Results 31 to 40 of about 165,308 (288)
Computing Sparse Multiples of Polynomials [PDF]
Algorithmica, 2010 We consider the problem of finding a sparse multiple of a polynomial. Given f in F[x] of degree d over a field F, and a desired sparsity t, our goal is to determine if there exists a multiple h in F[x] of f such that h has at most t non-zero terms, and if so, to find such an h.
Giesbrecht, Mark +2 more
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Computing the Rank and a Small Nullspace Basis of a Polynomial Matrix [PDF]
, 2005 We reduce the problem of computing the rank and a nullspace basis of a univariate polynomial matrix to polynomial matrix multiplication. For an input n x n matrix of degree d over a field K we give a rank and nullspace algorithm using about the same ...
Storjohann, Arne, Villard, Gilles
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anar Orthogonal Polynomials as Type I Multiple Orthogonal Polynomials
Symmetry, Integrability and Geometry: Methods and Applications, 2023 A recent result of S.-Y. Lee and M. Yang states that the planar orthogonal polynomials orthogonal with respect to a modified Gaussian measure are multiple orthogonal polynomials of type II on a contour in the complex plane. We show that the same polynomials are also type I orthogonal polynomials on a contour, provided the exponents in the weight are ...
Berezin, Sergey +2 more
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IEEE Access, 2020 In a distributed computing environment, there may exist slow processing workers, which are known as “stragglers”, and they can slow down the whole computing process.
Sangwoo Hong, Heecheol Yang, Jungwoo Lee
doaj +1 more source
Racing BIKE: Improved Polynomial Multiplication and Inversion in Hardware
Transactions on Cryptographic Hardware and Embedded Systems, 2021 BIKE is a Key Encapsulation Mechanism selected as an alternate candidate in NIST’s PQC standardization process, in which performance plays a significant role in the third round.
Jan Richter-Brockmann +3 more
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Depth-4 Lower Bounds, Determinantal Complexity : A Unified Approach [PDF]
, 2013 Tavenas has recently proved that any n^{O(1)}-variate and degree n polynomial in VP can be computed by a depth-4 circuit of size 2^{O(\sqrt{n}\log n)}. So to prove VP not equal to VNP, it is sufficient to show that an explicit polynomial in VNP of degree
Chillara, Suryajith +1 more
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Area-Efficient Polynomial Multiplication Hardware Implementation for Lattice-based Cryptography [PDF]
Jisuanji gongchengLattice-based post-quantum cryptography algorithms demonstrate significant potential in public-key cryptography. A key performance bottleneck in hardware implementation is the computational complexity of polynomial multiplication. To address the problems
XIE Jiaxing, PU Jinwei, FANG Weitian, ZHENG Xin, XIONG Xiaoming
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Global existence and blow up of solution for semi-linear hyperbolic equation with the product of logarithmic and power-type nonlinearity [PDF]
Opuscula Mathematica, 2020 In this paper we consider the semilinear wave equation with the multiplication of logarithmic and polynomial nonlinearities. We establish the global existence and finite time blow up of solutions at three different energy levels (\(E(0)\lt d\), \(E(0)=d\)
Wei Lian, Md Salik Ahmed, Runzhang Xu
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Efficient Homomorphic Encryption Accelerator With Integrated PRNG Using Low-Cost FPGA
IEEE Access, 2022 With recent development in internet speed and reliability, cloud computing has become a more reliable solution for the user. In many cases where data privacy is critical, fully homomorphic encryption (FHE) can be a security solution for securing cloud ...
Infall Syafalni +4 more
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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
core +3 more sources