Under the assumption of the generalized Riemann Hyothesis verifying the class number belongs to NPcapCo-NP

@inproceedings{Thiel1994UnderTA,
  title={Under the assumption of the generalized Riemann Hyothesis verifying the class number belongs to NPcapCo-NP},
  author={Christoph Thiel},
  booktitle={ANTS},
  year={1994}
}
We show that under the assumption of a certain Generalized Riemann Hypothesis the problem of verifying the value of the class number of an arbitrary algebraic number eld F of arbitrary degree belongs to the complexity class NP \ co ?NP. In order to prove this result we introduce a compact representation of algebraic integers which allows us to represent a system of fundamental units by (2 + log 2 ()) O(1) bits, where is the discriminant of F. 

From This Paper

Topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 20 references

A Course in Computational algebraic number theory, Springer Verlag

H. Cohen
1993

Algorithms Related to Multiplicative Representations of Algebraic Numbers, PhD

G. Ge
Thesis, University of California at Berkeley • 1993
View 1 Excerpt

Ein Algorithmus zur Zerlegung von Primzahlen in Primideale

D. Weber
Univer sitat des Saarlandes, Masterthesis • 1993
View 1 Excerpt

Algebraische Zahlentheorie

J. Neukirch
1992

Algorithms in algebraic number theory, Manuscript

J. Buchmann
1992
View 1 Excerpt

On Short Representations of Orders and Number Elds

Johannes Buchmann, Oliver van Sprang, FB 14-Informatik
1992
View 1 Excerpt

A subexponentional algorithm for the determination of class group and regulator of algebraic number elds, S eminaire de Th eorie des Nombres, Paris 1988-1989

J. Buchmann
Birkh auser Verlag • 1990
View 1 Excerpt

Cryptographic key distribution and computation in class groups, NATO Advanced Science Institutes

K. S. McCurley
Series C, • 1989
View 1 Excerpt

Similar Papers

Loading similar papers…