TY - GEN

T1 - Algorithms for ray class groups and Hilbert class fields

AU - Eisenträger, Kirsten

AU - Hallgren, Sean

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2010

Y1 - 2010

N2 - 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 error-correcting 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.

AB - 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 error-correcting 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.

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U2 - 10.1137/1.9781611973075.40

DO - 10.1137/1.9781611973075.40

M3 - Conference contribution

AN - SCOPUS:77951673113

SN - 9780898717013

T3 - Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

SP - 471

EP - 483

BT - Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms

PB - Association for Computing Machinery (ACM)

T2 - 21st Annual ACM-SIAM Symposium on Discrete Algorithms

Y2 - 17 January 2010 through 19 January 2010

ER -