2,150 research outputs found
Ninja: Automated Integrand Reduction via Laurent Expansion for One-Loop Amplitudes
We present the public C++ library Ninja, which implements the Integrand
Reduction via Laurent Expansion method for the computation of one-loop
integrals. The algorithm is suited for applications to complex one-loop
processes.Comment: Published versio
On the quaternion -isogeny path problem
Let \cO be a maximal order in a definite quaternion algebra over
of prime discriminant , and a small prime. We describe a
probabilistic algorithm, which for a given left -ideal, computes a
representative in its left ideal class of -power norm. In practice the
algorithm is efficient, and subject to heuristics on expected distributions of
primes, runs in expected polynomial time. This breaks the underlying problem
for a quaternion analog of the Charles-Goren-Lauter hash function, and has
security implications for the original CGL construction in terms of
supersingular elliptic curves.Comment: To appear in the LMS Journal of Computation and Mathematics, as a
special issue for ANTS (Algorithmic Number Theory Symposium) conferenc
- …