Results 241 to 250 of about 120,753 (284)

Isomorphic number theoretic transforms

Proceedings. Electrotechnical Conference Integrating Research, Industry and Education in Energy and Communication Engineering', 2003
It is noted that the computational cost of circular convolutions can be reduced to a large extent by using number-theoretic transforms (NTTs). The author proposes a novel algorithm for removing the necessity for the transforming element of the NTT to be coincident with a power of 2.
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FPGA Acceleration of Number Theoretic Transform

2021
Fully Homomorphic Encryption (FHE) is a technique that enables arbitrary computations on encrypted data directly. Number Theoretic Transform (NTT) is a fundamental component in FHE computations as it allows faster polynomial multiplication. However, it is computationally intensive and requires acceleration for practical deployment of FHE.
Tian Ye, Yang Yang, Sanmukh R. Kuppannagari, Rajgopal Kannan, Viktor K. Prasanna   +4 more
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Microprocessor implementation of number theoretic transforms

IEE Journal on Electronic Circuits and Systems, 1979
Consideration is given to the suitability of microprocessor systems for the fast implementation of number theoretic transforms (n.t.t.s). Fast-multiply instructions available on some microprocessors, or the use of external multipliers, relax the basic constraints on the choice of a particular n.t.t.
S.C.P. Martin, B.J. Stanier
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Number Theoretic Transformation Techniques

1989
Processing signals with a digital computer or with dedicated digital hardware involves the implementation of computational schemes on sequences of numbers. Practically, it is not possible to process an infinitely long sequence, although it is common practice to analyze many processing systems as though this were the case.
Robert King, Majid Ahmadi, Raouf Gorgui-Naguib, Alan Kwabwe, Mahmood Azimi-Sadjadi   +4 more
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Generalized Fermat-Mersenne number theoretic transform

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 1994
Let \(\mathbb{Z}_ p\) be the ring of integers \(\{0,1, \dots, p - 1\}\). The number theoretic transform of \(\{x(n)\}_{n = 0}^{N - 1}\) for \(x(n) \in \mathbb{Z}_ p\) is defined as \(X(k) = \sum_{n = 0}^{N - 1} x(n) \alpha^{nk}\), \(k = 0,1, \dots,N - 1\) where \(\alpha^ N \equiv 1 \pmod{p}\) while \(\alpha^ k \not\equiv 1\pmod{p}\) for all \(k < N ...
Dimitrov, Vassil S., Cooklev, Todor V., Donevsky, Borislav D.   +2 more
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Fast Multipliers for Number Theoretic Transforms

IEEE Transactions on Computers, 1978
Summary: When digital filters are implemented with number theoretic transforms (NTTs), the bulk of the computation usually corresponds to multiplications in residue arithmetic. We show that, with the most commonly used NTTs, multiplication can be speeded up at the expense of small additional storage requirements.
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Quantum number theoretic transforms on multipartite finite systems

Journal of the Optical Society of America A, 2009
A quantum system composed of p-1 subsystems, each of which is described with a p-dimensional Hilbert space (where p is a prime number), is considered. A quantum number theoretic transform on this system, which has properties similar to those of a Fourier transform, is studied.
A, Vourdas, S, Zhang
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Number Theoretic Transforms

1977
The theory of Number Theoretic Transforms having circular convolution properties is developed from the definition of circular convolution. The application of these transforms to digital signal processing is discussed. The lectures include the following sections. 1. Circular convolution; 2. Circulant diagonalisation; 3.
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A Fast Number Theoretic Finite Radon Transform

2009 Digital Image Computing: Techniques and Applications, 2009
This paper presents a new fast method to map between images and their digital projections based on the Number Theoretic Transform (NTT) and the Finite Radon Transform (FRT). The FRT is a Discrete Radon Transform (DRT) defined on the same finite geometry as the Finite or Discrete Fourier Transform (DFT).
Shekhar Chandra, Imants Svalbe
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Number Theoretic Transforms

1981
Most of the fast convolution techniques discussed so far are essentially algebraic methods which can be implemented with any type of arithmetic. In this chapter, we shall show that the computation of convolutions can be greatly simplified when special arithmetic is used.
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