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CAP
2010
14 years 10 months ago
A high-performance algorithm for calculating cyclotomic polynomials
The nth cyclotomic polynomial, n(z), is the monic polynomial whose (n) distinct roots are the nth primitive roots of unity. n(z) can be computed efficiently as a quotient of terms...
Andrew Arnold, Michael B. Monagan
STOC
1989
ACM
99views Algorithms» more  STOC 1989»
15 years 7 months ago
A Random Polynomial Time Algorithm for Approximating the Volume of Convex Bodies
We present a randomised polynomial time algorithm for approximating the volume of a convex body K in n-dimensional Euclidean space. The proof of correctness of the algorithm relie...
Martin E. Dyer, Alan M. Frieze, Ravi Kannan
CASC
2011
Springer
262views Mathematics» more  CASC 2011»
14 years 2 months ago
Practical Divide-and-Conquer Algorithms for Polynomial Arithmetic
We investigate two practical divide-and-conquer style algorithms for univariate polynomial arithmetic. First we revisit an algorithm originally described by Brent and Kung for comp...
William Hart, Andrew Novocin
119
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EUROCRYPT
2000
Springer
15 years 6 months ago
Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations
The security of many recently proposed cryptosystems is based on the difficulty of solving large systems of quadratic multivariate polynomial equations. This problem is NP-hard ove...
Nicolas Courtois, Alexander Klimov, Jacques Patari...
ISTCS
1997
Springer
15 years 7 months ago
An Exact Quantum Polynomial-Time Algorithm for Simon's Problem
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the...
Gilles Brassard, Peter Høyer