Tangent Function and Chebyshev-Like Rational Maps Over Finite Fields

Lima, Juliano B.; Souza, Ricardo M. Campello de

doi:10.1109/tcsii.2019.2923879

Cited by 5 publications

(11 citation statements)

References 17 publications

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“…The above corollaries include generalizations of the main results from [8]. Specifically, [8,Prop. 7] is the odd q case of Corollary 3.4; [8,Prop.…”

Section: Tangent-chebyshev Functionsmentioning

confidence: 78%

“…The tangent-Chebyshev rational functions C n (x, α) were defined in [8] for any odd prime power q via a somewhat involved procedure. This led to the explicit expression [8, (9)], which we use as our definition: Definition 3.1.…”

Section: Tangent-chebyshev Functionsmentioning

confidence: 99%

“…Specifically, [8,Prop. 7] is the odd q case of Corollary 3.4; [8,Prop. 11] is the odd q case of Corollary 3.8; [8, Prop.…”

Section: Tangent-chebyshev Functionsmentioning

confidence: 99%

“…Recently Lima and Campello de Souza [8] introduced a family of rational functions over odd-characteristic finite fields, which they called tangent-Chebyshev maps. They showed that these functions have properties suitable for use in cryptography.…”

Section: Introductionmentioning

confidence: 99%

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Tangent-Chebyshev rational maps and Redei functions

Ding,

Zieve

2021

Preprint

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Recently Lima and Campello de Souza introduced a new class of rational functions over odd-order finite fields, and explained their potential usefulness in cryptography. We show that these new functions are conjugate to the classical family of Rédei rational functions, so that the properties of the new functions follow from properties of Rédei functions. We also prove new properties of these functions, and introduce analogous functions in characteristic 2, while also introducing a new version of trigonometry over finite fields of even order, which is of independent interest.

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“…The above corollaries include generalizations of the main results from [8]. Specifically, [8,Prop. 7] is the odd q case of Corollary 3.4; [8,Prop.…”

Section: Tangent-chebyshev Functionsmentioning

confidence: 78%

Section: Tangent-chebyshev Functionsmentioning

confidence: 99%

“…Specifically, [8,Prop. 7] is the odd q case of Corollary 3.4; [8,Prop. 11] is the odd q case of Corollary 3.8; [8, Prop.…”

Section: Tangent-chebyshev Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Tangent-Chebyshev rational maps and Redei functions

Ding,

Zieve

2021

Preprint

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“…The first ideas related to trigonometry over finite fields were introduced in [2], as a requirement for defining a Hartley number transform. In subsequent works, new definitions and results were presented, as well as new applications for the referred theory were proposed [9,10,12]. In what follows, we review the concepts of trigonometry over finite fields that are needed throughout this article.…”

Section: Trigonometry Over Finite Fieldsmentioning

confidence: 99%

A Novel Approach for Defining a Hilbert Number Transform

Lima

Gondim

Souza

2021

Circuits Syst Signal Process

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In this brief, we introduce a new definition for the Hilbert number transform (HNT). Our approach employs concepts related to trigonometry over finite fields and uses as a starting point a specific definition for the Fourier number transform (FNT); one demonstrates that such an FNT allows to define an HNT which is analogous to the real-valued version of the corresponding transform. Additionally, we present a method to obtain the proposed HNT from the recently proposed steerable Fourier number transform.

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Tangent-chebyshev maps over finite fields: New properties and functional graphs

Lima

2022

Cryptogr. Commun.

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Tangent Function and Chebyshev-Like Rational Maps Over Finite Fields

Cited by 5 publications

References 17 publications

Tangent-Chebyshev rational maps and Redei functions

Tangent-Chebyshev rational maps and Redei functions

A Novel Approach for Defining a Hilbert Number Transform

Tangent-chebyshev maps over finite fields: New properties and functional graphs

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