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SODA
2010
ACM

Algorithms for ray class groups and Hilbert class fields

14 years 9 months ago
Algorithms for ray class groups and Hilbert class fields
This paper analyzes the complexity of problems from class field theory. Class field theory can be used to show the existence of infinite families of number fields with constant root discriminant. Such families have been proposed for use in lattice-based cryptography and for constructing errorcorrecting codes. Little is known about the complexity of computing them. We show that computing the ray class group and computing certain subfields of Hilbert class fields efficiently reduce to known computationally difficult problems. These include computing the unit group and class group, the principal ideal problem, factoring, and discrete log. As a consequence, efficient quantum algorithms for these problems exist in constant degree number fields.
Sean Hallgren, Kirsten Eisentraeger
Added 01 Mar 2010
Updated 02 Mar 2010
Type Conference
Year 2010
Where SODA
Authors Sean Hallgren, Kirsten Eisentraeger
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