Cosine transforms over fields of characteristic 2

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

doi:10.1016/j.ffa.2015.10.005

Cited by 7 publications

(6 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The same permutation polynomial is chosen and parameterized with parameters ε 4 , θ 4 , α 4 as: (19) where ε 4 , θ 4 F 2 8, and 0 < α 4 = s 4 /t 4 < 255, and s 4 , t 4 are positive integers with (s 4 , 255) = 1, (t 4 , 255) = 1, and (s 4 , t 4 ) = 1.…”

Section: Post-scrambling Of Diffusion Results Based On Permutation Polynomialmentioning

confidence: 99%

“…Figure 5 shows the decrypted results of Goldhill with a key minimally different from the right key. On specifics, the 16 cipher keys, ε 1 , ε 2 , ε 3 , ε 4 , θ 1 , θ 2 , θ 3 , θ 4 , s 1 , s 2 , s 3 , s 4 , t 1 , t 2 , t 3 and t 4 are changed, one at a time, from their correct values into ω 12 , ω 51 , ω 51 , ω 127 , ω 16 , ω 19 , ω 27 , ω 12 , 193, 49, 104, 182, 197, 43, 103 and 131. Taking Goldhill as an example, the resulting 16 decrypted images are shown in Fig.…”

Section: Key Sensitivitymentioning

confidence: 99%

“…For this purpose, researchers further proposed various transforms based on finite fields. LIMA and others have proposed the finite field fractional Fourier transform in [17], fractional cosine and sine transforms over finite fields in [18], cosine transforms over finite fields of characteristic 2 [19,20] successively. Subsequently, image encryption based on the fractional Fourier transform over finite fields [21] and image encryption based on the finite field cosine transform [22] are proposed by LIMA and others.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Image encryption based on permutation polynomials over finite fields

Wu¹,

Liu²,

Zhu³

2020

Optica Applicata

View full text Add to dashboard Cite

In this paper, we propose an image encryption algorithm based on a permutation polynomial over finite fields proposed by the authors. The proposed image encryption process consists of four stages: i) a mapping from pixel gray-levels into finite field, ii) a pre-scrambling of pixels’ positions based on the parameterized permutation polynomial, iii) a symmetric matrix transform over finite fields which completes the operation of diffusion and, iv) a post-scrambling based on the permutation polynomial with different parameters. The parameters used for the polynomial parameterization and for constructing the symmetric matrix are used as cipher keys. Theoretical analysis and simulation demonstrate that the proposed image encryption scheme is feasible with a high efficiency and a strong ability of resisting various common attacks. In addition, there are not any round-off errors in computation over finite fields, thus guaranteeing a strictly lossless image encryption. Due to the intrinsic nonlinearity of permutation polynomials in finite fields, the proposed image encryption system is nonlinear and can resist known-plaintext and chosen-plaintext attacks.

show abstract

Section: Post-scrambling Of Diffusion Results Based On Permutation Polynomialmentioning

confidence: 99%

Section: Key Sensitivitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Image encryption based on permutation polynomials over finite fields

Wu¹,

Liu²,

Zhu³

2020

Optica Applicata

View full text Add to dashboard Cite

show abstract

“…Analogues of the tangent and inverse tangent function for odd q were introduced in [8] and used in the definition of C n (x, α) for odd q. An analogue of cos x was introduced in [7] for even q. It appears that the literature does not contain an analogue of sin x or tan x over finite fields of even order.…”

Section: Trigonometry In Characteristicmentioning

confidence: 99%

Tangent-Chebyshev rational maps and Redei functions

Ding,

Zieve

2021

Preprint

View full text Add to dashboard Cite

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.

show abstract

“…Neste artigo, são construídos exemplos particulares das recém-definidas transformadas do cosseno sobre corpos finitos de característica 2 [7], as quais são denotadas por FFCT (do inglês, finite field cosine transform). Inicialmente, constróise uma FFCT com 8-pontos sobre GF(2 8 ) e descreve-se um algoritmo rápido para o seu cálculo.…”

Section: Introductionunclassified