Results 1 to 10 of about 5,404 (164)
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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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
exaly +2 more sources
Straggler- and Adversary-Tolerant Secure Distributed Matrix Multiplication Using Polynomial Codes
Entropy, 2023 Large matrix multiplications commonly take place in large-scale machine-learning applications. Often, the sheer size of these matrices prevent carrying out the multiplication at a single server.
Eimear Byrne +2 more
exaly +3 more sources
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
doaj +1 more source
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
doaj +3 more sources
NTT Multiplication for NTT-unfriendly Rings
Transactions on Cryptographic Hardware and Embedded Systems, 2021 In this paper, we show how multiplication for polynomial rings used in the NIST PQC finalists Saber and NTRU can be efficiently implemented using the Number-theoretic transform (NTT).
Chi-Ming Marvin Chung +5 more
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Multiplicity of zeros of polynomials [PDF]
Journal of Approximation Theory, 2021 The paper grew out of the known result of \textit{P. Erdős} and \textit{P. Túran} [Ann. Math. (2) 41, 162--173 (1940; Zbl 0023.02201)] on zero distributions and bounds for their multiplicities of monic polynomials with all their zeros in \([-1,1]\). Theorem 1.1.
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