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Bent function: Applications, Definition and properties & Overview

In the mathematical field of combinatorics, a bent function is a Boolean function that 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…

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Bent function topic overview

The analysis highlights Applications, Definition and properties and Overview as prominent areas in the source structure around Bent function.

Related topics
56
Source areas
5
Connected nodes
61
Extracted relationships
44
Related term clusters
19
Bridge connections
61

What this topic covers Research coverage

Source areas are shown by the number of related topics found in each part of the analysis. Use smaller areas too: they can reveal specialized angles and content gaps.

Applications · 21 topics
Overview · 16 topics
Definition and properties · 13 topics
Generalizations · 4 topics
Walsh transform · 2 topics

Smaller areas are not necessarily less important. They contain fewer connections in this analysis and can be useful for finding specialized angles or coverage gaps.

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Explore all related topics Closing gaps

Browse the complete topic structure, not only the most central items. Less prominent entities and concepts can reveal missing angles, specialized context and useful research gaps. Each item opens a new analysis centered on that subject.

Overview

Walsh transform

Definition and properties

Applications

Generalizations

For the semantics nerds

You can skip this section if you’re here for content ideas and keyword inspiration.

Advanced semantic analysis

How Bent function connects Entity context

The extracted context around Bent function shows recurring relationship patterns in the source. For example, Bent function → Canteaut, Charpin, Combinatorial, Dillon, Dillon's, Dobbertin's, Gold, Kasami, Kuyreghyan, Leander, Maiorana, McFarland, Niho Another extracted example is Bent function → Boolean, CDMA, Forré, Furthermore, Gold, Indeed, Kasami, S-boxes, SAC, Walsh. Use these groups to spot repeated connection types before inspecting the individual relationships.

Bent function

Top relations

related to Constructions · 13
Bent function → Canteaut, Charpin, Combinatorial, Dillon, Dillon's, Dobbertin's, Gold, Kasami, Kuyreghyan, Leander, Maiorana, McFarland, Niho
has application · 10
Bent function → Boolean, CDMA, Forré, Furthermore, Gold, Indeed, Kasami, S-boxes, SAC, Walsh
related to Walsh transform · 8
Bent function → Alternatively, Bent, Boolean, S0, S1, The Walsh, Walsh, Zn
related to Generalizations · 6
Bent function → Abelian, Boolean, G-bent, Schmidt, Tokareva's, Z-bent
related to Definition and properties · 5
Bent function → Bent, Boolean, Rothaus, Walsh, Zn
is a · 1
Bent function → Boolean function that is maximally non-linear

Important terminology

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

functions bent function boolean displaystyle linear properties affine possible nonlinearity transform balanced cryptographic value walsh also mathbb nonlinear output known

Bent function relationships Subject–Predicate–Object triples

TTTA extracted 44 structured relationships around Bent function. Examples in this analysis include Bent function → is a → Boolean function that is maximally non-linear and S-boxes → instance of → bent functions might at first seem the ideal choice for secure cryptographic functions. The table shows each extracted connection, where it came from and its confidence.

SubjectPredicateObjectConfidenceSrc
Bent functionis aBoolean function that is maximally non-linear0.90text
S-boxesinstance ofbent functions might at first seem the ideal choice for secure cryptographic functions0.80text
Bent functionhas applicationGold0.60section
Bent functionhas applicationKasami0.60section
Bent functionhas applicationCDMA0.60section
Bent functionhas applicationForré0.60section
Bent functionhas applicationWalsh0.60section
Bent functionhas applicationSAC0.60section
Bent functionhas applicationS-boxes0.60section
Bent functionhas applicationIndeed0.60section
Bent functionhas applicationFurthermore0.60section
Bent functionhas applicationBoolean0.60section

Related concept clusters Related term clusters

The concept neighborhoods around Bent function bring nearby vocabulary together. In this analysis, examples include Functions, Function and Boolean. Use the clusters to find adjacent concepts and terminology that may deserve separate research.

  • Bent function
    • Functions
    • Function
    • Boolean
    • Properties
    • 2n
    • Hat
    • Nonlinearity
    • Transform
    • Displaystyle
    • Output
    • Value
    • Zn
  • bent function
    • Functions
    • Function
    • Displaystyle
    • Linear
    • Value
    • Boolean
    • Properties
    • 2n
    • Hat
    • Mathbb
    • Nonlinearity
    • Transform
  • boolean function
    • Function
    • Value
    • Displaystyle
    • Field
    • Linear
    • 2n
    • Functions
    • Balanced
    • Transform
    • Hat
    • Affine
    • Cryptographic
  • affine functions
    • 2n
    • Linear
    • Function
    • Field
    • Number
    • Properties
    • Boolean
    • Nonlinearity
    • Possible
    • Value
    • Cryptographic
    • Displaystyle
  • cryptographic hash function
    • Good
    • Displaystyle
    • Linear
    • Many
    • Value
    • 2n
    • Hat
    • Mathbb
    • Nonlinearity
    • Possible
    • Transform
    • Properties
  • balanced
    • Cryptographic
    • Good
    • Boolean
    • Possible
    • Value
    • Function
    • Bent
    • Combinatorial
    • Cryptanalysis
    • Field
    • Generalizations
    • Many
  • linear cryptanalysis
    • Cryptanalysis
    • Linear
    • Possible
    • Output
    • Function
    • Good
    • Nonlinearity
    • Value
    • Called
    • Cryptographic
    • Nonlinear
    • Zn
  • linear
    • Cryptanalysis
    • Possible
    • Output
    • Called
    • Nonlinear
    • Zn
    • 2n
    • Good
    • Hat
    • Nonlinearity
    • Transform
    • Value

Connections between topic areas Semantic bridges

For Bent function, one of the stronger structural bridges in this analysis connects Bent function with Applications. Bridges highlight paths between different parts of the map and can reveal research angles that are easy to miss in a flat list.

Min side: 3
Bent function — Applications · splits 40 ⟂ 22
Bent function — Overview · splits 45 ⟂ 17
Bent function — Definition and properties · splits 48 ⟂ 14
Bent function — Generalizations · splits 57 ⟂ 5
Bent function — Walsh transform · splits 59 ⟂ 3

Map overview Semantic statistics

Bent function

Nodes62
Edges61
Triples44
Avg. degree1.97
Density0.032258
Components1

Source & methodology

TTTA analyzes the structure around Bent function to surface related topics, entities, relationships, concept neighborhoods and bridge connections. Use the map to explore areas such as Applications, Definition and properties & Overview, including less central topics that may reveal useful research gaps. Automatically extracted connections are research leads rather than rewritten encyclopedia content.

Source: Wikipedia — Bent function · EN edition · Analysis: TopicsToTalkAbout

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