Proceedings ArticleDOI
Hardware implementation of convolution using number theoretic transforms
A. Baraniecka,G. Jullien +1 more
- Vol. 4, pp 490-493
TLDR
Using the Residue Number System (RNS) as a basis for the hardware construction, two different hard-ware structures are discussed for implementing NTTs over a direct sum of Galois Fields GF(m i 2), offering trade offs between speed of operation, and cost.Abstract:
Using the Residue Number System (RNS) as a basis for the hardware construction, two different hard-ware structures are discussed for implementing NTTs over a direct sum of Galois Fields GF(m i 2). The first structure uses arrays of read only memories and the second uses arrays of microprocessors; in particular, single chip microprocessors are proposed. The two techniques offer trade offs between speed of operation, and cost. Using the RNS, rather than conventional binary arithmetic, allows more flexibility in the choice of the generator, α, and consequently more flexibility in allowable transform parameters. A selection of parameters, for the two realizations, are discussed when the Galois Field of m i 2elements is a finite field of Gaussian or quadratic integers.read more
Citations
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Journal ArticleDOI
Video filtering with Fermat number theoretic transforms using residue number system
Tuukka Toivonen,Janne Heikkilä +1 more
TL;DR: An efficient reconstruction circuit based on mixed radix conversion for converting the result from diminished-1 RNS into normal binary code is designed and implemented in VHDL and found to be very small in area.
Journal ArticleDOI
Processor Architectures for Two-Dimensional Convolvers Using a Single Multiplexed Computational Element with Finite Field Arithmetic
TL;DR: In this paper, the authors describe the theory, simulation, and construction of a two-dimensional number theoretic transform (NTT) convolver, which performs indirect convolution by using the cyclic convolution property of a class of generalized discrete Fourier transforms (DFT's) defined over rings isomorphic to direct sums of Galois fields.
Book
Processor architectures for two-dimensional convolvers using a single multiplexed computational element with finite field arithmetic
TL;DR: The theory, simulation, and construction of a two-dimensional number theoretic transform (NTT) convolver is described and the two theories are "married" to produce efficient, very high speed convolution architectures.
Frequency Domain Finite Field Arithmetic for Elliptic Curve Cryptography
TL;DR: It is shown that, especially in computationally constrained platforms, multiplication of finite field elements may be achieved more efficiently in the frequency domain than in the time domain for operand sizes relevant to elliptic curve cryptography (ECC).
Journal ArticleDOI
A residue arithmetic implementation of the fft
TL;DR: The result of this analysis suggests that the new single-modulus complex RNS may be significantly superior to the alternative FFT design choices.
References
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Journal ArticleDOI
The fast Fourier transform in a finite field
TL;DR: A transform analogous to the discrete Fourier transform may be defined in a finite field, and may be calculated efficiently by the Fast Fourier Transform (FFT) algorithm as discussed by the authors.
Journal ArticleDOI
Number theoretic transforms to implement fast digital convolution
R.C. Agarwal,C.S. Burrus +1 more
TL;DR: Transforms using number theoretic concepts developed as a method for fast and error-free calculation of finite digital convolution are shown to be ideally suited to digital computation by taking into account quantization of amplitude as well as time in their definition.
Journal ArticleDOI
Discrete Convolutions via Mersenne Transrorms
TL;DR: It is shown that the product of the transforms of two sequences is congruent to the transform of their circular convolution, and a method of computing circular convolutions without quantization error and with only very few multiplications is revealed.
Book
Residue number scaling and other operations using ROM arrays
TL;DR: This paper considers implementing systems with arrays of look-up tables placed in high density read-only memories with special attention to the scaling algorithm, and two different scaling algorithms are developed.
Journal ArticleDOI
Residue Number Scaling and Other Operations Using ROM Arrays
TL;DR: In this paper, the residue number system is implemented with arrays of look-up tables placed in high density read-only memories, where the only operations are addition, subtraction, multiplication and scaling by a predetermined constant.