Results 21 to 30 of about 165,308 (288)
IEEE Access, 2022 Polynomial multiplication is one of the heaviest operations for a lattice-based public key algorithm in Post-Quantum Cryptography (PQC). Many studies have been done to accelerate polynomial multiplication with newly developed hardware accelerators or ...
Jong-Yeon Park +4 more
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Multiple Askey–Wilson polynomials and related basic hypergeometric multiple orthogonal polynomials
Transactions of the American Mathematical Society, 2020 We first show how one can obtain Al-Salam--Chihara polynomials, continuous dual $q$-Hahn polynomials, and Askey--Wilson polynomials from the little $q$-Laguerre and the little $q$-Jacobi polynomials by using special transformations. This procedure is then extended to obtain multiple Askey--Wilson, multiple continuous dual $q$-Hahn, and multiple Al ...
Nuwacu, Jean Paul, Van Assche, Walter
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On multiple q-Laguerre polynomials
Journal of Classical Analysis, 2023 Summary: We study \(q\)-Laguerre multiple orthogonal polynomials. These polynomials are orthogonal with respect to \(q\)-analogues of Laguerre weight functions. We focus our attention on their structural properties. Raising and lowering operators as well as Rodrigues-type formulas are obtained and their explicit representations are given.
Sadjang, P. Njionou +2 more
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FourierPIM: High-throughput in-memory Fast Fourier Transform and polynomial multiplication
Memories - Materials, Devices, Circuits and Systems, 2023 The Discrete Fourier Transform (DFT) is essential for various applications ranging from signal processing to convolution and polynomial multiplication. The groundbreaking Fast Fourier Transform (FFT) algorithm reduces DFT time complexity from the naive O(
Orian Leitersdorf +4 more
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Configurable Mixed-Radix Number Theoretic Transform Architecture for Lattice-Based Cryptography
IEEE Access, 2022 Lattice-based cryptography continues to dominate in the second-round finalists of the National Institute of Standards and Technology post-quantum cryptography standardization process. Computational efficiency is primarily considered to evaluate promising
Phap Duong-Ngoc, Hanho Lee
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Multiplication Rules for Polynomials [PDF]
Proceedings of the American Mathematical Society, 1978 It is proved that the polynomial solutions of the functional equation \[ F ( z ) F ( z + 1 / a ) = F ( a z 2
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Some properties of generalized hypergeometric Appell polynomials [PDF]
, 2020 In this paper, we present a new real-valued Appell-type polynomial family $A_n^{(k)}(m,x), $ every member of which is expressed by mean of a generalized hypergeometric function.
Bedratyuk., L, Luno, N.
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Multiple q-Kravchuk polynomials
Integral Transforms and Special Functions, 2021 We study a family of type II multiple orthogonal polynomials. We consider orthogonality conditions with respect to a vector measure, in which each component is a q-analogue of the binomial distribution. The lowering and raising operators as well as the Rodrigues formula for these polynomials are obtained. The difference equation of order r+1 is studied.
Arvesú Carballo, Jorge +1 more
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Asymptotically fast polynomial matrix algorithms for multivariable systems [PDF]
, 2005 We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer algebra techniques,
Gilles Villard +5 more
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Fast Multiplication for Skew Polynomials [PDF]
Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation, 2017 We describe an algorithm for fast multiplication of skew polynomials. It is based on fast modular multiplication of such skew polynomials, for which we give an algorithm relying on evaluation and interpolation on normal bases. Our algorithms improve the best known complexity for these problems, and reach the optimal asymptotic complexity bound for ...
Caruso, Xavier, Le Borgne, Jérémy
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