Results 31 to 40 of about 165,252 (290)
Transactions on Cryptographic Hardware and Embedded Systems, 2020 In this paper, we present an instruction set coprocessor architecture for lattice-based cryptography and implement the module lattice-based post-quantum key encapsulation mechanism (KEM) Saber as a case study.
Sujoy Sinha Roy, Andrea Basso
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Chebyshev model arithmetic for factorable functions [PDF]
, 2016 This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating ...
Chachuat, B +3 more
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Polynomial degree reduction in the L2-norm on a symmetric interval for the canonical basis
Results in Applied Mathematics, 2021 In this paper, we develop a direct formula for determining the coefficients in the canonical basis of the best polynomial of degree M that approximates a polynomial of degree N>Mon a symmetric interval for the L2-norm.
Habib Ben Abdallah +2 more
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Multiple big q-Jacobi polynomials
Bulletin of Mathematical Sciences, 2020 Here, we investigate type II multiple big [Formula: see text]-Jacobi orthogonal polynomials. We provide their explicit formulae in terms of basic hypergeometric series, raising and lowering operators, Rodrigues formulae, third-order [Formula: see text]-difference equation, and we obtain recurrence relations.
Fethi Bouzeffour, Mubariz Garayev
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Ehrhart polynomial and multiplicity Tutte polynomial
, 2011 6 pages, 1 ...
D'Adderio, Michele, Moci, Luca
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Negacyclic Polynomial Multiplication
, 2022 In this article I’ll cover three techniques to compute special types of polynomial products that show up in lattice cryptography and fully homomorphic encryption. Namely, the negacyclic polynomial product, which is the product of two polynomials in the quotient ring $\mathbb{Z}[x] / (x^N + 1)$.
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Karatsuba-Ofman Multiplier with Integrated Modular Reduction for GF(2m)
Advances in Electrical and Computer Engineering, 2013 In this paper a novel GF(2m) multiplier based on Karatsuba-Ofman Algorithm is presented. A binary field multiplication in polynomial basis is typically viewed as a two steps process, a polynomial multiplication followed by a modular reduction step ...
CUEVAS-FARFAN, E. +6 more
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On Polynomial Multiplication in Chebyshev Basis
, 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.
Giorgi, Pascal
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Simple Multivariate Polynomial Multiplication
Journal of Symbolic Computation, 1994 Let \(u= u(x_1, \dots, x_m)\) and \(v= v(x_1, \dots, x_m)\) be \(m\)-variate polynomials over a field \(F\) and let \(N= c^m\), where \(c\) is chosen so that \(c\geq 2\deg_{x_i} (u)+ 1,2 \deg_{x_i} (v)+ 1\) \((1\leq i\leq m)\). It is known that the product \(uv\) can be computed in time \(O(N \log N\log \log N)\).
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Asymptotics for multiple Meixner polynomials
Journal of Mathematical Analysis and Applications, 2014 The n-root asymptotic behavior of multiple Meixner polynomials is studied. A method based on an algebraic function formulation in connection with some available techniques from logarithmic potential theory has been developed. It represents an alternative to the use of Riemann-Hilbert techniques and the steepest descent method for oscillatory RH ...
Aptekarev, A. I. +1 more
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