On real quadratic number fields suitable for cryptography.
Schielzeth, Daniel, Pohst, Michael E. (2005)
Experimental Mathematics
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Displaying similar documents to “Cryptography based on number fields with large regulator”
On real quadratic number fields suitable for cryptography.
The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent
Stéphane Louboutin, Hee-Sun Yang, Soun-Hi Kwon (2004)
Mathematica Slovaca
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On traces of the Brandt-Eichler matrices
Juliusz Brzezinski (1998)
Journal de théorie des nombres de Bordeaux
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We compute the numbers of locally principal ideals with given norm in a class of definite quaternion orders and the traces of the Brandt-Eichler matrices corresponding to these orders. As an application, we compute the numbers of representations of algebraic integers by the norm forms of definite quaternion orders with class number one as well as we obtain class number relations for some CM-fields.
On -class field towers of imaginary quadratic number fields
Franz Lemmermeyer (1994)
Journal de théorie des nombres de Bordeaux
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For a number field , let denote its Hilbert -class field, and put . We will determine all imaginary quadratic number fields such that is abelian or metacyclic, and we will give in terms of generators and relations.
Topics in computational algebraic number theory
Karim Belabas (2004)
Journal de Théorie des Nombres de Bordeaux
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We describe practical algorithms from computational algebraic number theory, with applications to class field theory. These include basic arithmetic, approximation and uniformizers, discrete logarithms and computation of class fields. All algorithms have been implemented in the system.
Equivalences between elliptic curves and real quadratic congruence function fields
Andreas Stein (1997)
Journal de théorie des nombres de Bordeaux
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In 1994, the well-known Diffie-Hellman key exchange protocol was for the first time implemented in a non-group based setting. Here, the underlying key space was the set of reduced principal ideals of a real quadratic number field. This set does not possess a group structure, but instead exhibits a so-called infrastructure. More recently, the scheme was extended to real quadratic congruence function fields, whose set of reduced principal ideals has a similar infrastructure. As always,...
A generalization of Eichler's trace formula.
Juliusz Brzezinski (1997)
Collectanea Mathematica
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Eichler's trace formula for traces of the Brandt-Eichler matrices is proved for arbitrary totally definite orders in central simple algebras of prime index over global fields. A formula for type numbers of such orders is proved as an application.