Digital watermarking in the fractional Fourier transformation domain
Journal of Network and Computer Applications
Fragile watermarking using finite field trigonometrical transforms
Image Communication
Public-key encryption based on Chebyshev polynomials over GF(q)
Information Processing Letters
Multiplicity of fractional Fourier transforms and theirrelationships
IEEE Transactions on Signal Processing
The fractional discrete cosine transform
IEEE Transactions on Signal Processing
The discrete fractional Fourier transform
IEEE Transactions on Signal Processing
Fractional cosine, sine, and Hartley transforms
IEEE Transactions on Signal Processing
The fractional Fourier transform and time-frequency representations
IEEE Transactions on Signal Processing
A block cipher cryptosystem using wavelet transforms over finite fields
IEEE Transactions on Signal Processing - Part II
The use of finite fields to compute convolutions
IEEE Transactions on Information Theory
Closed-Form Orthogonal Number Theoretic Transform Eigenvectors and the Fast Fractional NTT
IEEE Transactions on Signal Processing
Image encryption based on the finite field cosine transform
Image Communication
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The central contribution of this paper is the definition of the fractional Fourier transform over finite fields (GFrFT). In order to introduce the GFrFT, concepts related to trigonometry in finite fields are reviewed and some new ideas put forward. In particular, graphic representations of elements in a finite field are suggested and analogies with real and complex numbers are discussed. A modified version of the finite field Fourier transform is given and its eigenstructure is analyzed. This allows us to develop GFrFT theory and investigate its main characteristics. Some illustrative examples are also given throughout the paper.