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Equivalences between elliptic curves and real quadratic congruence function fields

Andreas Stein (1997)

Journal de théorie des nombres de Bordeaux

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, the security...

Explicit construction of integral bases of radical function fields

Qingquan Wu (2010)

Journal de Théorie des Nombres de Bordeaux

We give an explicit construction of an integral basis for a radical function field K = k ( t , ρ ) , where ρ n = D k [ t ] , under the assumptions [ K : k ( t ) ] = n and c h a r ( k ) n . The field discriminant of K is also computed. We explain why these questions are substantially easier than the corresponding ones in number fields. Some formulae for the P -signatures of a radical function field are also discussed in this paper.

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