symmetric-key cryptography Duality (mathematics) Finite field Balanced boolean function Carlisle Adams Differential cryptanalysis Gold code Grain (cipher) Boolean algebra Hamming distance Boolean derivative Prime number S-box Theory of cryptography Kasami code Bijection Coding theory Homogeneous polynomial Dot product Boolean function CAST-128 CAST-256 Maximum length sequence Walsh matrix Walsh transform NLFSR Stafford Tavares Stream cipher Lexicographical order Affine function Strict avalanche criterion dbr:Oscar_Rothaus
Link from a Wikipage to an external page	https://archive.org/details/handbookofcombin0000unse/page/337
sameAs	Bent function Bent function Bent function Bent function Bent function Bent function Bent function
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thumbnail	wiki-commons:Special:FilePath/Boolean_functions_like_1000_nonlinearity.svg?width=300

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