Fast algorithm for computing cosine number transform

Lima, Juliano B.

doi:10.1049/el.2015.0905

Cited by 10 publications

(4 citation statements)

References 9 publications

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“…Accordingly, the computational complexity of the proposed encryption/decryption scheme is ( 2 ), where × is the source image resolution. Moreover, the computational complexity can be improved by using fast algorithms for computing the FFCT by ( log ) as in [23].…”

Section: Computational Complexity Analysismentioning

confidence: 99%

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Two-Phase Image Encryption Scheme Based on FFCT and Fractals

Mikhail

Abouelseoud

Elkobrosy

2017

Security and Communication Networks

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This paper blends the ideas from recent researches into a simple, yet efficient image encryption scheme for colored images. It is based on the finite field cosine transform (FFCT) and symmetric-key cryptography. The FFCT is used to scramble the image yielding an image with a uniform histogram. The FFCT has been chosen as it works with integers modulo p and hence avoids numerical inaccuracies inherent to other transforms. Fractals are used as a source of randomness to generate a one-time-pad keystream to be employed in enciphering step. The fractal images are scanned in zigzag manner to ensure decorrelation of adjacent pixels values in order to guarantee a strong key. The performance of the proposed algorithm is evaluated using standard statistical analysis techniques. Moreover, sensitivity analysis techniques such as resistance to differential attacks measures, mean square error, and one bit change in system key have been investigated. Furthermore, security of the proposed scheme against classical cryptographic attacks has been analyzed. The obtained results show great potential of the proposed scheme and competitiveness with other schemes in literature. Additionally, the algorithm lends itself to parallel processing adding to its computational efficiency.

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Section: Computational Complexity Analysismentioning

confidence: 99%

“…The block-by-block FFCT computation makes it possible to reduce the time required by the proposed scheme if parallel processing is employed. Moreover, there are fast algorithms for computing the FFCT as in [23].…”

Section: Speed Analysismentioning

confidence: 99%

Two-Phase Image Encryption Scheme Based on FFCT and Fractals

Mikhail

Abouelseoud

Elkobrosy

2017

Security and Communication Networks

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“…An NTT is usually defined as a Fourier-type transform, where the complex N -th root of unity used as transform kernel is replaced by an N -th root of unity in a finite algebraic structure [1]. Trigonometric number transforms can also be defined; they employ a finite field trigonometry and include cosine, sine and Hartley number transforms, which have analysis and synthesis expressions similar to those of the corresponding real-valued transforms [8,10,13]. Naturally, all computations necessary to calculate an NTT are carried out by using modular arithmetic.…”

Section: Introductionmentioning

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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“…The entries of

M

depend on the transform kernel, which can be of Fourier, cosine, sine or Hartley type, for instance [1, 2]. A discrete transform can also be defined over infinite (complex and real fields) or finite algebraic structures (finite fields and rings) [2–4]. Finally, discrete transforms can be fractionalised, i.e.…”

Section: Introductionmentioning

confidence: 99%

Fractional angular transform: a number‐theoretic approach

Lima

2019

Electron. lett.

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In this Letter, the authors introduce a fractional angular number transform (FrANT). The new transform corresponds to a finite field version of the complex-valued discrete fractional angular transform and, therefore, its computation requires integer arithmetic only. Differently from other number-theoretic transforms, the possible lengths of an FrANT do not depend on the algebraic structure where it is defined. This provides more flexibility regarding the application of the transform in communications, cryptography and error correcting codes, for instance.

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Fast algorithm for computing cosine number transform

Cited by 10 publications

References 9 publications

Two-Phase Image Encryption Scheme Based on FFCT and Fractals

Two-Phase Image Encryption Scheme Based on FFCT and Fractals

A Novel Approach for Defining a Hilbert Number Transform

Fractional angular transform: a number‐theoretic approach

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