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...
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...
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...
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...
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...