Image encryption based on the fractional Fourier transform over finite fields

In this paper, we introduce fractional Fourier transforms over finite fields GF(p), where p≡1(mod4). Such a definition is based on the approach given in [1], which corresponds to a finite field extension of the commuting matrix method for defining discrete fractional Fourier transforms [2]. The tran...

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Bibliographic Details
Published in:Signal processing 2014-01, Vol.94, p.521-530
Main Authors: Lima, J.B., Novaes, L.F.G.
Format: Article
Language:English
Subjects:
Applied sciences
Computer simulation
Cryptography
Detection, estimation, filtering, equalization, prediction
Encryption
Exact sciences and technology
Finite fields
Fourier transforms
Fractional Fourier transforms
Image encryption
Information, signal and communications theory
Mathematical analysis
Security aspects
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Transforms
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Summary:In this paper, we introduce fractional Fourier transforms over finite fields GF(p), where p≡1(mod4). Such a definition is based on the approach given in [1], which corresponds to a finite field extension of the commuting matrix method for defining discrete fractional Fourier transforms [2]. The transforms we have constructed are then used as the basis of a novel image encryption scheme. Security aspects of such a scheme are analyzed through computer simulations and specific metrics. •Fractional Fourier transforms over GF(p), where ρ≡1(mod4), are introduced.•The constructed transforms are used as the basis of a novel image encryption scheme.•Security aspects of the proposed scheme are analyzed.
ISSN:0165-1684
1872-7557
DOI:10.1016/j.sigpro.2013.07.020