Relations between arithmetic geometry and public key cryptography
Gerhard Frey  Institute for Experimental Mathematics, University of DuisburgEssen, Ellernstrasse 29, 45326 Essen, Germany (email) Abstract:
In the article we shall try to give an overview of the interplay between the design of public key cryptosystems and algorithmic arithmetic geometry. We begin in Section 2 with a very abstract setting and try to avoid all structures which are not necessary for protocols like DiffieHellman key exchange, ElGamal signature and pairing based cryptography (e.g. short signatures). As an unavoidable consequence of the generality the result is difficult to read and clumsy. But nevertheless it may be worthwhile because there are suggestions for systems which do not use the full strength of group structures (see Subsection 2.2.1) and it may motivate to look for
alternatives to known groupbased systems.
Keywords: Discrete logarithms, bilinear structures, divisor class groups, public key systems.
Received: July 2009; Revised: November 2009; Available Online: May 2010. 
2015 Impact Factor.631
