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» The Complexity of the Annihilating Polynomial
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MOC
2011
14 years 5 months ago
Regeneration homotopies for solving systems of polynomials
We present a new technique, based on polynomial continuation, for solving systems of n polynomials in N complex variables. The method allows equations to be introduced one-by-one o...
Jonathan D. Hauenstein, Andrew J. Sommese, Charles...
JCP
2007
104views more  JCP 2007»
14 years 10 months ago
Cyclic Convolution Algorithm Formulations Using Polynomial Transform Theory
— This work presents a mathematical framework for the development of efficient algorithms for cyclic convolution computations. The framework is based on the Chinese Reminder Theo...
Abraham H. Diaz-Perez, Domingo Rodríguez
FOCS
1998
IEEE
15 years 2 months ago
Quantum Lower Bounds by Polynomials
We examine the number T of queries that a quantum network requires to compute several Boolean functions on f0;1gN in the black-box model. We show that, in the blackbox model, the ...
Robert Beals, Harry Buhrman, Richard Cleve, Michel...
CRYPTO
2007
Springer
144views Cryptology» more  CRYPTO 2007»
15 years 4 months ago
Finding Small Roots of Bivariate Integer Polynomial Equations: A Direct Approach
Coppersmith described at Eurocrypt 96 an algorithm for finding small roots of bivariate integer polynomial equations, based on lattice reduction. A simpler algorithm was later pro...
Jean-Sébastien Coron
STACS
2005
Springer
15 years 3 months ago
Robust Polynomials and Quantum Algorithms
We define and study the complexity of robust polynomials for Boolean functions and the related fault-tolerant quantum decision trees, where input bits are perturbed by noise. We ...
Harry Buhrman, Ilan Newman, Hein Röhrig, Rona...