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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, the security...

Equivariant Form of the Deuring-Safarevic Formula for Hasse-Witt Invariants.

Shoichi Nakajima (1985)

Mathematische Zeitschrift

Estimates of regulators and class numbers in function fields.

H.-G. Quebbemann (1991)

Journal für die reine und angewandte Mathematik

Euclidean function fields.

Manohar L. Madan, Clifford S. Queen (1973)

Journal für die reine und angewandte Mathematik

Euclid's algorithm in algebraic function fields, II

J. Armitage (1971)

Acta Arithmetica

Existence of and computation of integral bases

Erich Lamprecht (1998)

Acta Mathematica et Informatica Universitatis Ostraviensis

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 $ρ^{n} = D \in k [t]$ , 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.

Explicit form of the modular equation.

Noriko Yui (1978)

Journal für die reine und angewandte Mathematik

Explicit global function fields over the binary field with many rational places

Harald Niederreiter, Chaoping Xing (1996)

Acta Arithmetica

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