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Cryptography is, in the true sense of the word, a classic discipline: we find it in Mesopotamia
and Caesar used it. Typically, the historical examples involve secret services and military …

In this article we want to make evident that Brauer groups of local and global fields play an
important role in public key cryptopgraphy. In the first section we show that all ideal class …

This thesis presents an asymptotically fast algorithm to count points on typical genus-2
hyperelliptic curves over large prime fields [special characters omitted]. Specifically, the …

This thesis studies the implications of using public key cryptographic primitives that are
based in, or map to, the multiplicative group of finite fields with small extension degree. A …

Duality theorems are in the heart of class field theory both for number fields and geometric
objects like curves and abelian varieties. In particular, class groups of rings of integers and …

A CASE OF STANDARD ATTACKS AGAINST THE DLP AND ECDLP Joseph Spring
Department of Computing, University of Hertfordshire, College Page 1 A CASE OF STANDARD …

1 Duality Theorems in Arithmetic Geometry and Applications in Data Security Gerhard Frey
Institute for Experimental Mathematics Page 1 1 Duality Theorems in Arithmetic Geometry and …

It is shown that the computational complexity of Tate local duality is closely related to that of
the discrete logarithm problem over finite fields. Local duality in the multiplicative case and …

It is well known that duality theorems are of utmost importance for the arithmetic of local and
global fields and that Brauer groups appear in this context unavoidably. The key word here …