Explicit infrastructure for real quadratic function fields and real hyperelliptic curves
نویسندگان
چکیده
منابع مشابه
Explicit Infrastructure for Real Quadratic Function Fields and Real Hyperelliptic Curves
In 1989, Koblitz first proposed the Jacobian of a an imaginary hyperelliptic curve for use in public-key cryptographic protocols. This concept is a generalization of elliptic curve cryptography. It can be used with the same assumed key-per-bit strength for small genus. More recently, real hyperelliptic curves of small genus have been introduced as another source for cryptographic protocols. The...
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The principal topic of this article is to extend Shanks' infrastructure ideas in real quadratic number elds to the case of real quadratic congruence function elds. In this view, this paper is intended as a \low-brow" approach to the theory of ideals and operations in the ideal class group. We summarize some basic properties of ideals and provide elementary proofs of the main results. For the pu...
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A hyperelliptic function field can be always be represented as a real quadratic extension of the rational function field. If at least one of the rational prime divisors is rational over the field of constants, then it also can be represented as an imaginary quadratic extension of the rational function field. The arithmetic in the divisor class group can be realized in the second case by Cantor’...
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In 1994, the well-known Diie-Hellman key exchange protocol was for the rst 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 eld. 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 e...
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ژورنال
عنوان ژورنال: Glasnik Matematicki
سال: 2009
ISSN: 0017-095X
DOI: 10.3336/gm.44.1.05