Convolution and Polynomial Multiplication

1988 ◽  
pp. 27-60
Author(s):  
Michael T. Heideman
Keyword(s):  
Polynomial Multiplication

Overlap-free Karatsuba–Ofman polynomial multiplication algorithms

2010 ◽  
Vol 4 (1) ◽  
pp. 8 ◽  
Author(s):  
H. Fan ◽  
J. Sun ◽  
M. Gu ◽  
K.-Y. Lam
Keyword(s):  
Polynomial Multiplication

High-Speed NTT-based Polynomial Multiplication Accelerator for Post-Quantum Cryptography

2021 ◽  
Author(s):  
Mojtaba Bisheh-Niasar ◽  
Reza Azarderakhsh ◽  
Mehran Mozaffari-Kermani
Keyword(s):  
Quantum Cryptography ◽  
High Speed ◽  
Polynomial Multiplication ◽  
Post Quantum Cryptography

Polynomial multiplication over finite fields: from quadratic to straight-line complexity

2006 ◽  
Vol 15 (3) ◽  
pp. 252-262 ◽  
Author(s):  
Nader H. Bshouty ◽  
Michael Kaminski
Keyword(s):  
Finite Fields ◽  
Polynomial Multiplication ◽  
Straight Line

scholarly journals BALANCED DENSE POLYNOMIAL MULTIPLICATION ON MULTI-CORES

2011 ◽  
Vol 22 (05) ◽  
pp. 1035-1055 ◽  
Author(s):  
MARC MORENO MAZA ◽  
YUZHEN XIE
Keyword(s):  
Numerical Computation ◽  
Symbolic Computation ◽  
Input Data ◽  
Matrix Multiplication ◽  
Implementation Strategies ◽  
Efficient Implementation ◽  
Fundamental Operation ◽  
Polynomial Multiplication ◽  
Parallel Speedup

In symbolic computation, polynomial multiplication is a fundamental operation akin to matrix multiplication in numerical computation. We present efficient implementation strategies for FFT-based dense polynomial multiplication targeting multi-cores. We show that balanced input data can maximize parallel speedup and minimize cache complexity for bivariate multiplication. However, unbalanced input data, which are common in symbolic computation, are challenging. We provide efficient techniques, that we call contraction and extension, to reduce multivariate (and univariate) multiplication to balanced bivariate multiplication. Our implementation in Cilk++ demonstrates good speedup on multi-cores.

Exploring Logarithms with a Ruler

2013 ◽  
Vol 106 (9) ◽  
pp. 668-673
Author(s):  
Elliott Ostler
Keyword(s):  
Linear Measurement ◽  
Polynomial Multiplication

Processes using linear measurement can be adapted to teach complex topics such as polynomial multiplication, rational exponents, and logarithms.

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