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A Note on the Implementation of the Number Theoretic Transform
2017The 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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Hartley number theoretic transforms
Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252), 2002The Hartley number theoretic transform (HNTT) is introduced, in particular, the Mersenne HNTT is defined and some multiplication free transforms are given.
R.M. Campello de Souza +3 more
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Mersenne numbers rooted on 3 for number theoretic transforms
ICASSP '80. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005Number Theoretic Transforms (NTT) have been shown capable of implementing efficiently finite digital convolutions for signal processing applications in voice, video, and pattern recognition areas. In this paper the concept of Generalized Mersenne Numbers (GMN) is introduced with the goal of obtaining a new discrete transform having certain desirable ...
Daniel Minoli, Wendell Nakamine
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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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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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Number theoretic transform based on ternary arithmetic
ICASSP '83. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005A number theoretic transform (NTT) is proposed, which can efficiently be computed by using ternary modular arithmetic. The new NTT relaxes the restriction imposed on the convolution length and, as in other efficient NTT's, its computation can be performed by means of data shifts and additions.
Prabhakara C. Balla, Andreas Antoniou
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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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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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The eigenstructure of the number theoretic transforms
Signal Processing, 1982Abstract 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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The design space of the number theoretic transform: A survey
2017 International Conference on Embedded Computer Systems: Architectures, Modeling, and Simulation (SAMOS), 2017The Number Theoretic Transform (NTT) is a necessary part of most Lattice-based cryptographic schemes. In particular, it offers an efficient means to achieve polynomial multiplication within the more efficient ring-based schemes. The NTT is also a crucial component which needs to be implemented in a critical way, since it is often the bottle-neck and ...
Felipe Valencia +3 more
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Number Theoretic Transformation Techniques
1989Processing 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 +4 more
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Isomorphic number theoretic transforms
Proceedings. Electrotechnical Conference Integrating Research, Industry and Education in Energy and Communication Engineering', 2003It 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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