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An algorithm for the multiplication of symmetric polynomials [PDF]
ACM Transactions on Mathematical Software, 1988 Although the cycle index polynomial for a permutation group can often be easily determined, expansion of the figure counting series in a Po´lya enumeration presents computational difficulties for object sets with higher degrees of symmetry and more than modest size.
John S. Garavelli
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Generic reductions for in-place polynomial multiplication [PDF]
Proceedings of the 2019 International Symposium on Symbolic and Algebraic Computation, 2019 The polynomial multiplication problem has attracted considerable attention since the early days of computer algebra, and several algorithms have been designed to achieve the best possible time complexity. More recently, efforts have been made to improve the space complexity, developing modified versions of a few specific algorithms to use no extra ...
Pascal Giorgi +2 more
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On the Polynomial Multiplication in Chebyshev Form
IEEE Transactions on Computers, 2012 We give an efficient multiplication method for polynomials in Chebyshev form. This multiplication method is different from the previous ones. Theoretically, we show that the number of multiplications is at least as good as Karatsuba-based algorithm. Moreover, using the proposed method, we improve the number of additions slightly.
Sedat Akleylek +2 more
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On Polynomial Multiplication in Chebyshev Basis [PDF]
IEEE Transactions on Computers, 2012 In a recent paper Lima, Panario and Wang have provided a new method to multiply polynomials in Chebyshev basis which aims at reducing the total number of multiplication when polynomials have small degree. Their idea is to use Karatsuba's multiplication scheme to improve upon the naive method but without being able to get rid of its quadratic complexity.
Pascal Giorgi
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Practical fast polynomial multiplication [PDF]
Proceedings of the third ACM symposium on Symbolic and algebraic computation - SYMSAC '76, 1976 The “fast” polynomial multiplication algorithms for dense univariate polynomials are those which are asymptotically faster than the classical O(N2) method. These “fast” algorithms suffer from a common defect that the size of the problem at which they start to be better than the classical method is quite large; so large, in fact that it is impractical ...
Robert T. Moenck
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Multivariate Polynomial Multiplication on GPU
Procedia Computer Science, 2016 AbstractMultivariate polynomial multiplication is a fundamental operation which is used in many scientific domains, for example in the optics code for particle accelerator design at CERN. We present a novel and efficient multivariate polynomial multiplication algorithm for GPUs using floating-point double precision coefficients implemented using the ...
Diana Andréea Popescu +1 more
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On the ω-multiple Charlier polynomials [PDF]
Advances in Difference Equations, 2021 AbstractThe main aim of this paper is to define and investigate more general multiple Charlier polynomials on the linear lattice $\omega \mathbb{N} = \{ 0,\omega ,2\omega ,\ldots \} $ ω N = { 0 , ω ,
Ozarslan, Mehmet Ali, Baran, Gizem
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Neon NTT: Faster Dilithium, Kyber, and Saber on Cortex-A72 and Apple M1
Transactions on Cryptographic Hardware and Embedded Systems, 2021 We present new speed records on the Armv8-A architecture for the latticebased schemes Dilithium, Kyber, and Saber. The core novelty in this paper is the combination of Montgomery multiplication and Barrett reduction resulting in “Barrett multiplication ...
Hanno Becker +4 more
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Kavach: Lightweight masking techniques for polynomial arithmetic in lattice-based cryptography
Transactions on Cryptographic Hardware and Embedded Systems, 2023 Lattice-based cryptography has laid the foundation of various modern-day cryptosystems that cater to several applications, including post-quantum cryptography. For structured lattice-based schemes, polynomial arithmetic is a fundamental part. In several
Aikata Aikata +4 more
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Polynomial Multiplication in NTRU Prime
Transactions on Cryptographic Hardware and Embedded Systems, 2020 This paper proposes two different methods to perform NTT-based polynomial multiplication in polynomial rings that do not naturally support such a multiplication. We demonstrate these methods on the NTRU Prime key-encapsulation mechanism (KEM) proposed by
Erdem Alkim +10 more
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