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Generalizing the Number Theoretic Transform

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Conditions for the Existence of Fast Number Theoretic Transforms

IEEE Transactions on Computers, 1981
A new theorem that gives necessary and sufficient conditions for the existence of computationally fast number theoretic transforms is presented. The theorem combines the general conditions for the existence of number theoretic transforms in the rings of integers modulo m with two conditions for high computational efficiency.
exaly   +3 more sources

Arithmetic for ternary number-theoretic transforms

IEEE Transactions on Circuits and Systems Part 2: Express Briefs, 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.
Andreas Antoniou, S Sunder
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Asymmetric Fragile Watermarking Using a Number Theoretic Transform [PDF]

IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2009
We propose an asymmetric fragile watermarking technique that uses a number theoretic transform (NTT). Signature data is extracted from a watermarked image by determining correlation functions that are computed using the NTT.
Tsuyoshi Yamamoto
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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 0002, Yang Yang 0111, Sanmukh R. Kuppannagari, Rajgopal Kannan, Viktor K. Prasanna   +4 more
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Fast Fourier Transformation Based on Number Theoretic Transforms

Journal of the Franklin Institute, 1988
A technique, denoted as FFT/NTT \((FFT=fast\) Fourier transform, \(NTT=number\) theoretic transform), is proposed for the fast computation of DFT (discrete Fourier transform) of a real sequence with prime length \(p=2^ M+1\). This technique is essentially a modification of \textit{Rader}'s method [Proc. IEEE, Vol.
Adhami, Reza, Polge, Robert J.
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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 D. Svalbe
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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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