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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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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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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
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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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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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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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The multiple polynomial quadratic sieve [PDF]
Mathematics of Computation, 1987 A modification, due to Peter Montgomery, of Pomerance’s Quadratic Sieve for factoring large integers is discussed along with its implementation. Using it, allows factorization with over an order of magnitude less sieving than the basic algorithm. It enables one to factor numbers in the 60-digit range in about a day, using a large minicomputer.
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Planar orthogonal polynomials as Type II multiple orthogonal polynomials [PDF]
Journal of Physics A: Mathematical and Theoretical, 2019 We show that the planar orthogonal polynomials with $l$ logarithmic singularities in the potential are the multiple orthogonal polynomials (Hermite-Pad polynomials) of Type II with $l$ measures. We also find the ratio between the determinant of the moment matrix corresponding to the multiple orthogonal polynomials and the determinant of the moment ...
Seung-Yeop Lee, Meng Yang
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