The Discrete Cosine Transform over Prime Finite Fields

Abstract

This paper examines finite field trigonometry as a tool to construct trigonometric digital transforms. In particular, by using properties of the k-cosine function over GF(p), the Finite Field Discrete Cosine Transform (FFDCT) is introduced. The FFDCT pair in GF(p) is defined, having blocklengths that are divisors of (p+1)/2. A special case is the Mersenne FFDCT, defined when p is a Mersenne prime. In this instance blocklengths that are powers of two are possible and radix-2 fast algorithms can be used to compute the transform.Comment: 5 pages, 1 table, Lecture Notes in Computer Science, LNCS 3124, Heidelberg: Springer Verlag, 2004, vol.1, pp.482-487, 200

Histogram Uniformization for Digital Image Encryption

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“…The FFCT was originally introduced in [8]. Actually, there are 8 types of finite field cosine transforms and also 8 types of finite field sine transforms.…”

“…The uniformization technique proposed in this work is based on the finite field cosine transform (FFCT), the application of which requires operations involving modular arithmetic only [8], [9]. This means that rounding is not necessary and efficient computations can be carried out; once the values of the pixels of the transformed images are integer numbers, their coding and, consequently, their transmission or storage are easier.…”

Derivatives over Certain Finite Rings

“…Then the image of ρ may sometimes be an array, see de Souza, de Oliveira, de Souza, Vasconcelos [5]. For instance, the image of a function on R is an 1 s × -array.…”

Design method for two-channel cyclic filter banks over fields of characteristic two

“…Examples of such systems include cyclic filter banks [2] and systems based on the discrete Fourier transform [3]. Many engineering tools have appeared for structures defined over finite fields [4][5][6][7][8]. Such structures are attractive in the sense that they can be implemented in digital machines without the numerical precision problems that occur when floating point operations are used.…”