Results 221 to 230 of about 5,425 (258)

A Note on the Implementation of the Number Theoretic Transform

2017
The Number Theoretic Transform (NTT) is a time critical function required by many post-quantum cryptographic protocols based on lattices. For example it is commonly used in the context of the Ring Learning With Errors problem (RLWE), which is a popular basis for post-quantum key exchange, digital signature, and encryption.
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The eigenstructure of the number theoretic transforms

Signal Processing, 1982
Abstract Fast digital transforms are linear matrix operations and their eigenstructure is of fundamental interest. The eigensystem for the Fast Fourier transform, FFT, known for several years, can be used to design FFT algorithms. The Number Theoretic Transforms have a similar eigen problem, defined over ofZ /p which is solved in this paper. We find
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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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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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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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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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Arithmetic for ternary number-theoretic transforms

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 1993
Summary: A simplified arithmetic for the computation of ternary number-theoretic transforms is presented. The proposed arithmetic is based on the application of a code translation technique that was used by \textit{L. M. Leibowitz} [A simplified binary arithmetic for the Fermat number transform, IEEE Trans.
Sunder, S., Antoniou, A.
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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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Multiple radix fast fourier transformation based on number theoretic transforms

Journal of the Franklin Institute, 1991
Discrete Fourier transform on a prime number of samples is computed by means of the multiple radix fast Fourier transformation based on number theoretic transforms. This proposal is efficient in the transformation of samples \(P=2^{k1}3^{k2}5^{k3}\) with arbitrary integers ki \((i=1,2,3)\).
Lawrence, Brooks, Polge, Robert, Adhami, Reza   +2 more
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Number theoretic transforms for the calculation of convolutions

IEEE Transactions on Acoustics, Speech, and Signal Processing, 1983
We present new algorithms for the calculation of convolutions by means of number theoretic transforms over modulo rings. Not only are these algorithms more efficient than currently used methods, but they are also very flexible. Indeed, using special algorithms for short convolutions allows trading computational efficiency for structural simplicity.
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